Texas Go Math

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 3.3 Answer Key Multiplying Dividing Fractions.

Texas Go Math Grade 6 Lesson 3.3 Answer Key Dividing Fractions

Reflect

Question 1.
Write the division shown by each model.
Answer:
In A, the total amount is given by the fraction \(\frac{3}{4}\) and the divisor is \(\frac{1}{8}\), therefore the division expression is \(\frac{3}{4} \div \frac{1}{8}\)

In B, the total amount is given by the fraction \(\frac{1}{2}\) and the divisor is 5, therefore the division expression is \(\frac{1}{2}\) ÷ 5.

Go Math Grade 6 Lesson 3.3 Answer Key Question 2.
Is any number its own reciprocal? If so, what number(s)? Justify your answer.
Answer:
OnLy 1 and – 1 are number which are its own reciprocal.
We can write 1 as a fraction on following way;
1 = \(\frac{1}{1}\)
The reciprocal we can find switching numerator and denominator and get:
\(\frac{1}{1}\) = 1
So, conclusion is that 1 is its own reciprocal.
Also, – 1 we can write as a fraction on the following way:
– 1 = \(\frac{-1}{1}\)
We can find the reciprocal switching numerator and denominator and get:
\(\frac{1}{-1}\) = – 1
So, Conclusion is that – 1 is its own reciprocal.

Question 3.
Communicate Mathematical Ideas Does every number have a reciprocal? Explain.
Answer:
Any number except 0 has a reciprocal. 0 has no reciprocal because of the following:
0 = \(\frac{0}{1}\)
But if switch the numerator and denominator, we will get \(\frac{1}{0}\) but fraction is not defined when denominator is 0.
Because of previous, 0 is the only number which has no reciprocal.

Question 4.
The reciprocal of a whole number is a fraction with ___________ in the numerator.
Answer:
Missing word is 1. For example:
6 = \(\frac{6}{1}\)
Its reciprocal is \(\frac{1}{6}\).
So, always, the reciprocal of the whole number is a fraction with 1 in the numerator.
Missing word (number) is 1.

Your Turn

Find the reciprocal of each number.

Question 5.
\(\frac{7}{8}\)
Answer:
We have to switch the numerator and the denominator in order to find the reciprocal. After switching, we get that the reciprocal is \(\frac{8}{7}\).

Question 6.
9
Answer:
First, we will rewrite 6 as a fraction:
6 = \(\frac{6}{1}\)
Now, we will switch the numerator and the denominator and get that reciprocal of 6 is:
\(\frac{1}{6}\)

Question 7.
\(\frac{1}{11}\)
Answer:
We have to switch the numerator and the denominator in order to find the reciprocal. After switching, we get that the reciprocal is \(\frac{11}{1}\) = 11.

Reflect

Question 8.
Make a Conjecture Use the pattern in the table to make a conjecture about how you can use multiplication to divide one fraction by another.
Answer:
From the table we can see that division is actually multiplying the one fraction by reciprocal of the other fraction
So, first we have to find reciprocal of the other fraction and by it multiplying the first one.

Division is multiplying one fraction by reciprocal of the other fraction.

Go Math Lesson 3.3 6th Grade Answer Key Question 9.
Write a division problem and a corresponding multiplication problem like those in the table. Assuming your conjecture in 8 is correct, what is the answer to your division problem?
Answer:
For example, we would divide the following fractions:
\(\frac{6}{7} \div \frac{3}{4}=\frac{8}{7}\)
Now, we will divide those two fractions as we explained at previous task. Reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\)
Next thing we will do will be to multiply \(\frac{6}{7}\) by \(\frac{4}{3}\).

We can see that those two results are equals, so, this explained way for dividing to fractions is correct.
\(\frac{6}{7} \div \frac{3}{4}=\frac{6}{7} \times \frac{4}{3}=\frac{8}{7}\)

Divide.

Question 10.
\(\frac{9}{10} \div \frac{2}{5}\)
Answer:
First, we have to find reciprocal of \(\frac{3}{5}\), it is \(\frac{5}{3}\). Then multiply \(\frac{9}{10}\) by \(\frac{5}{2}\) multiplying their numerators and denominators and then write result in the simplest form:

So, \(\frac{9}{10} \div \frac{2}{5}=\frac{9}{4}\)

Question 11.
\(\frac{9}{10} \div \frac{3}{5}\)
Answer:
First, we have to find reciprocal of \(\frac{3}{5}\), it is \(\frac{5}{3}\). Then multiply \(\frac{9}{10}\) by \(\frac{5}{3}\) multiplying their numerators and denominators and then write result in the simplest form:

So, \(\frac{9}{10} \div \frac{3}{5}\) = \(\frac{3}{2}\)

Texas Go Math Grade 6 Lesson 3.3 Guided Practice Answer Key

Find the reciprocal of each fraction.

Question 1.
\(\frac{2}{5}\)
Answer:
In order to find the reciprocal of \(\frac{2}{5}\), we have to switch the numerator and denominator. So, applying this we get that reciprocal of \(\frac{2}{5}\) is \(\frac{5}{2}\).

Question 2.
\(\frac{1}{9}\)
Answer:
In order to find the reciprocal of \(\frac{1}{9}\), we have to switch the numerator and denominator. So, applying this we get that reciprocal of \(\frac{1}{9}\) is \(\frac{9}{1}\) = 9.

Lesson 3.3 Dividing Fractions Answer Key Question 3.
\(\frac{10}{3}\)
Answer:
In order to find the reciprocal of \(\frac{10}{3}\), we have to switch the numerator and denominator. So, applying this we get that reciprocal of \(\frac{10}{3}\) is \(\frac{3}{10}\)

Divide.

Question 4.
\(\frac{4}{3} \div \frac{5}{3}\)
Answer:
First, we have to find the reciprocal of \(\frac{5}{3}\), it is \(\frac{3}{5}\). Then multiply \(\frac{4}{3}\) by \(\frac{3}{5}\), multiplying their nominators and denominators and then write the result in the simplest form:

So, \(\frac{4}{3} \div \frac{5}{3}\) = \(\frac{4}{5}\)

Question 5.
\(\frac{3}{10} \div \frac{4}{5}\)
Answer:
First, we have to find the reciprocal of \(\frac{4}{5}\), it is \(\frac{5}{4}\). Then multiply \(\frac{3}{10}\) by \(\frac{5}{4}\), multiplying their nominators and denominators and then write the result in the simplest form:

So, \(\frac{3}{10} \div \frac{4}{5}\) = \(\frac{3}{8}\)

Question 6.
\(\frac{1}{2} \div \frac{2}{5}\)
Answer:
First, we have to find the reciprocal of \(\frac{2}{5}\), it is \(\frac{5}{2}\). Then multiply \(\frac{1}{2}\) by \(\frac{5}{2}\), multiplying their nominators and denominators and then write the result in the simplest form:

So, \(\frac{1}{2} \div \frac{2}{5}\) = \(\frac{5}{4}\)

Essential Question Check-In

Question 7.
How do you divide fractions?
Answer:
We divide two fractions on that way we actually multiply the first one by reciprocal of the second fraction.

Question 8.
Alison has \(\frac{1}{2}\) cup of yogurt for making fruit parfaits. Each parfait requires \(\frac{1}{8}\) cup of yogurt. How many parfaits can she make?
Answer:
In order to find how many parfaits Alison can make, we have to divide \(\frac{1}{2}\) by \(\frac{1}{8}\) and get:

So, she can make 4 par falts with \(\frac{1}{2}\) cup of yogurt.

Question 9.
A team of runners is needed to run a \(\frac{1}{4}\)-mile relay race. If each runner must run \(\frac{1}{16}\) mile, how many runners will be needed?
Answer:
In order to find how many parfaits Alison can make, we have to divide \(\frac{1}{4}\) by \(\frac{1}{16}\) and get:

So, there will be needed 4 runners.

Dividing Fractions Grade 6 Answer Key Question 10.
Trevor paints \(\frac{1}{6}\) of the fence surrounding his farm each day. How many days will it take him to paint \(\frac{3}{4}\) of the fence?
Answer:
If we want to find how many days will take Trevor to point \(\frac{3}{4}\) of the fence, we need to divide \(\frac{3}{4}\) by \(\frac{1}{6}\) and get:

So, Trevor will take 4 and a half days to paint \(\frac{3}{4}\) of the fence.

Question 11.
Six people share \(\frac{3}{5}\) pound of peanuts equally. What fraction of a pound of peanuts does each person receive?
Answer:
In order to calculate what fraction of a pound of peanuts each person receives, we have to divide \(\frac{3}{5}\) by 6 and get:

So, each person receives \(\frac{1}{10}\) of pound of peanuts.

Question 12.
Biology If one honeybee makes \(\frac{1}{12}\) teaspoon of honey during its lifetime, how many honeybees are needed to make \(\frac{1}{2}\) teaspoon of honey?

Answer:
In order to calculate how many noneybees are needed to make \(\frac{1}{2}\) teaspoon of honey, we have to divide \(\frac{1}{2}\) by \(\frac{1}{12}\) and get:

So, 6 honeybees are needed to make \(\frac{1}{2}\) teaspoon of honey

Question 13.
Jackson wants to divide a \(\frac{3}{4}\) -pound box of trail mix into small bags. Each of the bags will hold \(\frac{1}{12}\) pound of trail mix. How many bags of trail mix can Jackson fill?
Answer:
If we want to find how many bags of trail mix Jackson can fill, we have to divide \(\frac{3}{4}\) by \(\frac{1}{12}\) and get:

So, Jackson can fill 9 bags of trail mix.

Question 14.
A pitcher contains \(\frac{2}{3}\) quart of lemonade. If an equal amount of lemonade is poured into each of 6 glasses, how much lemonade will each glass contain?
Answer:
In order to find how much Lemonade each glass will contain, we have to divide \(\frac{2}{3}\) by 6 and get:

So, each glass will contain \(\frac{1}{9}\) of lemonade.

Question 15.
How many tenths are there in \(\frac{4}{5}\)?
Answer:
To calculate how many tenths are in \(\frac{4}{5}\), we need to divide \(\frac{4}{5}\) by 10 and get:

So, there are \(\frac{2}{25}\) tenths in \(\frac{4}{5}\).

Lesson 3.3 Multiplying and Dividing Fractions Question 16.
You make a large bowl of salad to share with your friends. Your brother eats \(\frac{1}{3}\) of it before they come over.

a. You want to divide the leftover salad evenly among six friends. What expression describes the situation? Explain.
Answer:
If there was \(\frac{3}{3}\) = 1 salad and brother eats \(\frac{1}{3}\) of it, we suppose to subtract \(\frac{1}{3}\) from \(\frac{3}{3}\) and the result will be the leftover.
Then, that leftover we need to divide among six friends, so \(\frac{3}{5}\) – \(\frac{1}{3}\) we need to divide by 6.
The following expression describes the situation in the task:
\(\left(\frac{3}{3}-\frac{1}{3}\right)\) ÷ \(\frac{1}{6}\)

b. What fractional portion of the original bowl of salad does each friend receive?
Answer:
Required fractional portion of the original bowl of salad each friends receives is result of following expression:

So, each friend receive \(\frac{1}{6}\) of the original salad.

H.O.T. Focus On Higher Order Thinking

Question 17.
Interpret the Answer The length of a ribbon is \(\frac{3}{4}\) meter. Sun Yi needs pieces measuring \(\frac{1}{3}\) meter for an art project. What is the greatest number of pieces measuring \(\frac{1}{3}\) meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon? Explain your reasoning.
Answer:
The greatest number of pieces measuring \(\frac{1}{3}\) meter that can be cut from the ribbon is:

So, there are 3 pieces whose length is \(\frac{1}{3}\) meter and can be cut from the ribbon whose length \(\frac{1}{3}\) meter
So, if Sun Yi cuts one piece of length \(\frac{1}{3}\) meter, there will be Left 2 more pieces whose length is \(\frac{1}{3}\) or
\(2 \times \frac{1}{3}=\frac{2 \times 1}{1 \times 3}=\frac{2}{3}\) = meter
So, there will be left \(\frac{2}{3}\) meter of ribbon.

Question 18.
Represent Real-World Problems Liam has \(\frac{9}{10}\) gallon of paint for painting the birdhouses he sells at the craft fair. Each birdhouse requires \(\frac{1}{20}\) gallon of paint. How many birdhouses can Liam paint? Show your work.
Answer:
In order to find how many birdhouses Liam can paint, we need to divide \(\frac{9}{10}\) by \(\frac{1}{20}\) and get:

Liam can paint 18 birdhouses.

Question 19.
Justify Reasoning When Kaitlin divided a fraction by \(\frac{1}{2}\), the result was a mixed number. Was the original fraction less than or greater than \(\frac{1}{2}\)? Explain your reasoning.
Answer:
Conclusion is that the original fraction was greater than \(\frac{1}{2}\).
Realty, for example let the original fraction be \(\frac{4}{3}\), it is greater than \(\frac{1}{2}\), and we will divide it by \(\frac{1}{2}\) and get:

We can see that result is mixed number.
The original fraction was greater than \(\frac{1}{2}\)

Question 20.
Communicate Mathematical Ideas The reciprocal of a fraction less than 1 is always a fraction greater than 1. Why is this?
Answer:
For example, fraction \(\frac{1}{3}\) is less than 1. Reciprocal of this fraction is \(\frac{3}{1}\) = 3 and it is greater than 1.
In general, reciprocal of a fraction which is less than 1 will always be greater than 1 because nominator and the denominator switches and we get fraction which is greater than 1, always.
\(\frac{1}{3}\) < 1 ⇒ \(\frac{3}{1}\) = 3 > 1

Question 21.
Make a Prediction Susan divides the fraction \(\frac{5}{8}\) by \(\frac{1}{16}\). Her friend Robyn divides \(\frac{5}{8}\) by \(\frac{1}{32}\). Predict which person will get the greater quotient. Explain and check your prediction.
Answer:
Robyn will get the greater quotient because he will actually multiply the same fraction as Susan, \(\frac{5}{8}\), by greater fraction, it is reciprocal of \(\frac{1}{32}\) and reciprocal of \(\frac{1}{32}\) is 32, while Susan will multiply the same fraction but smaller number, by reciprocal of \(\frac{1}{16}\) it is 16, and 16 is less than 32

Really:
Susan:

Robyn:

Robyn will get the greater quotient.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 4.1 Answer Key Multiplying Decimals.

