Prasanna

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!

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 1.3 Answer Key Absolute Value.

Texas Go Math Grade 6 Lesson 1.3 Answer Key Absolute Value

Reflect

Question 1.
Analyze Relationships Which pairs of numbers have the same absolute value? How are these numbers related?
Answer:
Numbers which have same absolute value are opposites.
Therefore, their distance from 0 is equal!

Go Math Grade 6 Lesson 1.3 Answer Key Question 2.
Justify Reasoning Negative numbers are less than positive numbers. Does this mean that the absolute value of a negative number must be less than the absolute value of a positive number? Explain.
Answer:
By definition of absolute value, it’s distance from 0 on a number Line.
Therefore, absolute value of a negative number mustn’t be
Less than the absolute value of a positive number!

Question 3.
Communicate Mathematical Ideas Explain why the absolute value of a number will never be negative.
Answer:
Absolute value of number can not be negative since it is defined as a distance from 0.
Therefore, it can not be less than 0.

Your Turn

Question 4.
The temperature at night reached – 13°F Write an equivalent statement about the temperature using the absolute value of the number.
Answer:
We can just write it like:
Temperature at night reached negative |-13|°F

Find each absolute value.

Question 5.
|-12| _________
Answer:
The absolute value of – 12 equals 12
Therefore, we write:
|-12| = 12

Question 6.
|-91| _________
Answer:
The absolute value of 91 equals 91
Therefore, we write:
|91| = 91

Question 7.
|-55| _________
Answer:
The absolute value of – 55 equals 55
Therefore, we write:
|-55| = 55

Go Math Grade 6 Lesson 1.3 Absolute Value Answer Key Question 8.
|0| _________
Answer:
The absolute value of 0 equals 0
Therefore, we write:
|0| = 0

Question 9.
|88| _________
Answer:
The absolute value of 88 equals 88
Therefore, we write:
|88| = 88

Question 10.
|1| _________
Answer:
The absolute value of 1 equals 1
Therefore, we write:
|1| = 1

Reflect

Question 11.
Analyze Relationships Use absolute value to describe the relationship between a negative credit card balance and the amount owed.
Answer:
Let’s show it by an example:

We can simply say that if we owe $70
that means our credit card is $ – 70.
So, by usage of absolute value:

Amount we owe = absolute value of our balance( if we assume that balance is negative)

Texas Go Math Grade 6 Lesson 1.3 Guided Practice Answer Key

Question 1.
Vocabulary If a number is _____________, then the number is less than its absolute value. (Explore Activity 1)
Answer:
If a number is negative, then we can say that number is smaller than its absolute value

Go Math Absolute Value Lesson 1.3 Practice Answer Key Question 2.
If Ryan pays his car insurance for the year in full, he will get a credit of $28. If he chooses to pay a monthly premium, he will pay a $10 late fee for any month that the payment is late. (Explore Activity 1 Example 1)

a. Which of these values could be represented with a negative number? Explain.
Answer:
We can represent the $10 late fee as an absolute value.
For example, we can say that $10 will be subtracted from his bank account for the mouth that the payment is late.

b. Use the number line to find the absolute value of the amount from part a. ____________

Answer:

Question 3.
Leo, Gabrielle, Sinea, and Tomas are playing a video game. Their scores are described in the table below. (Explore Activity 2)

a. Leo wants to earn enough points to have a positive score. Does he need to earn more than 100 points or less than 100 points?
Answer:
Leo has to earn more than 100 points.

b. Gabrielle wants to earn enough points to not have a negative score.
Does she need to earn more points than Leo or less points than Leo?
Answer:
Gabrielle has 20 points more than Leo, So she has less than – 80 points.
This means that she has to be earn less points than Leo.

C. Sinea wants to earn enough points to have a higher score than Leo.
Does she need to earn more than 50 points or less than 50 points?
Answer:
Sinea has 50 points less than Leo, so she has less than – 150 points.
This means that she has to earn more than 50 point to be greater than Leo.

Essential Question Check-In

Question 4.
When is the absolute value of a number equal to the number?
Answer:
Absolute value of a number equal to the number only when the number is positive.