Texas Go Math Grade 6 Lesson 4.1 Answer Key Multiplying Decimals

Texas Go Math Grade 6 Lesson 1.1 Explore Activity Answer Key

Use decimal grids or area models to find each product.

(A) 0.3 × 0.5
0.3 × 0.5 represents 0.3 of 0.5.
Use a decimal grid. Shade 5 rows of the grid to represent 0.5.
Shade 0.3 of each 0.1 that is already shaded to represent 0.3 of _____________ .
_____________ square(s) are double-shaded.
This represents ________ hundredth(s), or 0.15.
0.3 × 0.5 = _____________

(B) 3.2 × 2.1 ______
Use an area model. Each row contains 3 wholes + 2 tenths.
Each column contains _________ whole(s) + ________ tenth(s).
The entire area model represents
________ whole(s) + ________ tenth(s) + ________ hundredth(s).
3.2 × 2.1 = ________

Reflect

Question 1.
Analyze Relationships How are the products 2.1 × 3.2 and 21 × 32 alike? How are they different?
Answer:
The products of 2.1 × 3.2 and 21 × 32 will be the number with the same digits, but at 2.1 × 3.2 the result will have two decimal places and at 21 × 32 the result will be the whole number, that is the difference.
Products

Products with the same digits, but the product of 2.1 × 3.2 will have two decimal places while the product of 21 × 32 will be a whole number

Go Math Lesson 4.1 6th Grade Answer Key Question 2.
Communicate Mathematical Ideas How can you use estimation to check that you have placed the decimal point correctly in your product?
Answer:
We can check it by multiplying whole numbers which are the nearest to the given decimals. The result is supposed to be close to the right result.
We can check it by multiplying whole numbers which are the nearest to the given decimals.

Your Turn

Multiply.

Question 3.

Answer:
Here, in the first factor we have one decimal place as well as in the second factor. So, product will have two decimal places. We have the following:

So, the result is 192.78

Question 4.

Answer:
In both factors there are two decimal places, so, the product will have four decimal places We have the following:

So, the product is 4.4896

Multiply

Question 5.

Answer:
In both factors there are two decimal places, so, the product will have four decimal places We have the following:

So, the product is 48.4092

Go Math Grade 6 Lesson 4.1 Answer Key Question 6.

Answer:
In both factors there are two decimal places, so, the product will have four decimal places We have the following:

So, the product is 95.0223

Question 7.
Rico bicycles at an average speed of 15.5 miles per hour.
What distance will Rico bicycle in 2.5 hours? ___________ miles
Answer:
In order to find what distance Roco will bicycle in 2.5 hours multiplying 15.5 by 2.5. First factor has one decimal place, the second has one decimal place, so, the product will has two decimal places.

both factors there are two decimal places, so, the product will have four decimal places. We have the following:

Conclusion is that Roco will bicycle 38.75 miles in 2.5 hours

Question 8.
Use estimation to show that your answer to 7 is reasonable.
Answer:
We can multiply 15 by 2 and get 30. After that, we can multiply 16 by 3 and get 48 We can add 30 and 48 and we get 78. After this, we can divide 78 by 2 and get 39.

So, the answer is reasonable because 39 is close to 38.75.
Multiply 15 by 2.16 by 3 and sum the product. Divide that sum by 2.

Texas Go Math Grade 6 Lesson 4.1 Guided Practice Answer Key

Question 1.
Use the grid to multiply 0.4 × 0.7

0.4 × 0.7 = _______________
Answer:
0.4 × 0.7 represents 0.4 of 0.7. We will use a decimal grid and shade 7 rows of the grid to represent 0.7. Now, we will shade 0.4 of each 0.1 that is already shaded to represent 0.4 of 1. So, now we have 28 squares which are double-shaded. This actually represents 28 hundredths, or 28. So, we have the following:
0.4 × 0.7 = 0.28

Multiplying Decimals Grade 6 Lesson 4.1 Question 2.
Draw an area model to multiply 1.1 × 2.4

1.1 × 2.4 _______________
Answer:
We will use an area model. Here, each row contains 1 whole + 1 tenth. Also, each column contains 2 wholes + 4 tenths. So, the entire area model represents:
2 wholes + 6 tenths + 4 hundreths.

Conclusion is that:
1.1 × 2.4 = 2.64

Multiply.

Question 3.
0.18 × 0.06 = _______________
Answer:
In both factors there are two decimal places, so, the product will have four decimal places We have the following:

So, the product is 0.0108

Question 4.
35.15 × 3.7 = _______________
Answer:
Here, in the first factor we have two decimal. places, but in the second we have one decimal. place, so, the product will have three decimal places.

So, the result is 130.055

Question 5.
0.96 × 0.12 = _______________
Answer:
In both factors there are two decimal places, so, the product will have four decimal places. We have the following:

So, the product is 0.1152

Go Math Lesson 4.1 Answer Key Multiplying Decimals 6th Grade Question 6.
62.19 × 32.5 = _______________
Answer:
In both factors there are two decimal places, so, the product will have four decimal places. We have the following:

So, the product is 2.021.75

Question 7.
3.4 × 4.37 = _______________
Answer:
Here, in the first factor there is one decimal place, but in the second there are two decimal places, so, the product will has three decimal places.
In both factors there are two decimal places, so, the product will have four decimal places. We have the following:

So, the product is 14.858

Question 8.
3.762 × 0.66 = _______________
Answer:
Here, in the first factor there are three decimal places, but in the second there are two, so, the product will has five decimal places.

So, the product is 2.48292.

Question 9.
Chan Hee bought 3.4 pounds of coffee that cost $6.95 per pound.
How much did he spend on coffee? $ ___________________
Answer:
In order to calculate how much money Chan Hee spent on cotte, we need to multiply 3.4 by 6.95. First factor has one decimal place, but the second factor has two decimal places.
So, the product will has three decimal places.

So, chan Hee spent 23.630 $ on coffee.

Question 10.
Adita earns $9.40 per hour working at an animal shelter.
How much money will she earn for 18.5 hours of work? $_______________
Answer:
In order to calculate how much money Adita will earn for 18.5 hours, we need to multiply 9.40 by 18.5. In the first factor there are two decimal places but in the second there is one decimal place.
So, the product will have three decimal places:

So, Adita will earn 173.900$ for 18.5$ hours of work.

Catherin tracked her gas purchases for one month.

Go Math Lesson 4.1 6th Grade Multiplying Decimals Question 11.
How much did Catherin spend on gas in week 2?
$ ___________________________
Answer:
In order to calculate how much Catherine spent on gas in week 2, we have to multiply 11.5 by 2.54 We can notice that the result will have three decimal places:

Catherine spent 29.210 on gas in week 2$

Question 12.
How much more did she spend in week 4 than in week 1?
$ ____________________________
Answer:
First, we have to calculate how much Catherine spent on gas in week 1. we have to multiply 10.4 by 2.65. Here, the first factor has one decimal place hut the second one has two. the product will has three decimal places.

Conclusion is that Catherine spent $ 27.560 on gas in week 1.
Now. we will calculate how much Catherine spent on gas in week 4.
We actually need to multiply 10.6 by 2.70.
We can notice that time result will hase three decimal places:

We can see that Catherine spent $ 28.620 on gas in week 4.
Finally, we will subtract 27.560 from 28.620 in order to find how much more
Catherine spent on gas in week 4 than in week 1.
28.620 – 27.560 = 1.06
Catherine spent $ 1.06 more on gas in week 4 than in week 1.

Essential Question Check-In

Question 13.
How can you check the answer to a decimal multiplication problem?
Answer:
We can check our answer to a decimal multiplication problem using the grid or draw an area model.

Make a reasonable estimate for each situation.

Question 14.
A gallon of water weighs 8.354 pounds. Simon uses 11.81 gallons of water while taking a shower. About how many pounds of water did Simon use?
Answer:
In order to find how many pounds of water Simon used, we need to multiply 8.354 by 11.81.
First factor has three decimals but the second one has two decimals, so, the result will has five decimals

Simon used 98.66074 pounds of water.

Question 15.
A snail moves at a speed of 2.394 inches per minute. If the snail keeps moving at this rate, about how many inches will it travel in 7.489 minutes?
Answer:
In order to calculate how many inches snail wilL travel in 7.489 minutes, we need to multiply 2.394 by 7.489. Both factors have three decimal places, so, the product will has six decimals

The snail will travel 17.928666 inches if he keeps moving at this rate.

6th Grade Go Math Multiplying Decimals Lesson 4.1 Question 16.
Tricia’s garden is 9.87 meters long and 1.09 meters wide. What is the area of her garden?
Answer:
In order to calculate the area of Tricia’s garden, we need to multiply 9.87 by 1.09. Both factors have two decimals,
so, the product will have four decimal places.

So, the area of Tricia’s garden is 10.7583 square meters.

Kaylynn and Amanda both work at the same store. The table shows how much each person earns, and the number of hours each person works in a week.

Question 17.
Estimate how much Kaylynn earns in a week.
Answer:
We will multiply 9, because 9 is closest to 8.75 by 37. So, we have the following:
9 × 37 = 333
So, kaylyum earns about 333$ per week

Question 18.
Estimate how much Amanda earns in a week.
Answer:
We will multiply 10, because 10 is closest to 10.25 by 31. So, we have the following:
10 × 31 = 310
So, Amanda earns about 310$ per week

Question 19.
Calculate the exact difference between Kaylynn and Amandas weekly salaries.
Answer:
We will multiply 8.75 by 37.5 in order to calculate Kaylyun’s weekly salanes.
First factor has two decimals but the second one has decimal place, so, the product will has three decimals.

So, Amanda earns $ 328.125 per week.
Now. we will calculate how much Amanda earns per week. So. we will multiply 10.25 by 30.5. Here, the first factor has two decimals but the second one has one decimal. so, the product will has three decimal places.

So, Amanda earns $ 812.625 per week.
Now, we will calculate the exact difference between Kaylyun and Amanda’s weekly salanes subtracting 312.625 from 328.125 and get:
328.125 – 312.625 = 15.5
So the exact difference between their salaries is $ 15.5.

Question 20.
Victoria’s printer can print 8.804 pages in one minute. If Victoria prints pages for 0.903 minutes, about how many pages will she have?
Answer:
In order to calculate how many pages Victoria will have, we need to multiply 8.804 by 0.903. Both factors have three decimals, so, their product will have six decimals.

So, Victoria will have 7.950012 pages.

A taxi charges a flat fee of $4.00 plus $2.25 per mile.

Question 21.
How much will it cost to travel 8.7 miles? ___________________
Answer:
In order to calculate how much it will cost to travel 8.7 miles, we need to multiply 8.7 by 2.25 and on that product add 4 flat fee. First factor has one decimal but these can done has two decimals.
So, the product will have three decimals.

19.575 we will add 4.00 and get:
19.574 + 4.00 = 23.575$

So. it will cost $ 23.575 to travel 8.7 miles.

Question 22.
Multistep How much will the taxi driver earn if he takes one passenger 4.8 miles and another passenger 7.3 miles? Explain your process.
Answer:
If taxi driver takes one passenger 4.8 miles, we will calculate how much he will earn in this case. We will first multiply 4.8 by 2.25 and on that product will add 4.00 flat fee.
The first factor has one decimal but the second has two decimals, so, the product will have three decimals.

Now, on 10.800 we will add 4.00 and get
10.800 + 4.00 = 14.800

So, it will cost 14.800 if taxi driver takes this passenger 4.8 miles. Now, we will calculate how much he will earn if he takes another passenger 73 miles. We will first multiply 73 by 2.25 and on that product we will add 4.00 flat fee. The first factor has on decimal but the second has two decimals, so, the product will have three decimals.

16.425 we will add 4.00 and get:
16.425 + 4.00 = 20.425$
So, it will cost $ 20.425 if taxi driver takes this passenger 7.3 mites.
If he takes both passengers, he will earn:
14.800 + 20.425 = 35.225
So, the taxi driver will earn 35.225$.

Kay goes for several bike rides one week. The table shows her speed and the number of hours spent per ride.

Question 23.
How many miles did Kay bike on Thursday?
Answer:
In order to calculate how many mites Kay biked on Thursday, we need to multiply 10.75 by 1.9.
First factor has two decimals but the second has one, so, the product will have three decimals.

The conclusion is that Kay biked 20.425 miles on Thursday.

Multiplying Decimals for 6th Grade Go Math Lesson 4.1 Question 24.
On which day did Kay bike a whole number of miles?
Answer:
We can notice that on Friday Kay biked a whole number of mites. Really, to calculate it, we need to multiply 8.8 by 3.75.
The product will have three decimal places, so, we have the following:

We can see that kay biked 33 miles on Friday.

Question 25.
What is the difference in miles between Kay’s longest bike ride and her shortest bike ride?
Answer:
Kay’s Longest bike ride was on Monday. Really, we need to multiply 8.2 by 4.25 in order to calculate length of this bike ride.
We can notice that the product will have three decimals.