Question 5.
Financial Literacy Jacob earned $80 babysitting and deposited the money into his savings account. The next week he spent $85 on video games. Use integers to describe the weekly changes in Jacob’s savings account balance.
Answer:
Jacob firstly gained $80 and then he spent $85 so this is equivalent to expression:
$80 – $85 = -$5
Now we can conclude that Jacob owes:
|-$5| = $5
Jacob owes $5

Question 6.
Financial Literacy Sara’s savings account balance changed by $34 one week and by – $67 the next week. Which amount represents the greatest change?
Answer:
We can describe greatest change by biggest distance from 0 on a number line
Therefore, we can use absolute value to calculate it:
|-$67| = $67
$|34| = $31
We know that number 67 is greater than 34 so now we can conclude that greatest change is – $67.

Go Math 6th Grade Lesson 1.3 Answer Key Question 7.
Analyze Relationships Bertrand collects movie posters. The number of movie posters in his collection changes each month as he buys and sells posters. The table shows how many posters he bought or sold in the given months.

a. Which months have changes that can be represented by positive numbers? Which months have changes that can be represented by negative numbers? Explain.
Answer:
We can say that buying can be represented by positive value
and selling can be represented by negative value.
Therefore, we can write:
March and February can be represented by positive number
January and April can be represented by negative number

b. According to the table, in which month did the size of Bertrand’s poster collection change the most? Use absolute value to explain your answer.
Answer:
Here, we take numbers from table and compare them and get:
Number 12 is smaller than 20 which is smaller than 22 which is smaller than 28.
So now we know that 28 is greatest which means that:
Ir April the size of Bertrand’s poster changed the most!

Question 8.
Earth Science Death Valley has an elevation of – 282 feet relative to sea level. Explain how to use absolute value to describe the elevation of Death Valley as a positive integer.
Answer:
Here, we can use absoLute vaLue to determine depth of Death Valley:
|- 282| = 282 feet
We can say that Death Walley lies 282 feet below sea level.

Algebra Lesson 1.3 6th Grade Math Absolute Value Question 9.
Communicate Mathematical Ideas Lisa and Alice are playing a game. Each player either receives or has to pay play money based on the result of their spin. The table lists how much a player receives or pays for various spins.

a. Express the amounts in the table as positive and negative numbers.
Answer:
We can express received value as positive number and paid value as negative number.

b. Describe the change to Lisa’s amount of money when the spinner lands on red.
Answer:
When the spinner lands on red. Lisa has to pay $2.
We can say that her amount of money will change by -$2

Question 10.
Financial Literacy Sam’s credit card balance is less than – $36. Does Sam owe more or less than $36?
Answer:
Since Sam has less tIin – $36 card balance
It means that we go left from – $36 on a number line!
That implies that he owes more than $36.
Sam owes more than $36.

Question 11.
Financial Literacy Emily spent $55 from her savings on a new dress. Explain how to describe the change in Emily’s savings balance in two different ways.
Answer:
We can say that her balance change is: – $55

Other way would be say that her balance decreased by $55.

H.O.T. Focus on Higher Order Thinking

Question 12.
Make a Conjecture Can two different numbers have the same absolute value? If yes, give an example. If no, explain why not.
Answer:
Two different numbers can have same absolute value if they are opposites!
Yes, if they are opposites

Question 13.
Communicate Mathematical ideas Does -|-4| = |-(-4)|? Justify your answer.
Answer:
Note that absolute value will always give positive value!
– |- 4| = – 4
Right side is of equation is similar:
|- (- 4)| = 4
It is not equal.

6th Grade Go Math Lesson 1.3 Answer Key Question 14.
Critique Reasoning Angelique says that finding the absolute value of a number is the same as finding the opposite of the number. For example, |-5| = 5. Explain her error.
Answer:
Angelique said the truth is if the given number is negative
What if the given number is positive?
We know that the absolute value will give the same value back if the given number is positive
Therefore, it does not give the opposite for positive numbers!

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 1.2 Answer Key Comparing and Ordering integers.

Texas Go Math Grade 6 Lesson 1.2 Answer Key Comparing and Ordering integers

Reflect

Question 1.
Analyze Relationships Explain what the data tell you about the win/loss records of the teams in the league.
Answer:
Given data tells us:

• Whether each team has more wins or more losses.
• It tells us which team has most wins and which least.

Your Turn

Graph the values in each table on a number line. Then list the numbers in order from greatest to least.

Question 2.


Answer:

Number 4 is greater than 3 which is greater than 0 which is greater than – 1
which is greater than – 2 which is greater than – 3 which is greater than
Therefore, we write:
4 > 3 > 0 > – 1 > – 2 > – 3 > – 5

Go Math Grade 6 Answer Key Pdf Lesson 1.2 Question 3.

Answer:

Number 9 is greater than 8 which is greater than 5 which is greater than 2
which is greater than 0 which is greater than – 1 which is greater than – 6
which is greater than – 10
Therefore, we write:
9 > 8 > 5 > 2 > 0 > – 1 > – 6 > – 10

Compare. Write > or <. Use the number line to help you.

Question 4.
– 10 ________ – 2
Answer:
Number – 10 is smaller than – 2
Therefore, we write:
– 10 < – 2

Question 5.
– 6 ________ 6
Answer:
Number – 6 is smaller than 6
Therefore, we write:
– 6 < 6

Question 6.
– 7 ________ – 8
Answer:
Number – 7 is greater than – 8
Therefore, we write:
– 7 > – 8

Question 7.
Write two inequalities to compare – 2 and – 18.
Answer:
Number – 18 is smaller than – 2
Therefore, we write:
– 18 < – 2

Go Math Lesson 1.2 6th Grade Answer Key Question 8.
Write two inequalities to compare 39 and – 39.
Answer:
Number – 39 is smaller than 396
Therefore, we write:
– 39 < 39

Texas Go Math Grade 6 Lesson 1.2 Guided Practice Answer Key

Question 1.
a. Graph the temperature for each city on the number line. (Explore Activity)

Answer:

b. Which city was coldest? ______________
Answer:
Coldest city was A

c. Which city was warmest? _____________
Answer:
Warmest city was B

List the numbers in order from least to greatest. (Example 1)

Question 2.
4, – 6, 0, 8, – 9, 1, – 3
Answer:
Number – 9 is smaller than – 6 which is smaller than – 3 which is smaller than 0
which is smaller than 1 which is smaller than 4 which is smaller than 8
Therefore, we write
– 9 < – 6 < – 3 < 0 < 1 < 4 < 8

Question 3.
– 65, 34, 7, – 13, 55, 62, – 7
Answer:
Number – 65 is smaller than – 13 which is smaller than – 7
which is smaller than 7 which is smaller than 34 which is smaller than 55 which is smaller than 62
Therefore, we write:
– 65 < – 13 < – 7 < 7 < 34 < 55 < 62

Go Math Grade 6 Lesson 1.2 Comparing and Ordering Integers Question 4.
Write two inequalities to compare – 17 and – 22.
Answer:
Number – 17 is greater than – 22
Therefore, we write:
– 17 > – 22

Number – 22 is smaller than – 17
Therefore, we write:
– 22 < – 17

Compare. Write < or >.

Question 5.
– 9 _______ 2
Answer:
Number – 9 is smaller than 2
Therefore, we write:
– 9 < 2

Question 6.
0 _______ 6
Answer:
Number 0 is smaller than 6
Therefore, we write:
0 < 6

Question 7.
3 _______ – 7
Answer:
Number 3 is greater than – 7
Therefore, we write:
3 > – 7

Question 8.
5 _______ – 10
Answer:
Number 5 is greater than – 10
Therefore, we write:
– 5 > – 10

Question 9.
– 1 _______ – 3
Answer:
Number – 1 is greater than – 3
Therefore, we write:
– 1 > – 3

Question 10.
– 8 _______ – 4
Answer:
Number – 8 is smaller than – 4
Therefore, we write:
– 8 < – 4

Lesson 1.2 Identifying Integers and Their Opposites Answer Key Question 11.
– 4 _______ 1
Answer:
Number – 4 is smaller than 1
Therefore, we write:
– 4 < 1

Question 12.
– 2 _______ – 6
Answer:
Number – 2 is greater than – 6
Therefore, we write:
– 2 > – 6

Question 13.
Compare the temperatures for the following cities. Write < or >.

a. Alexandria and Winona
Answer:
Temperature in Alexandria is – 3° and temperature in Winona is 2° so
Number – 3 is smaller than 2
Therefore we write:
– 3 < 2

b. Redwood Falls and International Falls
Answer:
Temperature in Redwood Falls is 0° and
temperature in International Falls is – 4° s0
Number 0 is greater than – 4
Therefore, we write:
0 > – 4

Essential Question Check-In

Question 14.
How can you use a number line to compare and order numbers?
Answer:
We can use number line to determine which number is greater or smaller!
The farthest number on left is least and farthest number on right is greatest!
Analogically, we can order all the other given numbers!