So, Kay biked 34.850 miles on Monday.
Her shortest bike ride was on Thursday, we already calculated it in the task 23. According to it, Kay biked 20.425 miles on Thursday.
Now we will calculate the difference in miles between Kay’s longest and her shortest bike ride subtracting miles on
Monday and miles on Thursday and get the following:
34.850 – 20.425 = 14.425
So, required difference was 14.425 mites.

Question 26.
Check for Reasonableness Kay estimates that Wednesday’s ride was about 3 miles longer than Tuesday’s ride. Is her estimate reasonable? Explain.
Answer:
Yes, her estimate is reasonable. We will estimate first Kay’s bike ride on Tuesday. In order to estimate it, we will multiply 10 by 3 and get:
10 × 3 = 30
Now, we will estimate Kay’s bike side on Wednesday. In order to estimate it, we will multiply 11 by 3 and get:
11 × 3 = 33.
So, according to it, Kay’s reasonable was correct

H.O.T. Higher Order Thinking

Question 27.
Explain the Error To estimate the product 3.48 × 7.33, Marisa multiplied 4 × 8 to get 32. Explain how she can make a closer estimate.
Answer:
She can make a closer estimate by multiplying 3 by 7 because 3 is the closest whole number to 3.48 and 7 is the closest whole number to 7.33
Multiply 3 by 7

Question 28.
Represent Real-World Problems A jeweler buys gold jewelry and resells the gold to a refinery. The jeweler buys gold for $1,235.55 per ounce and then resells it for $1,376.44 per ounce. How much profit does the jeweler make from buying and reselling 73.5 ounces of gold?
Answer:
We will first calculate how much the jeweler pays for 73.5 ounces of gold multiplying 1.235.55 by 73.5. The first factor has two decimals but the second one has one decimal, so, the product will have three decimals.

So, the jeweler will pay $90,812.925.

Now, we will calculate how much he will get if he resells 73.5 ounces multiplying 1,376.44 by 73.5. The first factor has two decimals but the second one has one decimal, so, the product will have three decimals.

So, he will get $101, 168.340 if he resells gold.

Now, we wilt calculate how much profit the jeweler will make from bying and reselling subtracting 101, 168.340 and 90, 812.925 and get:
101, 168.340 – 90,812.925 = 10, 355.415
So, his profit will be $10, 355.415.

Question 29.
Problem Solving To find the weight of the gold in a 22 karat gold object, multiply the object’s weight by 0.916. To find the weight of gold in a 14 karat gold object, multiply the object’s weight by 0.585. Which contains more gold, a 22 karat gold object or a 14 karat gold object that each weigh 73.5 ounces? How much more gold does it contain?
Answer:
First we will calculate contain of gold of 22 karat object multiplying the object’s weight, which is 73.5 ounces, by 0.916. The product will have four decimals:

So, a 22 karat gold object contains 67.326 ounces of gold.
Now we will calculate contain of gold of 14 karat gold object multiplying the object’s weight, which is 73.5 ounces, by 0.585. The product will have four decimals:

So, a 14karat gold object contains 42.9975 ounces of gold.
We can see that more gold contains a 22 karat gold object.

Now we will calculate how much more gold it contains subtracting 42.9975 from 67.3260 and get:
67.3260 – 42.9975 = 24.3285
So, a 22 karat gold object contains 24.3285 ounces of gold more than a 14 karat gold object with equal weights.
a 22 karat object; 24.3285

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 2 Quiz Answer Key.

Texas Go Math Grade 6 Module 2 Quiz Answer Key

Texas Go Math Grade 6 Module 2 Ready to Go On? Answer Key

2.1 Classifying Rational Numbers

Question 1.
Five friends divide three bags of apples equally between them.
Write the division represented in this situation as a fraction.
Answer:
As 5 friends divide 3 bags of apples equally between them, we can write it as fraction as:
\(\frac{3}{5}\)

Write each rational number as \(\frac{a}{b}\)

Question 2.
5\(\frac{1}{6}\) __________________
Answer:
Firstly, we will write the whole number as a sum of ones
Secondly, we will use the denominator to find corresponding fractions for ones.
Thirdly, we will calculate sum of numerators!
To reach our final solution: improper fraction.
5\(\frac{1}{6}\) = 1 + 1 + 1 + 1 + 1 + \(\frac{1}{6}\)
= \(\frac{6}{6}+\frac{6}{6}+\frac{6}{6}+\frac{6}{6}+\frac{6}{6}+\frac{1}{6}\)
= \(\frac{31}{6}\)

Grade 6 Module 2 Form A Module Test Answer Key Question 3.
– 12 __________________
Answer:
Number – 12 can be written as a fraction:
– 12 = – \(\frac{12}{1}\)

Determine if each number is a whole number, integer, or rational number. Include all sets to which each number belongs.

Question 4.
– 12 __________________
Answer:
Number – 12 belongs to set of Integers
Therefore, it also belongs to set of Rational numbers

Question 5.
\(\frac{7}{8}\) __________________
Answer:
Number \(\frac{7}{8}\) belongs to set of Rational Numbers

2.2 Identifying Opposites and Absolute Value of Rational Numbers

Question 6.
Graph – 3, 1\(\frac{3}{4}\), – 0.5, and 3 on the number line.

Answer:
Firstly, we transform fractions into decimals!
1\(\frac{3}{4}\) = 1 + \(\frac{3}{4}\) = 1 + 0.75 = 1.75

Division:

Question 7.
Find the opposite of \(\frac{1}{3}\) and – \(\frac{7}{12}\) __________
Answer:
As i mentioned before, opposite of any number is number with added – sign on left side!
Opposite of \(\frac{1}{3}\) is –\(\frac{1}{3}\)
Opposite of – \(\frac{7}{12}\) is \(\frac{7}{12}\)
– \(\frac{1}{3}\) and \(\frac{7}{12}\)

Go Math Grade 6 Module 2 Answer Key Pdf Question 8.
Find the absolute value of 9.8 and –\(\frac{7}{8}\) __________
Answer:
Absolute value of some number is its distance from 0 on the number line!
|9.8| = 9.8
|- \(\frac{10}{3}\)| = \(\frac{10}{3}\)
9.8 and \(\frac{10}{3}\)

2.3 Comparing and Ordering Rational Numbers

Question 9.
Over the last week, the daily low temperatures in degrees Fahrenheit have been – 4, 6.2, 18\(\frac{1}{2}\), – 5.9, 21, – \(\frac{1}{4}\), and 1.75. List these numbers in order from greatest to least.
Answer:
First thing will be writing fractions as equivalent decimals!
18\(\frac{1}{2}\) = 18 + \(\frac{1}{2}\) = 18 + 0.5 = 18.5
– \(\frac{1}{4}\) = – 0.25

Now we know that number 21 is greater than 18.5 which is greater than 6.2 which is greater than 1.75 which is
greater than – 0.25 which ¡s greater than – 4 which is greater than – 5.9.
One last thing to do is to return decimals to given expressions and write it in order from greatest to least!
21, 18\(\frac{1}{2}\), 6.2, 1.75, –\(\frac{1}{2}\), – 4, – 5.9

Division:
\(\frac{1}{2}\) is very easy, so we won’t show it!

Essential Question

Question 10.
How can you solve problems by ordering rational numbers from least to greatest?
Answer:
Firstly, we have to convert all expressions into same, as shown in examples above, we can work with fractions or
decimals, depending on given terms!
Secondly, we compare our decimals/fractions and order them from least to greatest!
Note that we compare numerators when dealing with fractions. That works because we get them to have same denominator!
One last thing to do is to return them in given format and write a final solution!

Texas Go Math Grade 6 Module 2 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
Suki split five dog treats equally among her six dogs. Which fraction represents this division?
(A) \(\frac{6}{5}\) of a treat
(B) \(\frac{5}{6}\) of a treat
(C) \(\frac{1}{5}\) of a treat
(D) \(\frac{1}{6}\) of a treat
Answer:
As Suki splits 5 dog treats among 6 dogs.
Each dog will get
\(\frac{5}{6}\) treats

(B) \(\frac{5}{6}\) of a treat

Question 2.
Which set or sets does the number 15 belong to?
(A) whole numbers only
(B) rational numbers only
(C) integers and rational numbers only
(D) whole numbers, integers, and rational
Answer:
The number 15 belongs to a set of Whole numbers and therefore to a set of Integers and Rational numbers.
We can say that because we know that a set of Whole numbers is included in the set of Integers, and a set of Integers is included in the set of Rational numbers.

Integers Quiz Grade 6 Module 2 Test Answers Math Question 3.
Which of the following statements about rational numbers is correct?
(A) All rational numbers are also whole numbers.
(B) All rational numbers are also integers.
(C) All rational numbers can be written in the form \(\frac{a}{b}\).
(D) Rational numbers cannot be negative.
Answer:
Statement that all rational numbers are also whole numbers is surely incorrect!
For example, 0.5 is a decimal, which is not whole number!

Statement that all rational numbers are also integers is also incorrect!
We can use same example from last statement to prove it.

Statement that all rational numbers can be written in form of \(\frac{a}{b}\) is correct!
Really, it is…take a look at some examples that prove our theory:
0.5 = \(\frac{1}{2}\)
– 5 = \(\frac{-5}{1}\)
5 = \(\frac{5}{1}\)

Statement that rational numbers cannot be negative is incorrect!
We can simply take a look on Venn’s diagram(which we worked in previous lecture) to convince ourselves that this is false statement!

(C) All rational numbers can be written in the form \(\frac{a}{b}\).

Question 4.
Which of the following shows the numbers in order from least to greatest?
(A) –\(\frac{1}{5}\), – \(\frac{2}{3}\), 2, 0.4
(B) 2, –\(\frac{2}{3}\), 0.4, – \(\frac{1}{5}\)
(C) – \(\frac{2}{3}\), 0.4, – \(\frac{1}{5}\), 2
(D) – \(\frac{2}{3}\), – \(\frac{1}{5}\), 0.4, 2
Answer:
Let’s transform all the given numbers into fractions first and make them have 15 as common denominator

Now, we compare their numerators to find out their order
30, 6, – 3, – 10
Number – 10 is less than – 3 which is less than 6 which is Less than 30.
So, now we know order of numerators, and therefore we know order of whole fractions

So, numbers in order from least to greatest are:
\(-\frac{10}{15},-\frac{3}{15}, \frac{6}{15}, \frac{30}{15}\)
Now, we can return them in given form and get:
– \(\frac{2}{3}\), – \(\frac{1}{5}\), 0.4, 2

(D) – \(\frac{2}{3}\), – \(\frac{1}{5}\), 0.4, 2

Question 5.
What is the absolute value of – 12.5?
(A) 12.5
(B) 1
(C) – 1
(D) – 12.5
Answer:
Absolute value of some number is its distance from 0 on the number line!
|- 12.5| = 12.5

(D) – 12.5

Grade 6 Module 2 Rational Numbers Quiz Answer Key Question 6.
Which number line shows –\(\frac{1}{4}\) and its opposite?
(A)
(B)
(C)
(D)
Answer:
Let’s draw our number line to find out the solution:

Note that we used 0.25 instead of \(\frac{1}{4}\) since these expressions are equivalent!

(B)

Question 7.
Horatio climbed to the top of a ladder that was 10 feet high. What is the opposite of Horatio’s height on the ladder?
(A) – 10 feet
(B) 10 feet
(C) 0 feet
(D) \(\frac{1}{10}\) foot
Answer:
Opposite of some number is that same number with an added – sign on the left side.
So, in our case, the opposite of 10 is -10 feet.

(A) – 10 feet

Gridded Response

Go Math Grade 6 Module 2 Quiz Answers Question 8.
The heights of four students in Mrs. Patel’s class are 5\(\frac{1}{2}\)feet, 5.35 feet, 5\(\frac{4}{10}\) feet, and 5.5 feet. What is the height in feet of the shortest student written as a decimal?

Answer:
Here, we will transform given expressions into decimals and then compare them to reach our solution!
5\(\frac{1}{2}\) = 5 + \(\frac{1}{2}\) = 5 + 0.5 = 5.5
5\(\frac{4}{10}\) = 5 + \(\frac{4}{10}\) = 5 + \(\frac{4 / 2}{10 / 2}\) = 5 + \(\frac{2}{5}\) = 5 + 0.4 = 5.4

Now, when we have them all in the wanted form, we can compare them!
Number 5.5 is greater than 5.4 which is greater than 5.35.
Now we know that the shortest student is 5.35 feet high.

Division:

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Unit 1 Study Guide Review Answer Key.

Texas Go Math Grade 6 Unit 1 Study Guide Review Answer Key

Texas Go Math Grade 7 Unit 1 Exercises Answer Key

Question 1.
Graph each number on the number line.
7, – 2, 5, 1, – 1

Answer:

Write the opposite of each number.

Question 2.
8 ___________
Answer:
The opposite of a number is the number on the other side of the 0 number line, and the same distance from 0.
Opposite of 8 is – 8

Go Math 6th Grade Math Unit 1 Study Guide Answer Key Question 3.
– 3 ___________
Answer:
The opposite of a number is the number on the other side of 0 on the number tine and the same distance from 0.
Opposite of – 3 is 3.

List the numbers from the greatest of each number.

Question 4.
4, 0, – 2, 3 ___________
Answer:
Number – 2 is less than 0 which is less than 3 which is less than 4.
Therefore, we list them as: – 2, 0, 3, 4

Question 5.
– 3, – 5, 2, – 2 ___________
Answer:
Number – 5 is less than – 3 which is less than – 2 which is less than 2
Therefore, we list them as: – 5, – 3, – 2, 2

Use a number line to help you compare the numbers. Use < or >.

Question 6.
4 _________ 1
Answer:

It is clear that 1 is less than 4.
So, we can write: 1 < 4

Question 7.
– 2 _________ 2
Answer:

It is clear that – 2 is less than 2.
So, we can write: – 2 < 2

Question 8.
– 3 _________ – 5
Answer:

It is clear that – 3 is less than – 5.
So, we can write: – 3 > – 5

Unit 1 Study Guide Answer Key Go Math Grade 6 Question 9.
– 7 _________ 2
Answer:

It is clear that – 7 is less than 2.
So, we can write: – 7 < 2

Find each absolute value.