Question 15.
Multiple Representations A hockey league tracks the plus-minus records for each player. A plus-minus record is the difference in even strength goals for and against the team when a player is on the ice. The following table lists the plus-minus values for several hockey players.

a. Graph the values on the number line.

Answer:

b. Which player has the best plus-minus record? __________
Answer:
Viewing the number line we can determine which player has the best plus-minus record!
It is: E.Simpson

Astronomy The table lists the average surface temperature of some planets. Write an inequality to compare the temperatures of each pair of planets.

Go Math Grade 6 Answers Pdf Lesson 1.2 Question 16.
Uranus and Jupiter _____________________
Answer:
The temperature on Uranus is – 197°C and the temperature on Jupiter is – 110°C 50
Temperature – 197°C is smaller than – 110°C
Therefore, we write:
– 197°C < – 110°C

Question 17.
Mercury and Mars _____________________
Answer:
Temperature on Mercury is 167°C and temperature on Mars is – 65°C so
Temperature 167°C is greater than – 65°C
Therefore, we write:
167°C > – 65°C

Question 18.
Arrange the planets in order of average surface temperature from greatest to least. _____________________
Answer:
We write temperatures from table and separate theta in an order from greatest to smallest average surface temperature.

Temperature 167° is greater than 15° which is greater than – 65° which is greater than – 110°
which is greater than – 197° which is greater than 200°

Therefore, we write:
167° > 15° > 65° > – 110° > 197° > 200°

Question 19.
Represent Real-World Problems For a stock market project, five students each invested pretend money in one stock. They tracked gains and losses in the value of that stock for one week. In the following table, a gain is represented by a positive number and a loss is represented by a negative number.

Graph the students results on the number line. Then list them in order from least to greatest.

a. Graph the values on the number line.

Answer:

b. The results listed from least to greatest are ______________ .
Answer:
We can simply take a look to a graph above!
Just read student names connected with values from left to right
Doing that, we get:
– 5< – 2 < 2 < 4 < 7

Geography The table lists the lowest elevation for several countries. A negative number means the elevation is below sea level, and a positive number means the elevation is above sea level. Compare the lowest elevation for each pair of countries. Write < or >.

Go Math Grade 6 Lesson 1.2 Practice and Homework Question 20.
Argentina and the United States ______________
Answer:
Argentina has the lowest elevation of – 344 feet and United States has a Lowest elevation of – 281 feet.
Therefore, we can say:
Argentina’s lowest elevation is lower than Unites States lowest elevation as number – 344 is smaller than – 281 .
And we write:
– 344 < – 281
Argentina’s lowest elevation is lower than United State’s

Question 21.
Czech Republic and Hungary ______________
Answer:
Czech Republic has lowest elevation of 377 fret and Hungary has lowest elevation of 249 feet.
Therefore, we can say:
Czech Republic’s lowest elevation is higher than Hungary’s lowest elevation as number 377 is greater than 249 .
And We write:
377 > 249
Czech Republic’s Lowest elevation is higher than Hungary’s

Question 22.
Hungary and Argentina ______________
Answer:
Hungary has lowest elevation of 249 feet and Argentina has lowest eLevation of – 344 feet.

Therefore, we can say:
Hungary’s lowest elevation is higher than Argentina’s lowest elevation as number 249 is greater than – 344
And we write:
249 > – 344
Hungary’s lowest elevation is higher than Argentina’s!

Question 23.
Which country in the table has the lowest elevation? _______________
Answer:
When we are asked to find the lowest elevation of all countries, we just compare numbers connected to each country and find the smallest one and that will be our solution!

Therefore, we can say:
Number – 344 is smallest number of given ones!
So, country that has lowest elevation is Argentina.
Lowest elevation is Argentina!

Question 24.
Analyze Relationships There are three numbers a, b, and c, where a > b and b > c. Describe the positions of the numbers on a number line.
Answer:
If we have some random 3 numbers on a number line a, b and c.
We know that a > b and b > c
We can conclude that a > c
So, we will have them placed:
a – farthest right
b – in middle
c – farthest left

H.O.T. Focus on Higher Order Thinking

Texas Go Math Lesson 1.2 Prime Factorization Answers 6th Grade Question 25.
Critique Reasoning At 9 A.M. the outside temperature was – 3°F. By noon, the temperature was – 12°F. Jorge said that it was getting warmer outside. Is he correct? Explain.
Answer:
Jorge is, surely wrong because the temperature actually decreased by noon
We can write these temperatures as numbers and compare them to prove our theory:
Number – 3 is greater than – 12
Therefore, we write:
– 3 > – 12
So temperature actually decreased from – 3°F to – 12°F
Jorge made a mistake!