Question 10.
|6| _________
Answer:
Absolute value of some number is its distance from 0 on the number line!
Therefore, we know:
|6| = 6

Question 11.
|- 2| _________
Answer:
Absolute value of some number is its distance from 0 on the number line!
Therefore, we know
|- 2| = 2

Texas Go Math Grade 7 Unit 2 Exercises Answer Key

Classify each number by indicating in which set or sets it belongs.

Question 1.
8
Answer:
Number 8 is positive Whole number.
Therefore, it belongs to set of Whole numbers, Integers and Rational numbers!

Question 2.
0.25
Answer:
Number 0.25 is Rational number.
Therefore, it belongs to set of Rational numbers!

Find the absolute value of each rational number.

Question 3.
|3.7| _______________
Answer:
Absolute value of some number is its distance from 0 on the number line!
Therefore, we know
|3.7| = 3.7

Question 4.
|- \(\frac{2}{3}\)|
Answer:
Absolute value of some number is its distance from 0 on the number line!
Therefore, we know
|- \(\frac{2}{3}\)| = \(\frac{2}{3}\)

Graph each set of numbers on the number line and order the numbers from greatest to least.

Question 5.
– 0.5, – 1, –\(\frac{1}{4}\), 0

Answer:
Firstly, we transform fractions into decimals!
–\(\frac{1}{4}\) = – 0.25

Now we can say that:
Number 0 is greater than – 0.25 which is greater than – 0.5 which is greater than – 1.

Division:

Texas Go Math Grade 6 Unit 1 Performance Task Answer Key

Question 1.
CAPEEPS IN MATH Climatologist Each year a tree is alive, it adds a layer of growth, called a tree ring, between its core and its bark. A climatologist measures the width of tree rings of a particular tree for different years:

The average temperature during the growing season is directly related to the width of the ring, with a greater width corresponding to a higher average temperature.

a. List the years in order of increasing ring width.
Answer:
Here. we want to order years based on va1ue given below, from least increase to greatest increase!
Firstly, we get all fractions to have common denominator which, in this case, will be 100.

Now, we compare numerators 53, 58, 56, 60, 65
Number 53 is less than 56 which is less than 58 which is less than 60 which is less than 65.
So, we can write them us:
35 < 56 < 58 < 60 < 65
Final thing to do ¡s to return numbers into given formats and write solution
\(\frac{53}{100}<\frac{14}{25}<\frac{29}{50}<\frac{3}{5}<\frac{13}{20}\)
Now, we want to write years corresponding to width of ring in increasing order:
1920, 1900, 1910, 1940, 1930

b. Which year was hottest? How do you know?
Answer:
Hottest year, by previous calculations was 1930
we can say that because we know that 1930, the width of ring was greatest!

c. Which year was coldest? How do you know?
Answer:
Coldest year, by previous calculations, was 1920
We can say that because we know that in 1920, the width of the ring was the least

Multiplication: You can do it by yourselves as an exercise!

Unit 1 Review Answer Key Go Math Grade 6 Question 2.
A parking garage has floors above and below ground level. For a scavenger hunt, Gaia’s friends are given a list of objects they need to find on the third and fourth level below ground, the first and fourth levels above ground, and ground level.

a. If ground level is 0 and the first level above ground is 1, which integers can you use to represent the other levels where objects are hidden? Explain your reasoning.
Answer:
As we know that the ground level is labeled as 0 and that the first level above ground is labeled as 1, we can conclude that the third level below ground is labeled as – 3,
fourth level below ground is Labeled as – 4 and the fourth level above ground is labeled as 4.
Our reasoning is quite simple here, we present levels below ground as negative integers, and levels above ground as positive integers

b. Graph the set of numbers on the number line.

Answer:

c. Gala wants to start at the lowest level and work her way up. List the levels in the order that Gala will search them.
Answer:
As we can see on the number line above, Gaia will have to search levels in order.
– 4, – 3, 0, 1, 4
Note that reading our number line from left to right allows us to order numbers from least to greatest.

d. If she takes the stairs, how many flights of stairs will she have to climb? How do you know?
Answer:
As we can see on the number line above, lowest level is 4
If she take the stairs, she will have to pass some levels that she won’t search.
If she starts at lowest level – 4, then she will have to climb 4 flights of stairs in order to get to ground Level 0.
Also, after she reaches 0 level she still has 4 flights of stairs to climb till fourth level above ground!
ALtogether, she has to climb:
4 + 4 = 8 flights of stairs!
We can also observe this using absolute value, as we are speaking about distance, 4 levels means 4 flights of stairs, so it doesn’t matter whether we are above/below ground, we are crossing same distance.

Texas Go Math Grade 6 Unit 1 Mixed Review Answer Key

Selected Response

Question 1.
What is the opposite of – 9?
(A) 9
(B) –\(\frac{1}{9}\)
(C) 0
(D) \(\frac{1}{9}\)
Answer:
(A) 9

Explaination:
The opposite of a number ¡s the number on the other side of 0 number line, and the same distance from 0.
Opposite of – 9 is 9.

Question 2.
Kyle is currently 60 feet above sea level. Which correctly describes the opposite of Kyle’s elevation?
(A) 60 feet below sea level
(B) 60 feet above sea level
(C) 6 feet below sea level
(D) At sea level
Answer:
(A) 60 feet below sea level

Explaination:
The opposite of a number is the number on the other side of 0 number tine, and the same distance from 0. We can use this statement in our case!
As kyle is 60 feet above sea level, opposite of his elevation would be: 60 feet below sea level!

6th Grade Math Unit 1 Review Test Answer Key Question 3.
What is the absolute value of 27?
(A) – 27
(B) 0
(C) 3
(D) 27
Answer:
(D) 27

Explaination:
Absolute value of some number is its distance from 0 in the number line.
|27| = 27

Question 4.
In Albany it is – 4°F, in Chicago it is – 14°F, in Minneapolis it is – 11°F, and in Toronto it is – 13°F. In which city is it the coldest?
(A) Albany
(B) Chicago
(C) Minneapolis
(D) Toronto
Answer:
(B) Chicago

Explaination:
Here, we will compare given temperature to find out, which is lowest.
When we find lowest temperature, we will know which city is the oldest!

Temperature of – 4°F is greater than – 1°F which is greater than – 13°F which is greater than – 14°F.
Now, we can concLude that the lowest temperature is -14°F.
That temperature is measured in Chicago.
So, coldest is in Chicago.

Question 5.
Which shows the integers in order from greatest to least?
(A) 18, 4, 3, – 2, – 15
(B) – 2, 3, 4, – 15, 18
(C) – 15, – 2, 3, 4, 18
(D) 18, – 15, 4, 3, 2
Answer:
(A) 18, 4, 3, – 2, – 15

Explaination:
We have integers 18, 4, 3, – 2, – 15 given!
We want to order them from greatest to least.

Number 18 is greater than 4 which is greater than 3 which is greater than – 2 which is greater than – 15.
Therefore, we can write:
18 > 4 > 3 > – 2 > – 15
Order from greatest to least is: 18, 4, 3, – 2, – 15.

Question 6.
Joanna split three pitchers of water equally among her eight plants. What fraction of a pitcher did each plant get?
(A) \(\frac{1}{8}\) of a pitcher
(B) \(\frac{1}{3}\) of a pitcher
(C) \(\frac{3}{8}\) of a pitcher
(D) \(\frac{8}{3}\) of a pitcher
Answer:
(C) \(\frac{3}{8}\) of a pitcher

Explaination:
It is obvious that we want to write a fraction including 3 as a numerator and 8 as a denominator.
This is how it looks: \(\frac{3}{8}\)

Question 7.
Which set or sets does the number – 22 belong to?
(A) Whole numbers only
(B) Rational numbers only
(C) Integers and rational numbers only
(D) Whole numbers, integers, and rational numbers
Answer:
(C) Integers and rational numbers only

Explaination:
Number – 22 is opposite of Whole number 22, therefore is belongs to set of Integers.
As Rational numbers include set of Integers, therefore it also belongs to set of Rational numbers.

Question 8.
Carlos swam to the bottom of a pool that is 12 feet deep. What is the opposite of Carlos’s elevation relative to the surface?
(A) – 12feet
(B) 0 feet
(C) 12 feet
(D) \(\frac{1}{12}\) foot
Answer:
(C) 12 feet

Explaination:
The opposite of a number is the number on the other side of the 0 number line, and the same distance from 0.
As elevation is a negative number, in this case, that means the opposite of Carlos’s elevation is 12 feet.

Unit 1 Mid Unit Assessment Grade 6 Answer Key Question 9.
Which number line shows \(\frac{1}{3}\) and its opposite?
(A)
(B)
(C)
(D)
Answer:
(D)

Explaination:
The opposite of a number is the number on the other side of the number line, and the same distance from 0.
Let’s draw our number line which will include \(\frac{1}{3}\) and its opposite, –\(\frac{1}{3}\)

Note that we used 1/3 instead of \(\frac{1}{3}\).

Question 10.
Which of the following shows the numbers in order from least to greatest?
(A) – \(\frac{2}{3}\), –\(\frac{3}{4}\), 0.7, 0
(B) 0.7, 0, – \(\frac{2}{3}\), – \(\frac{3}{4}\),
(C) – \(\frac{2}{3}\), – \(\frac{3}{4}\), 0, 0.7
(D) – \(\frac{3}{4}\), – \(\frac{2}{3}\), 0, 0.7
Answer:
(D) – \(\frac{3}{4}\), – \(\frac{2}{3}\), 0, 0.7

Explaination:
Given numbers are: – \(\frac{2}{3}\), –\(\frac{3}{4}\), 0.7, 0
Let’s order them from least to greatest!
The first thing is to transform them into equal form(decimals)!
– \(\frac{2}{3}\) = – 0.\(\dot{6}\)
– \(\frac{3}{4}\) = – 0.75
Now we can say that:
Number – 0.75 in less than – 0.\(\dot{6}\) which in less than 0 which is less than 0.7
Therefore, we can write the an:
– 0.75 < – 0.\(\dot{6}\) < 0 < 0.7
Now, we can return them into given forms and write them in the right order!
– \(\frac{3}{4}\), – \(\frac{2}{3}\), 0, 0.7

Division:

Question 11.
Which number line shows an integer and its opposite?
(A)
(B)
(C)
(D)
Answer:
(B)

Explaination:
Here, we could draw all 4 of given number tines, and conclude which one is correct!
However, there is no purpose to do so.
Let’s see what are we actually looking for, when finding our answer.
We want to find the one, which shows an integer and its opposite.
As by definition, the opposite of a number is the number on the other side of 0 number line, and the same distance from 0
So, we should have same distance from 0 on both sides!
There is only 1 graph that satisfies our terms.
It is:

Gridded Response

Question 12.
Which is the greatest out of \(\frac{1}{3}\), – 1.2, 0.45, and – \(\frac{4}{5}\)?

Answer:
Given numbers are: \(\frac{1}{3}\), – \(\frac{4}{5}\), – 1.2. 0.45
Let’s order them from least to greatest, and then we will know our final solution!
First thing is to transform them into equal form(decimals)!
\(\frac{1}{3}\) = 0.3
– \(\frac{4}{5}\) = – 0.8
Now, we can say that:
Number – 1.2 is less than – 0.8 which is less than 0.\(\dot{3}\) which is less than 0.45.
Therefore, we can write them as:
– 1.2 < – 0.8 < 0.\(\dot{3}\) < 0.45
Now, if we take a look on previous expression, we can see that 0.45 is the greatest number among given ones!

Division:

Question 13.
As part of a research team, Ryanne climbed into a cavern to an elevation of – 117.6 feet. What is the absolute value of Ryanne’s elevation, in feet?

Answer:
In this task, we want to find the absolute value of given elevation!
Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies.
The absolute value of a number is never negative.
|- 117.6| = 117.6 feet
= 117.6

Hot Tip: Correct answers in gridded problems can be positive or negative. Enter the negative sign in the first column when it is appropriate. Check your work!

Question 14.
Melvin has a certain number of files on his computer. The opposite of this number is – 653. How many files are on Melvin’s computer?

Answer:
Here, we have to understand that opposite of opposite is given number
The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.
If opposite of some number is – 653, that means that the number is: 653

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 3.1 Answer Key Multiplying Fractions.

Texas Go Math Grade 6 Lesson 3.1 Answer Key Multiplying Fractions

Texas Go Math Grade 6 Lesson 3.1 Explore Activity Answer Key

Modeling Fraction Multiplication
Sam and Pete had a party. After the party, they discovered that \(\frac{3}{4}\) of a casserole was left over. Sam and Pete ate \(\frac{1}{2}\) of the leftover casserole. What fraction of the original casserole did Sam and Pete eat?

Shade the model to show .

(A) Shade the rectangle to represent the \(\frac{3}{4}\) of the casserole that was left over after the party.

(B) Double shade \(\frac{1}{2}\) of \(\frac{3}{4}\). Divide the remaining fourth into two parts so that all of the parts are equal.

(C) Sam and Pete ate ____ of the original casserole.

(D) Did the amount of casserole increase or decrease when multiplied by \(\frac{1}{2}\)? How does the model show this? Explain.

(E) Write the multiplication shown by the model.

Reflect

Go Math Grade 6 Lesson 3.1 Answer Key Question 1.
Communicate Mathematical Ideas Will the product of \(\frac{1}{2}\) and \(\frac{2}{3}\) be greater or less than \(\frac{2}{3}\)? Explain.
Answer:
We can calculate the product of \(\frac{1}{2}\) and \(\frac{2}{3}\) and then compare the result with \(\frac{2}{3}\).