Question 26.
Problem-Solving Golf scores represent the number of strokes above or below par. A negative score means that you hit a number below par while a positive score means that you hit a number above par. The winner in golf has the lowest score. During a round of golf, Angela’s score was – 5 and Lisa’s score was – 8. Who won the game? Explain.
Answer:
We can watch the given number of strokes as ordinary numbers and conclude:
Number – 5 is greater than – 8
Therefore, we write:
– 5 > – 8
So the winner is Lisa since we are Looking for a smaller value!
Lisa won the game!

Go Math Lesson 1.2 6th Grade Question 27.
Look for a Pattern Order – 3, 5, 16, and – 10 from least to greatest. Then order the same numbers from closest to zero to farthest from zero. Describe how your lists are similar. Would this be true if the numbers were – 3, 5, – 16 and – 10?
Answer:
Number – 10 is smaller than – 3 which is smaller than 5 which is smaller than 16

Therefore, we write:
– 10 < – 3 < 5 < 16

Here, we can use a number line to determine which is closest/farthest from 0.

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 2.3 Answer Key Comparing and Ordering Rational Numbers.

Texas Go Math Grade 6 Lesson 2.3 Answer Key Comparing and Ordering Rational Numbers

Reflect

Question 1.
Communicate Mathematical Ideas How does a number line represent equivalent fractions and decimals?
Answer:
The number line represents equivalent fractions and decimals as the same exact points on it!

Lesson 2.3 Comparing and Ordering Rational Numbers Question 2.
Name a decimal between 0.4 and 0.5.
Answer:
A decimal between 0.4 and 0.5 would be any number that is greater than 0.4 and smaller than 0.5.

Now, we know that our decimal could be 0.45 or even 0.46754. We could pick any decimal whose value is between 0.4 and 0.5

Your Turn

Order the fractions and decimals from least to greatest.

Question 3.
0.85, \(\frac{3}{5}\), 0.15, \(\frac{7}{10}\)
Answer:
First thing will be writing decimals as equivalent fractions!

Second thing will be finding common denominator for our fractions!
Let’s get all the numbers to have 20 as common denominator!
We multiply both, the numerator and denominator with same number to get equivalent expression!
\(\frac{3}{5}=\frac{3 \cdot 4}{5 \cdot 4}\) = \(\frac{12}{20}\)
\(\frac{7}{10}=\frac{7 \cdot 2}{10 \cdot 2}\) = \(\frac{14}{20}\)

Now we compare numerators of fractions!
17, 3, 12, 14
So, now we know that 3 is smaller than 12 which is smaller than 14 which is smaller than 17 .
Now we can write them as: 3 < 12 < 11 < 17
Therefore:
\(\frac{3}{20}<\frac{12}{20}<\frac{14}{20}<\frac{17}{20}\)

Last thing that we want to do is to return expressions to given ones!
So, we have:
0.15 < \(\frac{3}{5}\) < \(\frac{7}{10}\) < 0.85
So, now we have ordered them from Least to greatest and we can write the order as:
0.15, \(\frac{3}{5}\), \(\frac{7}{10}\), 0.85

Reflect

Question 4.
Communicate Mathematical Ideas Describe a different way to order the numbers.
Answer:
Different ways to order the numbers would be:
Firstly, write them all as fractions!
Secondly, find equivalent fractions with common denominator!
Thirdly, compare numerators and list them from greatest to least.

Your Turn

Question 5.
To compare their bike times, the friends created a table that shows the difference between each person’s time and the average bike time. Order the bike times from least to greatest.

Answer:
First thing will be writing fractions as equivalent decimals!

Now we use number line to conclude relation between numbers!

Now, we know that:
Number – 1.8 is smaller than – 1.25 which is smaller than 1 which is smaller than 1.4 which is smaller than 1.9.
We can write it as:
– 1.8 < – 1.25 < 1 < 1.4 < 4.9

One last thing to do is to return decimals to given expressions and write it ¡n order from least to greatest!
– 1.8, – 1.25, 1, 1\(\frac{2}{5}\), 1\(\frac{9}{10}\)

Texas Go Math Grade 6 Lesson 2.3 Guided Practice Answer Key

Find the equivalent fraction or decimal for each number.