Now, we can compare \(\frac{1}{2}\) and \(\frac{2}{3}\)
Easiest way is to compare their numerators.
Number 1 is less than 2.
Therefore. we can write: 1 < 2
That implies that \(\frac{1}{3}\) is less than \(\frac{2}{3}\).

Question 2.
Communicate Mathematical Ideas Is the product less than or greater than the factors? Explain.
Answer:
This question depends on whether we multiply numbers whose value is greater than 1 or less than 1.
If both factors are greater than 1, then we get number which is greater than factors.
If any of factors is less than 1, then we get number which is less than at least one factor.

Question 3.
Analyze Relationships How can you determine when to simplify using the GCF before multiplying?
Answer:
We simplify our fractions using GCF when we see some common factor in numerator and denominator.

Your Turn

Multiply. Write each product in simplest form.

Question 4.
\(\frac{1}{6} \times \frac{3}{5}\) ____________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify expression by dividing by the Greatest Common Factor
And finally, we write our answer in simplest form!

Go Math Grade 6 Answer Key Lesson 3.1 Multiplying Fractions Question 5.
\(\frac{3}{4} \times \frac{7}{9}\) ____________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify the expression by dividing by the Greatest Common Factor
And finally, we write our answer in simplest form!

Question 6.
\(\frac{3}{7} \times \frac{2}{3}\) ____________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify expression by dividing by the Greatest Common Factor
And finally, we write our answer in simplest form!

Question 7.
\(\frac{4}{5} \times \frac{2}{7}\) ____________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify expression by dividing by the Greatest Common Factor
And finally, we write our answer in simplest form!
\(\frac{4}{5} \times \frac{2}{7}=\frac{4 \times 2}{5 \times 7}\)
= \(\frac{8}{35}\)

Reflect

Question 8.
Analyze Relationships Is the product of a fraction and a whole number greater than or less than the whole number? Explain.
Answer:
Product of a fraction and a whole number is greater than the whole number
if fraction numerator is greater than its denominator.

If fraction numerator is less than its denominator then the product is less than the whole number
There is also special case when fraction numerator and denominator are same, then the product is same as whole number.

Your Turn

Multiply. Write each product in simplest form.

Question 9.
\(\frac{5}{8}\) × 24 _______________
Answer:
Here, before we start the process of multiplication, we must write whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as whole number if possible!

Multiplying Fractions with Answers Go Math Lesson 6th Grade Question 10.
\(\frac{3}{5}\) × 20 _______________
Answer:
Here, before we start the process of multiplication, we must write the whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as a whole number if possible!

Question 11.
\(\frac{1}{3}\) × 8 _______________
Answer:
Here, before we start the process of multiplication, we must write the whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as a whole number if possible!

Question 12.
\(\frac{1}{4}\) × 14 _______________
Answer:
Here, before we start the process of multiplication, we must write the whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as a whole number if possible!

Question 13.
\(\frac{7}{10}\) × 7 _______________
Answer:
Here, before we start the process of multiplication, we must write whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as whole number if possible!
\(\frac{7}{10}\) × 7 = \(\frac{7}{10} \times \frac{7}{1}\)
= \(\frac{7 \times 7}{10 \times 1}\)
= \(\frac{49}{10}\) = 4.9

Question 14.
\(\frac{7}{10}\) × 10 _______________
Answer:
Here, before we start the process of multiplication, we must write whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as whole number if possible!

Texas Go Math Grade 6 Lesson 3.1 Guided Practice Answer Key

Question 1.
Lisa, Taryn, and Catherine go to a store to buy party supplies. The store has a sale on the supplies they want for the original price. The girls agree to each pay \(\frac{1}{3}\) of the cost. (Explore Activity)

a. Draw a model to show what fraction of the original price they will each pay.
Answer:
Discount:
Lisa
Taryn
Catherine

b. What fraction of the original price did each girl pay?
Answer:
As original, price was discounted to \(\frac{3}{4}\), and the girls agree to each pay \(\frac{1}{3}\) of the cost
So, each of them pays a third of a discounted price. We can write it as:

Now we know that each girl will pay \(\frac{1}{4}\) of the cost.

c. Write the multiplication shown by the model.
Answer:
As original, price was discounted to \(\frac{3}{4}\), and the girls agree to each pay \(\frac{1}{3}\) of the cost
So, each of them pays a third of a discounted price. We can write it as:

Now we know that each girl will pay \(\frac{1}{4}\) of the cost.
Done in task.

d. Did the fraction representing the sale price increase or decrease when multiplied by \(\frac{1}{3}\)? Explain.
Answer:
As we multiplied by a fraction whose numerator is less than the denominator, we got a number that is less than the original one!

Multiply. Write each product in the simplest form.

Question 2.
\(\frac{1}{2} \times \frac{5}{8}\) _______________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify the expression by dividing by the Greatest Common Factor.
And finally, we write our answer in simplest form!
\(\frac{1}{2} \times \frac{5}{8}=\frac{1 \times 5}{2 \times 8}\)
= \(\frac{5}{16}\)

Lesson 3.1 Answer Key 6th Grade Multiplying Fractions Question 3.
\(\frac{3}{5} \times \frac{5}{9}\) _______________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify the expression by dividing by the Greatest Common Factor.
And finally, we write our answer in simplest form!

Question 4.
\(\frac{3}{8} \times \frac{2}{5}\) _______________
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify expression by dividing by the Greatest Common Factor.
And finally, we write our answer in simplest form!

Find each amount.

Question 5.
\(\frac{1}{4}\) of 12 bottles of water = ______ bottles
Answer:
Here, if we want to get some ‘piece of stuff, we have to multiply the original value with given fractions!

Here, before we start the process of multiplication, we must write whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as whole number if possible!

Therefore, \(\frac{1}{4}\) of 12 bottles of water equals 3 bottles of water!

Question 6.
\(\frac{2}{3}\) of 24 bananas = ______ bananas
Answer:
If we want to get some ‘piece of stuff, we have to multiply the original value with given fractions!

Here, before we start the process of multiplication, we must write whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as whole number if possible!

Therefore, \(\frac{2}{3}\) of 24 bananas equals 16 bananas

Question 7.
\(\frac{3}{5}\) of $40 restaurant bill = $ ______
Answer:
If we want to get some ‘piece of stuff, we have to multiply the original value with given fractions!

Here, before we start the process of multiplication, we must write whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as whole number if possible!

Therefore, \(\frac{3}{5}\) of $40 bill equals $24!

Lesson 3.1 Answer Key Multiplying Fractions Grade 6 Question 8.
\(\frac{5}{6}\) of 18 pencils = ______ pencils
Answer:
If we want to get some ‘piece of stuff, we have to multiply the original value with given fractions!

Here, before we start the process of multiplication, we must write the whole number as an equivalent fraction.
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we simplify before multiplying using the Greatest Common Factor.
Thirdly, we multiply numerators and denominators.
And finally, we write our solution in simplest form, as a whole number if possible!

Thferefore, \(\frac{5}{8}\) of 18 pencils equals 15 pencils!

Essential Question Check-In

Question 9.
How can you multiply two fractions?
Answer:
Process of fractions multiplication:
Firstly, we write the problem as a single fraction.
Secondly, we multiply numerators and denominators!
Thirdly, we simplify expression by dividing by the Greatest Common Factor.
And finally, we write our answer in simplest form!

Solve. Write each answer in the simplest form.

Question 10.
Erin buys a bag of peanuts that weighs \(\frac{3}{4}\) of a pound. Later that week, the bag is \(\frac{2}{3}\) full. How much does the bag of peanuts weigh now? Show your work.
Answer:
In this task, we have a full, bag of peanuts that weights \(\frac{3}{4}\) pounds.
Later that week, there is only \(\frac{2}{3}\) of peanuts bag left
Now, we can conclude that the only way to find our solution is to multiply full bag weight with “new” weight
Note that we won’t write process of multiplication here since it can be found in previous tasks explained briefly!

Question 11.
Multistep Marianne buys 16 bags of potting soil that comes in \(\frac{5}{8}\)-pound bags.

a. How many pounds of potting does Marianne buy?
Answer:
If we want to find weight of 16 bags of potting soil, we have to multiply the quantity with weight of single bag, which is \(\frac{5}{8}\) pounds.

Now we know that Marianne buys 10 pounds of potting!

b. If Marianne’s father calls and says he needs 13 pounds of potting soil, will 4 more bags be enough to cover the extra soil needed?
Answer:

Now, final thing to do is to compare the weight of 18 bags with needed 13 pounds of potting
10 + \(\frac{5}{2}\) = 10 + 2.5 = 12.5
Now, we know that: 12.5 < 13 pounds.
So, conclusion is that 4 extra soil bags won’t be enough to cover her father’s needs!

Division:

Question 12.
Analyze Relationships Name three different pairs of fractions that have the same product when multiplied. Explain how you found them.
Answer:
First
\(\frac{5}{4} \times \frac{5}{2}\) = \(\frac{25}{8}\)

Secondly

Third

As we can see, all the pairs were obtained by multiplying numerator/denominator of one fractions and denominator/numerator of second fraction by same number!

Question 13.
Marcial found a recipe for fruit salad that he wanted to try to make for his birthday party. He decided to triple the recipe.

a. What is the new amount for the oranges, apples, blueberries, and peaches?
Answer:
As she tripled the recipe, now we have to triple the original amount of each fruit.

Blueberries:
\(\frac{1}{4}\) × 3 = \(\frac{1}{4}\) × \(\frac{3}{1}\)
= \(\frac{1 \times 3}{4 \times 1}\)
= \(\frac{3}{4}\)
New amount of Blueberries is \(\frac{3}{4}\) cup.

Oranges:
\(\frac{1}{2}\) × 3= \(\frac{1}{2}\) × \(\frac{3}{1}\)
= \(\frac{1 \times 2}{3 \times 1}\)
= \(\frac{3}{2}\)
New amount of Orange is \(\frac{3}{2}\) pieces.

Apples:
\(\frac{3}{5}\) × 3 = \(\frac{3}{5}\) × \(\frac{3}{1}\)
= \(\frac{3 \times 5}{3 \times 1}\)
= \(\frac{9}{5}\)
New amount of Apples is \(\frac{9}{5}\) pieces.

Peaches.

New amount of peaches is 2 pieces.

b. Communicate Mathematical Ideas The amount of rhubarb in the original recipe is 3 cups. Using what you know of whole numbers and what you know of fractions, explain how you could triple that mixed number.
Answer:
Let’s write the process of tripling the amount of rhubarb.

(1) Transforming mixed number into fraction
3\(\frac{1}{2}\) = 1 + 1 + 1 + \(\frac{1}{2}\)
= \(\frac{2}{2}+\frac{2}{2}+\frac{2}{2}+\frac{1}{2}\)
= \(\frac{7}{2}\)

(2) Multiplying fraction by 3:

As Calculations says, new amount of rhubarb is \(\frac{21}{2}\) cups.

Question 14.
Music Two-fifths of the instruments in the marching band are brass. One-eighth of the brass instruments are tubas.
a. What fraction of the band is tubas?
Answer:
If there are \(\frac{2}{5}\) of instruments brass, and \(\frac{1}{8}\) of the brass instruments are tubas,
Amount of tubas is equal to product of those 2 fractions!

Now we know that \(\frac{1}{20}\) of all instruments in band are tubas.

b. If there are 240 band instruments total, how many are tubas?
Answer:
If there are 240 instruments in band, then there are:

Division:

Multiplying Fractions Lesson 3.1 Grade 6 Question 15.
Compare simplifying before multiplying fractions with simplifying after multiplying the fractions.
Answer:
Simplifying before multiplying fractions will give us the same result as simplifying after multiplying the fractions!

However, simplifying before multiplying fractions has some benefits.
For example, when we have some larger number in the numerator and denominator with a common factor greater than I, we can simply reduce them to lower the amount of work after multiplication.

Question 16.
Sports Kevin is a quarterback on the football team. He completed 36 passes during the season. His second-string replacement, Mark, completed \(\frac{2}{9}\) as many passes as Kevin. How many passes did Mark complete?
Answer:
Kevin completed 36 passes during the season and Mark completed \(\frac{2}{9}\) of Kevin’s amount.
So, Mark completed:

H.O.T. Focus On Higher Order Thinking

Question 17.
Represent Real-World Problems Kate wants to buy a new bicycle from a sporting goods store. The bicycle she wants normally sells for $360. The store has a sale where all bicycles cost \(\frac{5}{6}\) of the regular price. What is the sale price of the bicycle?

Answer:
As the original price of the bicycle is $360, \(\frac{5}{6}\) of the price would be:

Discounted price would be $ 300

Division:

Question 18.
Error Analysis To find the product \(\frac{3}{7}\) × \(\frac{4}{9}\) Cameron simplified to \(\frac{3}{7}\) to \(\frac{1}{7}\) and then multiplied the fractions \(\frac{1}{7}\) and \(\frac{4}{9}\) to find the product \(\frac{4}{63}\). What is Cameron’s error?
Answer:
Cameron made a mistake in the simplification process.
He simplified \(\frac{3}{7}\) into \(\frac{1}{7}\) which makes no sense.
When we simplify fractions, we divide both the numerator and denominator by the same number and get an equivalent fraction to an original one!
For example, in this task, he reached from \(\frac{3}{7}\) to \(\frac{1}{7}\), since we have the same denominators in both cases we can simply compare their numerators to see that they are not actually equal.
Let’s do it:
Number 3 is greater than 1, therefore, these fractions aren’t equivalent.