Question 1.
0.6 = __________
Answer:
Here, we want to find an equivalent fraction to the number 0.6
Firstly, we write it as a fraction!
Secondly, we simplify it by dividing with the greatest common divisor!

Go Math Practice and Homework Lesson 2.3 Answer Key Question 2.
\(\frac{1}{4}\) = __________
Answer:
Here, we want to write fraction \(\frac{1}{4}\) as equivalent decimal number!
We divide numbers 1 and 4 to get our solution!

\(\frac{1}{4}\) = 0.25

Question 3.
0.9 = __________
Answer:
Here, we want to find equivalent fraction to number 0.9
Firstly, we write it as fraction!
Secondly, we simplify it by dividing with greatest common divisor, only if we can!
0.9 = \(\frac{0.9 \cdot 10}{1 \cdot 10}=\frac{\mathbf{9}}{\mathbf{1 0}}\)

Question 4.
0.1 = __________
Answer:
Here, we want to find equivalent fraction to number 0.1
Firstly, we write it as fraction!
Secondly, we simplify it by dividing with greatest common divisor, only if we can!
0.1 = \(\frac{0.1 \cdot 10}{1 \cdot 10}=\frac{1}{10}\)

Question 5.
\(\frac{3}{10}\)
Answer:
Here, we want to write fraction \(\frac{3}{10}\) as equivalent decimal number!
We divide numbers 3 and 10 to get our solution!

\(\frac{3}{10}\) = 0.3

Question 6.
1.4 = __________
Answer:
Here, we want to find equivalent fraction to number 1.4
Firstly, we write it as fraction!
Secondly, we simplify it by dividing with greatest common divisor!

Question 7.
\(\frac{4}{5}\)
Answer:
Here, we want to write fraction \(\frac{4}{5}\) as equivalent decimal number!
We divide numbers 4 and 5 to get our solution!

\(\frac{4}{5}\) = 0.8

Question 8.
0.4 = __________
Answer:
Here, we want to find equivalent fraction to number 0.4
Firstly, we write it as fraction!
Secondly, we simplify it by dividing with greatest common divisor!

Question 9.
\(\frac{6}{8}\) = __________
Answer:
Here, we want to write fraction \(\frac{6}{8}\) as equivalent decimal number!
We divide numbers 6 and 8 to get our solution!

\(\frac{6}{8}\) = 0.75

Use the number line to order the fractions and decimals from least to greatest.

Question 10.
0.75, \(\frac{1}{2}\), 0.4, and \(\frac{1}{5}\)

Answer:
First thing will be writing fractions as equivalent decimals!
\(\frac{1}{2}\) = 0.5
\(\frac{1}{5}\) = 0.2

Now we know that number 0.25 is smaller than 0.4 which is smaller than 0.5 which is smaller than 0.75.
One last thing to do is to return decimals to given expressions and write it in order from least to greatest!
\(\frac{1}{5}\), 0.4, \(\frac{1}{2}\), 0.75

Compare Fractions and Decimals Lesson 2.3 Answer Key Question 11.
The table shows the lengths of fish caught by three friends at the lake last weekend. Write the lengths in order from greatest to least.

Answer:
First thing will be writing fractions as equivalent decimals!
12\(\frac{3}{5}\) = 12 + \(\frac{3}{5}\) = 12 + 0.6 = 12.6
12\(\frac{3}{4}\) = 12 + \(\frac{3}{4}\) = 12 + 0.75 = 12.75

Now we know that number 12.75 is greater than 12.7 which is greater than 12.6 .
One last thing to do is to return decimals to given expressions and write it in order from greatest to least!
12\(\frac{3}{5}\), 12.7, 12\(\frac{3}{4}\)

Like the fractions and decimals in order from least to greatest.

Question 12.
2.3, 2\(\frac{4}{5}\), 2.6
Answer:
First thing will be writing fractions as equivalent decimals!
2\(\frac{4}{5}\) = 2 + \(\frac{4}{5}\) = 2 + 0.8 = 2.8

Now we know that number 2.3 is smaller than 2.6 which is smaller than 2.8.
One Last thing to do is to return decimals to given expressions and write it in order from greatest to least!
2.3, 2.6, 2\(\frac{4}{5}\)

Question 13.
0.5, \(\frac{3}{16}\), 0.75, \(\frac{5}{48}\)
Answer:
First thing will be writing fractions as equivalent decimals!