Question 19.
Justify Reasoning When multiplying a whole number by a fraction, the whole number is written as a fraction by placing the value of the whole number in the numerator and 1 in the denominator. Does this change the final answer? Explain why or why not.
Answer:
As we multiply a whole number by a fraction, we transform that whole number into a fraction with 1 in the denominator, which surely can not change our final answer. Why?
The answer is pretty simple actually. Remember what they have taught you in lower grades
Dividing some number by 1 does not change it, the same is true with multiplying!
Since fractions represent the “division” of the numerator by the denominator, we got our answer.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 1 Quiz Answer Key.

Texas Go Math Grade 6 Module 1 Quiz Answer Key

Texas Go Math Grade 6 Module 1 Ready to Go On? Answer Key

1.1 Identifying Integers and Their Opposites

Question 1.
The table shows the elevations in feet of several locations around a coastal town. Graph and label the locations on the number line according to their elevations.


Answer:

Write the opposite of each number.

Question 2.
– 22 ______________
Answer:
Opposite of – 22 is clearly 22

Go Math Grade 6 Module 1 Quiz Answer Key Question 3.
0 ______________
Answer:
The Opposite of 0 is clearly 0

1.2 Comparing and Ordering Integers

List the numbers in order from least to greatest.

Question 4.
– 2, 8, – 15, – 5, 3, 1 ________________
Answer:
Number – 15 is smaller than – 5 which is smaller than – 2 which is smaller than 1 which is smaller than 3 which is smaller than 8
Therefore list from least to greatest goes:
– 15, – 5, – 2, 1, 3, 8

Compare. Write < or >.

Question 5.
– 3 _______ – 15
Answer:
Number – 3 is greater than – 15 so we can write:
– 3 > – 15

Question 6.
9 _________ – 10
Answer:
Number 9 is greater than – 10 so we can write:
9 > – 10

1.3 Absolute Value

Graph each number on the number line. Then use your number line to find the absolute value of each number.

Question 7.
2 ________
Answer:

By Looking at the graph we can see that distance from 2 to 0 is 2 units.
Therefore, an absolute value of 2 is 2

Module 1 Test Answers Go Math Grade 6 Question 8.
– 8 __________
Answer:

By Looking at the graph we can see that distance from – 8 to 0 is 8 units
Therefore, an absolute value of – 8 is 8

Question 9.
– 5__________
Answer:

By Looking at the graph we can see that distance from – 5 to 0 is 5 units.
Therefore, absolute value of – 5 is 5

Essential Question

Question 10.
How can you use absolute value to represent a negative number in a real-world situation?
Answer:
Absolute value in real world can be used to represent:
Amount of money we owe on a bank account or to represent depth of some place based on sea level…

Texas Go Math Grade 6 Module 1 Mixed Review Texas Test Prep Answer Key

Question 1.
Which number line shows 2, 3 and – 3?
(A)
(B)
(C)
(D)
Answer:
Let’s draw our number line and represent numbers 2, 3, – 3 on it!

(C)

Question 2.
What is the opposite of – 3?
(A) 3
(B) 0
(C) –\(\frac{1}{3}\)
(D) \(\frac{1}{3}\)
Answer:
Opposite of – 3 is 3
(A) 3

Go Math Grade 6 Module 1 Answer Key Pdf Question 3.
Darrel is currently 20 feet below sea level. Which correctly describes the opposite of Darrel’s elevation?
(A) 20 feet below sea level
(B) 20 feet above sea level
(C) 2 feet below sea level
(D) At sea level
Answer:
Opposite of 20 feet below sea level is 20 feet above sea level!
(B) 20 feet above sea level

Question 4.
Which has the same absolute value as – 55?
(A) 0
(B) 1
(C) 1
(D) 55
Answer:
Number 55 has same absolute value as – 55
(D) 55

Module 1 Quiz Answer Key Go Math Grade 6 Question 5.
In Bangor it is – 3°F, in Fairbanks it is – 12°F, in Fargo it is – 8°F, and in Calgary it is – 15°F. In which city is it the coldest?
(A) Bangor
(B) Fairbanks
(C) Fargo
(D) Calgary
Answer:
Temperature – 3°F is higher than – 8°F which is higher than – 12°F which is higher than – 15°F.
We add Bangor, Fargo, Fairbanks, Calgary to these values respectively!
Now, we can conclude that Calgary is coldest!
(D) Calgary

Question 6.
Which shows the integers in order from least to greatest?
(A) 20, 6, – 2, – 13
(B) – 2, 6, – 13, 20
(C) – 13, – 2, 6, 20
(D) 20, – 13, 6, – 2
Answer:
We have numbers – 2, – 13, 20, 6 and we want to find our order from least to greatest
Number – 13 is smaller than – 2 which is smaller than 6 which is smaller than 20
Therefore, the order from least to highest would be: – 13, – 2, 6, 20
(C) – 13, – 2, 6, 20

Grade 6 Module 1 Quiz Ready To Go On Answer Key Question 7.
How would you use a number line to put integers in order from greatest to least?
(A) Graph the integers, then read them from left to right.
(B) Graph the integers, then read them from right to left.
(C) Graph the absolute values of the integers, then read them from left to right.
(D) Graph the absolute values of the integers, then read them from right to left.
Answer:
I would graph the number line and then simply read numbers from right to Left side.
(B) Graph the integers, then read them from right to left.

Gridded Response

Question 8.
The table shows the change in several savings accounts over the past month. Which value represents the least change?


Answer:
Change of – $302 is higher than change of $108 which is higher than change 0 – $45 which is higher than change of $25.
Therefore, lowest change is $25.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 3 Answer Key Multiplying and Dividing Fractions.

Texas Go Math Grade 6 Module 3 Answer Key Multiplying and Dividing Fractions

Texas Go Math Grade 6 Module 3 Are You Ready? Answer Key

Write each improper fraction as a mixed number.

Question 1.
\(\frac{9}{4}\) ____________
Answer:

Question 2.
\(\frac{8}{3}\) ____________
Answer:

Question 3.
\(\frac{23}{6}\) ____________
Answer:

Go Math Grade 6 Module 3 Answer Key Question 4.
\(\frac{11}{2}\) ____________
Answer:

Question 5.
\(\frac{17}{5}\) ____________
Answer:

Question 6.
\(\frac{15}{8}\) ____________
Answer:

Question 7.
\(\frac{33}{10}\) ____________
Answer:

Question 8.
\(\frac{29}{12}\) ____________
Answer:

Multiply

Question 9.
6 × 5 ____________
Answer:
Use related fact you know
5 × 5 = 25

Think: 6 × 5 = (5 × 5) + 5
= 25 + 5
= 30

Question 10.
8 × 9 ____________
Answer:
Use related fact you know
8 × 8 = 64

Think: 8 × 9 = (8 × 8) + 8
= 64 + 8
= 72

Question 11.
10 × 11 ____________
Answer:
Use related fact you know
10 × 10 = 100

Think: 10 × 11 = (10 × 10) + 10
= 100 + 10
= 110

Question 12.
7 × 8 ____________
Answer:
Use related fact you know
7 × 7 = 49

Think: 7 × 8 = (7 × 7) = 7
= 49 + 7
= 56

Question 13.
9 × 7 ____________
Answer:
Use related fact you know
7 × 7 = 49

Think: 9 × 7 = (7 × 7) + 7 + 7
= 49 + 14
= 63

Question 14.
8 × 6 ____________
Answer:
Use related fact you know
6 × 6 = 36

Think: 8 × 6 = (6 × 6) + 6 + 6
= 36 + 12
= 48

Question 15.
9 × 11 ____________
Answer:
Use related fact you know
9 × 9 = 81

Think 9 × 11 = (9 × 9) + 9 + 9
= 81 + 18
= 99

Question 16.
11 × 12 ____________
Answer:
Use related fact you know
11 × 11 = 121

Think 11 × 12 = (11 × 11) + 11
= 121 + 11
= 132

Divide.

Question 17.
35 ÷ 7 ____________
Answer:
Solution to this example is given below

Think: 7 times what number equal 35?
7 × 5 = 35
so, 35 ÷ 7 = 5

Question 18.
56 ÷ 8 ____________
Answer:
Solution to this example is given below

Think: 8 times what number equal 56?
8 × 7 = 56
so, 56 ÷ 8 = 7

Question 19.
28 ÷ 7 ____________
Answer:
Solution to this example is given below

Think: 7 times what number equal 28?
7 × 4 = 28
so, 28 ÷ 7 = 4

Question 20.
48 ÷ 8 ____________
Answer:
Solution to this example is given below

Think: 8 times what number equal 48?
8 × 6 = 48
so, 48 ÷ 8 = 6

Question 21.
36 ÷ 4 ____________
Answer:
Solution to this example is given below

Think: 4 times what number equal 36?
4 × 9 = 36
so, 36 ÷ 4 = 9

Question 22.
45 ÷ 9 ____________
Answer:
Solution to this example is given below

Think: 9 times what number equal 45?
9 × 5 = 45
so, 45 ÷ 9 = 5

Question 23.
72 ÷ 8 ____________
Answer:
Solution to this example is given below

Think: 8 times what number equal 72?
8 × 9 = 72
so, 72 ÷ 8 = 9

Question 24.
40 ÷ 5 ____________
Answer:
Solution to this example is given below

Think: 5 times what number equal 40?
5 × 8 = 40
so, 40 ÷ 5 = 8

Texas Go Math Grade 6 Module 3 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓ words to complete the triangle. Write the review word that fits the description in each section of the triangle.

Understand Vocabulary

In each grouping, select the choice that is described by the given vocabulary word.

Question 1.
reciprocals
(A) 1:15
(B) \(\frac{3}{4} \div \frac{1}{6}\)
(C) \(\frac{3}{5}\) and \(\frac{5}{3}\)
Answer:
If the product of two numbers is 1, then the two numbers are said to be reciprocals of each other.

Only viable Solution is C, so let’s check it!
\(\frac{3}{5} \times \frac{5}{3}=\frac{15}{15}\) = 1
Therefore, this solution is valid1

Question 2.
Mixed Number
(A) \(\frac{1}{3}-\frac{1}{5}\)
(B) 3\(\frac{1}{2}\)
(C) – 5
Answer:
Mixed number is a number that is a combination of a whole number and a fraction.

Only B answer is Combination of whole number and a fraction!

Question 3.
Whole Number
(A) – 1
(B) 7
(C) \(\frac{2}{5}\)
Answer:
Whole number is a positive integer!

Only B answer
Only 7 is integer, and integer at the same time!

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 4 Quiz Answer Key.

Texas Go Math Grade 6 Module 4 Quiz Answer Key

Texas Go Math Grade 6 Module 4 Ready to Go On? Answer Key

4.1 Multiplying Decimals

Question 1.
Marta walked at 3.9 miles per hour for 0.72 hours. How far did she walk?
Answer:
Solution to this example is given below

She walks 2.808 mile

Multiply.

Go Math Grade 6 Module 4 Quiz Answer Key Question 2.
0.07 × 1.22
Answer:
Solution to this example is given below

Question 3.
4.7 × 2.65
Answer:
Solution to this example is given below

Question 4.
11.3 × 4.16
Answer:
Here, the first factor has one decimal but the second one has two decimals, so, the result will have three decimals:

So, the result is 47.008

Question 5.
53.2 × 17.6
Answer:
Here both factors has one decimal, so, the product will have two decimals:

So the product is 936.32

4.2 Dividing Decimals

Question 6.
Bryan paid $19.95 for 2.5 pounds of turkey. What was the price per pound?
Answer:
In order to find the price of turkey per pound, we will divide 19.95 by 2.5.
We will multiply by 10 and the dividend and the divisor and then divide:

So, the price per pound was $ 7.98.

Divide.

Module 4 Grade 6 Weekly Math Quiz Answer Key Question 7.
64 ÷ 0.4
Answer:
The divisor has one decimal place, so multiply both the dividend and the divisor by 10 so that the divisor is a whole number
0.4 × 10 = 4
64 × 10 = 640

Question 8.
4.7398 ÷ 0.26
Answer:
The divisor has one decimal place, so multiply both the dividend and the divisor by 100 so that the divisor is a whole number

0.26 × 100 = 26
4.7398 × 100 = 473.98

Question 9.
26.73 ÷ 9
Answer:
Solution to this example is given below

Question 10.
4 ÷ 3.2
Answer:
The divisor has one decimal place, so multiply both the dividend and the divisor by 10 so that the divisor is a whole number

3.2 × 10 = 32
4 × 10 = 40

4.3 Applying Multiplication and Division of Rational Numbers

Question 11.
Ramiro is \(\frac{3}{10}\) as tall as the flagpole. The flagpole is \(\frac{5}{9}\) as tall as a nearby tree. The tree is 32\(\frac{2}{5}\) feet tall. How tall is Ramiro?
Answer:
First we will calculate how tall flagpole is multiplying 32\(\frac{2}{5}\) by \(\frac{5}{9}\). We wilt first convert mixed number as a fraction then simplify and multiply.

Now, we will calculate how tall Ramiro is by multiplying 18 by \(\frac{3}{10}\).

So, Ramiro is 5\(\frac{2}{5}\) tall.

Module 4 Test Go Math Grade 6 Answer Key Question 12.
Doors for the small cabinets are 11.5 inches long. Doors for the large cabinets are 2.3 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 10 feet long?
Answer:
We will first calculate how long large doors are by multiplying 11.3 by 2.3 and getting:

So, large doors are 26.45 inches long. Next we will do is to calculate how man feet there is in 26.45 inches multiplying 26.45 by 0.083:

So, the larger doors are 2.19535 feet long. Now, we will divide 10 by 2.19535 in order to get how many large doors we can cut from given board. We will actually divide 10 by 2.2 because 2.2 is actually the previous result rounded to the tenths, but first we will multiply by lo and time dividend and time divisor and get:

So, we can cut 4 large doors from a 10 feet long board.

Question 13.
Tanisha ran \(\frac{3}{5}\) of a 26-mile race in 3.2 hours. If she ran at a constant rate, what was her speed in miles per hour?
Answer:
First we need to calculate how many miles she ran in order to calculate it, we will multiply \(\frac{3}{5}\) by 26 and get:
\(\frac{3}{5} \times 26=\frac{3 \times 26}{5 \times 1}=\frac{78}{5}\)
Now, we will divide \(\frac{78}{5}\) by 3.2 in order to find her speed. We will convert decimals to fraction:

So, her speed was 4\(\frac{7}{8}\) miles per hour.

Essential Question

Question 14.
Describe a real-world situation that could be modeled by dividing two rational numbers.
Answer:
For example, Samantha has \(\frac{5}{8}\) pounds of sugar. How many \(\frac{1}{8}\) -spoons of sugar there are in \(\frac{5}{8}\) pounds?

Texas Go Math Grade 6 Module 4 Texas Test Prep Answer Key

Question 1.
Javier reads 40 pages every hour. How many pages does Javier read in 2.25 hours?
(A) 80 pages
(B) 85 pages
(C) 90 pages
(D) 100 pages
Answer:
(C) 90 pages

Explaination:
In order to find how many pages Javier red, we will multiply 40 by 2.25. The result will have two decimals because of the second factor:

So, Javier read 90 pages. Correct. The correct answer is C

Grade 6 Module 4 Quiz Ready To Go On Answer Key Question 2.
Sumeet uses 0.4 gallons of gasoline each hour mowing lawns. How much gas does he use in 4.2 hours?
(A) 1.68 gallons
(B) 3.8 gallons
(C) 13 gallons
(D) 16 gallons
Answer:
(A) 1.68 gallons

Explaination:
Solution to this example is given below

Option A is correct answer
Total gas used 1.68 gallons

Question 3.
Sharon spent $3.45 on sunflower seeds. The price of sunflower seeds is $0.89 per pound. How many pounds of sunflower seeds did Sharon buy?
(A) 3.07 pounds
(B) 3.88 pounds
(C) 4.15 pounds
(D) 4.34 pounds
Answer:
(B) 3.88 pounds

Explaination:
The divisor has two decimal place, so multiply both the dividend and the divisor by 100 so that the divisor is a whore number
0.89 × 100 = 89
3.45 × 100 = 345

Divide

The final solution is rounded off to two decimals
Final Solution is 3.88

Grade 6 Module 4 Answer Key Go Math Question 4.
How many 0.4-liter glasses of water does it take to fill up a 3.4-liter pitcher?
(A) 1.36 glasses
(B) 3.8 glasses
(C) 8.2 glasses
(D) 8.5 glasses
Answer:
(D) 8.5 glasses

Explaination:
The divisor has one decimal place, so multiply both the dividend and the divisor by 10 so that the divisor is a whole number
0.4 × 10 = 4
3.4 × 10 = 34

Divide

Question 5.
Michelle’s family drove 272.48 miles. Michelle calculated that they drove 26.2 miles per gallon of gas. How many gallons of gas did the car use?
(A) 10 gallons
(B) 10.4 gallons
(C) 11.4 gallons
(D) 14 gallons
Answer:
(B) 10.4 gallons

Explaination:
In order to find how many gallons of gas car used. we need to divide 272.48 by 26.2. First we will multiply by 10 and then divide:

So, car used 10.4 gallons of gas. Correct answer is B.

Texas Go Math Grade 6 Module 4 Pdf Answer Key Question 6.
Each paper clip is \(\frac{3}{4}\) of an inch long and costs $0.02. Exactly enough paper clips are laid end to end to have a total length of 36 inches. What is the total cost of these paper clips?
(A) $0.36
(B) $0.54
(C) $0.96
(D) $1.20
Answer:
(C) $0.96

We will first divide 36 by \(\frac{3}{4}\) in order to get how many paper clips there are in 36 inches.

So, there are 1 $ paper clips and each costs $ 0.02. We will multiply 18 by 0.02 in order to find the total cost of till paper clips.

So, the total cost of these paper clips is $ 0.96. Correct answer is C.

Question 7.
Ken walks her dog every morning. The length of the walk is 0.55 kilometer on each weekday. On each weekend day, the walk is 1.4 times as long as a walk on a weekday. How many kilometers does Ken walk in one week?
(A) 2.75 kilometers
(B) 3.85 kilometers
(C) 4.29 kilometers
(D) 5.39 kilometers
Answer:
(C) 4.29 kilometers

Explaination:
We have five weekdays in one week, so, we will multiply 0.55 by 5 in order to calculate how many kilometers Keri walks on weekdays.
5 × 0.55 = 2.75
And in one week there are two weekend days, in each weekend day Ken walks:

So, each weekend day Ken waLks 0.770 kilometers, now we will multiply 0.770 by 2 to get how many kilometers Keri walks for weekend.
2 × 0.770 = 1.54
Now, we will sum 2.75 and 1.54 ¡n order to get how many kilometers Ken walks in one week.
2.75 × 1.54 = 4.29
So, Ken walks 4.29 kilometers in one week. Correct answer is C.

Gridded Response

Go Math Grade 6 Module 4 Answer Key Pdf Question 8.
In preparation for a wedding, Aiden bought 60 candles. He paid $0.37 for each candle. His sister bought 170 candles at the same price. How much more money, in dollars, did Aiden’s sister spend?

Answer:
First we will calculate how much money Aiden spent on candles multiplying 60 by 0.37 and get:

So, Aiden spent $ 22.2 on candles.
Now, we will calculate how much money his sister spent multiplying 1.70 by 0.37:

His sister spent $ 62.9 on candles.
Now, we will start 22.2 from 62.9 in order to calculate how much more money Aiden’s sister spent on candles:
62.9 – 22.2 = 40.7
So. she spent $ 40.7 more than Aiden.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 2.1 Answer Key Classifying Rational Numbers.

Texas Go Math Grade 6 Lesson 2.1 Answer Key Classifying Rational Numbers

Texas Go Math Grade 6 Lesson 2.1 Explore Activity Answer Key

Representing Division as a Fraction

Alicia and her friends Brittany, Kenji and Ellis are taking a pottery class. The four friends have to share 3 blocks of clay. How much clay will each of them receive if they divide the 3 blocks evenly?

(A) The top faces of the 3 blocks of clay can be represented by squares. Use the model to show the part of each block that each friend will receive. Explain.

(B) Each piece of one square is equal to what fraction of a block of clay?

(C) Explain how to arrange the pieces to model the amount of clay each person gets. Sketch the model.

(D) What fraction of a square does each person’s pieces cover? Explain.

(E) How much clay will each person receive?

(F) Multiple Representations How does this situation represent division?

Reflect

Question 1.
Communicate Mathematical Ideas 3 ÷ 4 can be written \(\frac{3}{4}\) How is the dividend and divisor of a division expression related to the parts of a fraction?
Answer:
Dividend and divisor are connected to the fraction as numerator and denominator respectively!

dividend – numerator;
divisor – denominator

Go Math Grade 6 Chapter 2 Lesson 2.1 Answer Key Question 2.
Analyze Relationships How could you represent the division as a fraction if 5 people shared 2 blocks? if 6 people shared 5 blocks?
Answer:
If 5 people shared 2 blocks, we can represent this as:
\(\frac{5}{2}\)

If 6 people shared 5 blocks, we can represent this as:
\(\frac{6}{5}\)

Write each rational number as \(\frac{a}{b}\).

Question 3.
– 15 ____________
Answer:
Number – 15 can be written by fraction \(\frac{a}{b}\) as:
– \(\frac{15}{1}\)

Question 4.
0.31 ____________
Answer:
Number 0.31 can be written by fraction \(\frac{a}{b}\) as:
\(\frac{31}{100}\)

Question 5.
4\(\frac{5}{9}\) ____________
Answer:
Number 4\(\frac{5}{9}\) can be written by fraction \(\frac{a}{b}\) as:
\(\frac{41}{9}\)

Question 6.
62 ____________
Answer:
Number 62 can be written by fraction \(\frac{a}{b}\) as:
\(\frac{62}{1}\)

Question 7.
Analyze Relationships Name two integers that are not also whole numbers.
Answer:
Here, we pick numbers that are negative so they don’t get involved in the whole numbers group:
– 7, – 10

Lesson 2.1 Answer Key Classifying Rational Numbers Worksheet 6th Grade Question 8.
Analyze Relationships Describe how the Venn diagram models the relationship between rational numbers, integers, and whole numbers.
Answer:
Venn diagram shows reference between groups.
It shows that Whole numbers are included in Integers and Integers in Rational numbers.

Your Turn

Place each number in the Venn diagram. Then classify each number by indicating in which set or sets it belongs.

Question 9.
14.1 ____________
Answer:

Number 14.1 belongs to Rational Numbers

Question 10.
7\(\frac{1}{5}\) ____________
Answer:

Please note that I wrote mixed number 7\(\frac{1}{5}\) as 7.2 because I cannot use alignment in editing pictures.
Number 7\(\frac{1}{5}\) belongs to Rational numbers

Classifying Rational Numbers Lesson 2.1 Answer Key Question 11.
– 8 ____________
Answer:

Number – 8 belongs to Integers.

Question 12.
101 ____________
Answer:

Number 101 belongs to whole numbers

Texas Go Math Grade 6 Lesson 2.1 Guided Practice Answer Key

Question 1.
Sarah and four friends are decorating picture frames with ribbon. They have 4 rolls of ribbon to share evenly. (Explore Activity)

a. How does this situation represent division?
Answer:
This situation can be represented by division as each person gets same amount of ribbon, therefore they have to split it into equal parts!

b. How much ribbon does each person receive?
Answer:
If Sarah has 4 friends, that means that 4 rolls of ribbon will be shared equally only if each gets:
\(\frac{4}{5}\)

Write each rational number in the form where a and b are integers.

Question 2.
0.7 ___________
Answer:
Number 0.7 can be written in the form of \(\frac{a}{b}\) as:
\(\frac{7}{10}\)

Question 3.
– 29 ___________
Answer:
Number – 29 can be written in the form of \(\frac{a}{b}\) as:
\(-\frac{29}{1}\)

Question 4.
8 ___________
Answer:
Mixed number 8\(\frac{1}{3}\) can be written in form of \(\frac{a}{b}\) as:
\(\frac{25}{3}\)

Place each number in the Venn diagram. Then classify each number by indicating in which set or sets each number belongs.

Go Math Grade 6 Lesson 2.1 Answer Key Rational Number Question 5.
– 15 ___________
Answer:

Number – 15 belongs to set of Integers

Question 6.
5\(\frac{10}{11}\) ___________
Answer:

Please note that i wrote mixed number 5\(\frac{10}{11}\) as 65/11 since i cannot use alignment in picture editing!
Number 5\(\frac{10}{11}\) beLongs to set of Rational numbers.

Essential Question Check-In

Question 7.
How is a rational number that is not an integer different from a rational number that is an integer?
Answer:
Number that is Rational and not Integer can not be written as whole number or its opposite.

List two numbers that fit each description. Then write the numbers in the appropriate location on the Venn diagram.

Question 8.
Integers that are not whole numbers
Answer:
Integers that are not Whole numbers are opposites of Whole numbers: – 3, – 5

Question 9.
Rational numbers that are not integers
Answer:
Rational numbers that are not Integers are numbers that are not Whole numbers or their opposites: \(\frac{5}{3}, \frac{7}{8}\)

Please note that i wrote \(\frac{5}{3}\) instead of \(\frac{5}{3}\) and \(\frac{7}{8}\) instead of \(\frac{7}{8}\)

Question 10.
Multistep A nature club is having its weekly hike. The table shows how many pieces of fruit and bottles of water each member of the club brought to share.

a. If the hikers want to share the fruit evenly, how many pieces should each person receive?
Answer:
If hikers wanted to share 14 pieces of fruit evenly, each of them would get: \(\frac{14}{4}\)

b. Which hikers received more fruit than they brought on the hike?
Answer:
To calculate, which of hikers got more fruit than brought, we have to change the format of our number to mixed number We know how to do it:
\(\frac{14}{4}\) = \(\frac{4}{4}+\frac{4}{4}+\frac{4}{4}+\frac{2}{4}\)
= 1 + 1 + 1 + \(\frac{2}{4}\)
= 3 + \(\frac{2}{4}\)
= 3\(\frac{2}{4}\)
Now we can conclude that Hendrick and Baxer will get more pieces than they brought1

c. The hikers want to share their water evenly so that each member has the same amount. How much water does each hiker receive?
Answer:
As there are 17 bottles of water altogether, if they split it in 4 parts that means each hiker is going to get: \(\frac{17}{4}\) bottles.
As this is not Whole number, some hiker will have to bring that one extra bottle so they could share it between
themselves!

Question 11.
Sherman has 3 cats and 2 dogs. He wants to buy a toy for each of his pets. Sherman has $22 to spend on pet toys. How much can he spend on each pet? Write your answer as a fraction and as an amount in dollars and cents.
Answer:
As Sherman has 5 pets in total. That means he has to share $22 into 5 equal parts.
He will spend on each: $\(\frac{22}{5}\)
He will spend $4 and 40 cents for each pet!

Question 12.
A group of 5 friends is sharing 2 pounds of trail mix. Write a division problem and a fraction to represent this situation.
Answer:
Since 5 of them share 2 pounds of milk, that means each will get:
\(\frac{5}{2}\) pounds.

Question 13.
Vocabulary A _____________ diagram can represent set relationships visually.
Answer:
A Venn diagram can visually represent set relationships.

Financial Literacy For 14-16, use the table. The table shows Jason’s utility bills for one month. Write a fraction to represent the division in each situation. Then classify each result by indicating the set or sets to which it belongs.

Question 14.
Jason and his 3 roommates share the cost of the electric bill evenly.
Answer:
So, the electricity payments bill is split into 4 equal parts!
We can express it via fraction as: $\(\frac{108}{4}\)
This number belongs to a set of whole numbers as it is equivalent to the number: 27

Classifying Rational Numbers 6th Grade Lesson 2.1 Answer Key Question 15.
Jason plans to pay the water bill with 2 equal payments.
Answer:
Jason is paying water bill with 2 equal payments.
That means he is going to pay: $\(\frac{35}{2}\)
This number belongs to a set of Rational numbers.

Question 16.
Jason owes $15 for last month’s gas bill. The total amount of the two gas bills is split evenly among the 4 roommates.
Answer:
As he owes $15 from last month, they will have to pay: $15 + $14 = $29
They split it into 4 parts and each pays: $\(\frac{29}{4}\)
This number belongs to set of Rational numbers.

Question 17.
Lynn has a watering can that holds 16 cups of water, and she fills it half full. Then she waters her 15 plants so that each plant gets the same amount of water. How many cups of water will each plant get?
Answer:
Glass can holds 16 cups of water, and she filled it half, so she filled it with 8 cups of water.
Now, we know that if she has 15 plants, and wants to split that water equally,
she will spend: \(\frac{8}{15}\)
This number belongs to set of Rational numbers.

H.O.T. Focus on Higher Order Thinking

Question 18.
Critique Reasoning DaMarcus says the number \(\frac{24}{6}\) belongs only to the set of rational numbers. Explain his error.
Answer:
Number \(\frac{24}{6}\) can be written without a fraction as 4.
Therefore, it belongs to a set of Integers and Whole numbers.

Question 19.
Analyze Relationships Explain how the Venn diagrams in this lesson show that all integers and all whole numbers are rational numbers.
Answer:
Venn diagram shows that both ellipses named Integers and Whole numbers are included in one big ellipse called Rational numbers.

Question 20.
Critical Thinking Is it possible for a number to be a rational number that is not an integer but is a whole number? Explain.
Answer:
A number can not be a Whole number without being an Integer, because all Whole numbers are included in an integer set!
We can also take a look a task 19 and use the Venn diagram to conclude this!

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 2.2 Answer Key Identifying Opposites and Absolute Value of Rational Numbers.

Texas Go Math Grade 6 Lesson 2.2 Answer Key Identifying Opposites and Absolute Value of Rational Numbers

Reflect

Question 1.
Communicate Mathematical Ideas How would you graph – 2.25? Would it be left or right of point D?
Answer:
I would graph number – 2.25 by splitting distance between numbers – 2 and – 3 into 4 parts!
Than i would pick the first one on right and that would be number – 2.25
Number – 2.25 is on right of D.

Your Turn

Question 2.
What are the opposites of 7, – 3.5, 2.25, and 9\(\frac{1}{3}\)?
Answer:
Opposites of numbers, as we learned in previous section, are those same numbers with added – sign!
So, opposites of 7, – 3.5, 2.25, 9\(\frac{1}{3}\) are numbers – 7, 3.5, 2.25, – 9\(\frac{1}{3}\) respectively!

Reflect

Go Math 6th Grade Lesson 2.2 Absolute Value Question 3.
Communicate Mathematical Ideas What is the absolute value of the average January low temperature in 2011? How do you know?
Answer:

Distance from 3.8 to 0 is 3.8 units!
Therefore, its absolute value is 3.8

Your Turn

Graph each number on the number line. Then use your number line to find each absolute value.

Question 4.
– 4.5; |- 4.5| = __________
Answer:

As i mentioned before, absolute value of negative number is positive number!
As its absolute value, it must have same distance from 0 as number, so solution is 4.5

Question 5.
1\(\frac{1}{2}\); |1\(\frac{1}{2}\)| = __________
Answer:

Note that i used 1.5 instead of 1\(\frac{1}{2}\) as i can’t write that expression on graph.
As i mentioned before, absolute value of positive number is same number!
As its absolute value, it must have same distance from 0 as number,
so solution is 1\(\frac{1}{2}\)

Question 6.
4; |4| = __________
Answer:

As i mentioned before, absolute value of positive number is same number!
As its absolute value, it must have same distance from 0 as number,
so solution is 4

Question 7.
– 3\(\frac{1}{4}\); |- 3\(\frac{1}{4}\)| = __________
Answer:

Note that i used 3.25 instead of 3\(\frac{1}{4}\)
As i mentioned before, absolute value of negative number is positive number!
As its absolute value, it must have same distance from 0 as number,
so solution is 33\(\frac{1}{4}\)

Texas Go Math Grade 6 Lesson 2.1 Guided Practice Answer Key

Graph each number and Its opposite on a number line.

Question 1.
– 2.8

Answer:
Opposite of – 2.8 is 2.8

Go Math Grade 6 Lesson 2.2 Answer Key Question 2.
4.3

Answer:
Opposite of 4.3 is – 4.3

Question 3.
– 3\(\frac{4}{5}\)

Answer:
Opposite of – 3\(\frac{4}{5}\) is 3\(\frac{4}{5}\)

Note that i used 3.8 instead of 3\(\frac{4}{5}\) in my graph!

Question 4.
1\(\frac{1}{3}\)

Answer:
Opposite of 1\(\frac{1}{3}\) is – 1\(\frac{1}{3}\)

Note that i used 4/3 instead of 1\(\frac{1}{3}\) on my graph.

Find the opposite of each number.

Question 5.
3.78 ______________
Answer:
As i mentioned before, opposite of any number is number with added – sign on left side!
Opposite of 3.78 is – 3.78

Question 6.
– 7\(\frac{5}{12}\) ______________
Answer:
As i mentioned before, opposite of any number is number with added – sign on left side!
Opposite of –\(\frac{89}{12}\) is \(\frac{89}{12}\)
Note that we used – \(\frac{89}{12}\) instead of given expression, but they are equivalent.

Question 7.
0 ______________
Answer:
As i mentioned before, opposite of any number is number with added – sign on left side!
Opposite of 0 is 0.

Question 8.
4.2 ______________
Answer:
As i mentioned before, opposite of any number is number with added – sign on left side!
Opposite of 4.2 is – 4.2.

Question 9.
12.1 ______________
Answer:
As i mentioned before, opposite of any number is number with added – sign on left side!
Opposite of 12.1 is – 12.1.

Go Math Absolute Value Lesson 2.2 Answer Key Grade 6 Question 10.
2.6 ______________
Answer:
As I mentioned before, the opposite of any number is a number with an added – sign on left side!
Opposite of 2.6 is – 2.6.

Question 11.
Vocabulary Explain why 2.15 and – 2.15 are opposites.
Answer:
Numbers 2.15 and – 2.15 are opposites because they have same distances from 0 but are placed on different sides of 0.

Find the absolute value of each number.

Question 12.
5.23 ______________
Answer:
We define absolute value as distance from 0. So, it is surely positive number.
Now, when we know this, we can conclude that absolute value of positive number is that exact same number, and absolute value of negative number is its opposite!
|5.23| = 5.23

Question 13.
– 4\(\frac{2}{11}\) ______________
Answer:
We define absolute value as distance from 0. So, it is surely positive number.
Now, when we know this, we can conclude that absolute value of positive number is that exact same number, and absolute value of negative number is its opposite!
|-\(\frac{46}{11}\) | = \(\frac{46}{11}\)
Note that we used – \(\frac{46}{11}\) instead of given expression, but they are equivalent!

Question 14.
0 ______________
Answer:
We define absolute value as distance from 0. So, it is surely positive number.
Now, when we know this, we can conclude that absolute value of positive number is that exact same number, and absolute value of negative number is its opposite!
|0| = 0

Question 15.
– 6\(\frac{3}{5}\) ______________
Answer:
We define absolute value as distance from 0. So, it is surely positive number.
Now, when we know this, we can conclude that absolute value of positive number is that exact same number, and absolute value of negative number is its opposite!
|- 6\(\frac{3}{5}\) | = 6\(\frac{3}{5}\)

Question 16.
– 2.12 ______________
Answer:
We define absolute value as distance from 0. So, it is surely positive number.
Now, when we know this, we can conclude that absolute value of positive number is that exact same number, and absolute value of negative number is its opposite!
|- 2.12| = 2.12

Question 17.
8.2 ______________
Answer:
We define absolute value as distance from 0. So, it is surely positive number.
Now, when we know this, we can conclude that absolute value of positive number is that exact same number, and absolute value of negative number is its opposite!
|8.2| = 8.2

Essential Question Check-In

Question 18.
How do you identify the opposite and the absolute value of a rational number?
Answer:
Opposite of Rational number is the same distance on a number line from 0 but on the other side of 0 on a number line.

We define absolute value as distance from 0 on a number line
This definition is correct with Rational numbers
If a given number is negative, than its absolute value is its opposite!
If a given number is positive, than its absolute value is exact same number!

Question 19.
Financial Literacy A store’s balance sheet represents the amounts customers owe as negative numbers and credits to customers as positive numbers.

a. Write the opposite of each customer’s balance.
Answer:
Number 85.23 is opposite of – 85.23.
Number – 20.44 is opposite of 20.44.
Number 116.33 is opposite of – 116.33.
Number – 13.50 is opposite of 13.50.
Number – 9.85 is opposite of 9.85.

b. Mr. Yuan wants to use his credit to pay off the full amount that another customer owes. Which customer’s balance does Mr. Yuan have enough money to pay off?
Answer:
Mr.Yuan can only pay for Wenner because he owes $9.85 and Mr. Yuan has credit of $13.50

c. Which customer’s balance would be farthest from 0 on a number line? Explain.
Answer:
If we draw the number line, the farthest would be Stein.
The absolute value of his balance is the highest (- $116.33).

Lesson 2.2 Answer Key 6th Grade Go Math Question 20.
Multistep Trina and Jessie went on a vacation to Hawaii. Trina went scuba diving and reached an elevation of – 85.6 meters, which is below sea level. Jessie went hang-gliding and reached an altitude of 87.9 meters, which is above sea level.

a. Who is closer to the surface of the ocean? Explain.
Answer:
Here, we calculate the absolute values of both given numbers:
|- 85.6| = 85.6
|87.9| = 87.9
Now, as we know that 85.6 is less than 87.9, that implies:
Trina is closer to the ocean surface.

b. Trina wants to hang-glide at the same number of meters above sea level as she scuba-dived below sea level. Will she fly higher than Jessie did? Explain.
Answer:
She won’t fly higher than Jessie did. Why?
We know that she would like to hang-glide 85.6 meters, which is lower than 87.9 meters.

Question 21.
Critical Thinking Carlos finds the absolute value of – 5.3 and then finds the opposite of his answer. Jason finds the opposite of – 5.3, and then finds the absolute value of his answer. Whose final value is greater? Explain.
Answer:
Carlos firstly found absolute value of – 5.3 which is 5.3
Then he found opposite of 5.3 which is – 5.3
So his final value is: – 5.3

Jason firstly found opposite of – 5.3 which is 5.3.
Then he found absolute value of 5.3 which is 5.3
So his final value is: 5.3

Since 5.3 is greater than – 5.3, we can conclude that Jason’s final value is greater
Jason’s number is greater!

Question 22.
Explain the Error Two students are playing a math game. The object of the game is to make the least possible number by arranging the given digits inside absolute value bars on a card. In the first round, each player will use the digits 3, 5, and 7 to fill in the card.

a. One student arranges the numbers on the card as shown. What was this student’s mistake?
Answer:
This student didn’t find Least possible number.
He miss used operation of absolute value.
The key point was to find a number which is closer to 0, but he didn’t get the point!

b. What is the least possible number the card can show?
Answer:
Least possible number that card can show is – 3.57

H.O.T. Focus On Higher Order Thinking

Question 23.
Analyze Relationships If you plot the point – 8.85 on a number line, would you place it to the left or right of – 8.8? Explain.
Answer:
Number – 8.85 is smaller than – 8.80.
Therefore, number – 8.85 would be placed on Left of – 8.80

Question 24.
Make a Conjecture If the absolute value of a negative number is 2.78, what is the distance on the number line between the number and its absolute value? Explain your answer.
Answer:
Firstly, we calculate absolute value of 2.78:
|2.78| = 2.78
As given number is – 2.78, to calculate distance to its absolute value:
We must multiply its positive value by 2 because we have same distances from both sides of 0 on a number Line.

Result: 5.56

Question 25.
Multiple Representations The deepest point in the Indian Ocean is the Java Trench, which is 25,344 feet below sea level. Elevations below sea level are represented by negative numbers.

a. Write the elevation of the Java Trench.
Answer:
If we know that deepest point is 25. 344 feet beLow sea leveL.
Than we can concLude that our vaLue wiLL be negative.
Therefore, eLevation of Java Trench is: – 25. 344 feet

b. A mile is 5,280 feet. Between which two integers is the elevation in miles?
Answer:
As given. 1 mile equals 5,280 feet. So to get elevation in miles, We have to convert our value into miles!

We get:

Now we know that elevation of Java Trench is – 4.8 miles

So, now it is obvious to conclude that elevation of – 4.8 miles lies on a number line between integers – 4 and – 5.

c. Graph the elevation of the Java Trench in miles.

Answer:

Question 26.
Draw Conclusions A number and its absolute value are equal. If you subtract 2 from the number, the new number and its absolute value are not equal. What do you know about the number? What is a possible number that satisfies these conditions?
Answer:
Firstly, if a number and its absolute value are equal, that implies that number is positive.
Secondly, if a number and its absolute number are not equal, that implies that number is negative

So, let’s start:
We start from a positive number and end up having a negative number by subtracting 2 from our starting number
It is possible only if we use numbers 0 or 1 because only these 2 numbers will have their sign switched by subtracting 2 from them!