Second thing will be finding common denominator for our fractions!
Let’s get all the numbers to have 48 as common denominator!
We multiply both, numerator and denominator with same number to get equivalent expression!
\(\frac{3}{4}\) = \(\frac{3 \cdot 12}{4 \cdot 12}=\frac{36}{48}\)
\(\frac{1}{2}\) = \(\frac{1 \cdot 24}{2 \cdot 24}=\frac{24}{48}\)
\(\frac{3}{16}\) = \(\frac{3 \cdot 3}{16 \cdot 3}=\frac{9}{48}\)

Now we compare numerators of fractions!
5, 36, 24, 9
So, now we know that 5 is smaller than 9
which is smaller than 14 which is smaller than 17 .
Now we can write them as : 5 < 9 < 24 < 36
Therefore:
\(\frac{5}{48}<\frac{9}{48}<\frac{24}{48}<\frac{36}{48}\)

Last thing that we want to do is to return expressions to given ones!
So, we have:
\(\frac{5}{48}\) < \(\frac{3}{16}\) < 0.5 < 0.75
So, now we have ordered them from least to greatest and we can write the order as:
\(\frac{5}{48}\), \(\frac{3}{16}\), 0.5, 0.75

Question 14.
0.5, \(\frac{1}{5}\), 0.35, \(\frac{12}{25}\), \(\frac{4}{5}\)
Answer:
First thing will be writing fractions as equivalent decimals!
0.35 = \(\frac{35}{100}\)
0.5 = \(\frac{5}{10}=\frac{5 \cdot 10}{10 \cdot 10}=\frac{50}{100}\)

Second thing will be finding common denominator for our fractions!
Let’s get all the numbers to have 100 as common denominator!
We multiply both, numerator and denominator with same number to get equivalent expression!
\(\frac{4}{5}\) = \(\frac{4 \cdot 20}{5 \cdot 20}=\frac{80}{100}\)
\(\frac{12}{25}\) = \(\frac{12 \cdot 4}{25 \cdot 4}=\frac{48}{100}\)
\(\frac{1}{5}\) = \(\frac{1 \cdot 20}{5 \cdot 20}=\frac{20}{100}\)

Now we compare numerators of fractions!
20, 48, 80, 35, 50
So, now we know that 20 is smaller than 35
which is smaller than 48 which is smaller than 50 which is smaller than 80
Now we can write them as : 20 < 35 < 48 < 50 < 80
Therefore:
\(\frac{20}{100}<\frac{35}{100}<\frac{48}{100}<\frac{50}{100}<\frac{80}{100}\)

Last thing that we want to do is to return expressions to given ones!
So, we have:
\(\frac{1}{5}\) < 0.35 < \(\frac{12}{25}\) < \(\frac{1}{2}\) < \(\frac{4}{5}\)
So, now we have ordered them from least to greatest and we can write the order as:
\(\frac{1}{5}\), 0.35, \(\frac{12}{25}\), \(\frac{1}{2}\), \(\frac{4}{5}\)

Question 15.
\(\frac{3}{4},-\frac{7}{10},-\frac{3}{4}, \frac{8}{10}\)
Answer:
First thing will be writing decimals as equivalent fractions!
Since they are all given by fractions, we can skip this step!

Second thing will be finding common denominator for our fractions!
Let’s get all the numbers to have 20 as common denominator!
We multiply both, numerator and denominator with same number to get equivalent expression!

Now we compare numerators of fractions!
– 14, 15, 16, – 15
So, now we know that – 15 is smaller than – 14
which is smaller than 15 which is smaller than 16
Now we can write them as : – 15 < – 14 < 15 < 16
Therefore:
\(\frac{-15}{20}<\frac{-14}{20}<\frac{15}{20}<\frac{16}{20}\)

Last thing that we want to do is to return expressions to given ones!
So, we have:
– \(\frac{3}{4}\) < – \(\frac{7}{10}\) < \(\frac{3}{4}\) < \(\frac{8}{10}\)
So, now we have ordered them from least to greatest and we can write the order as:
– \(\frac{3}{4}\), – \(\frac{7}{10}\), \(\frac{3}{4}\), \(\frac{8}{10}\)

Question 16.
– \(\frac{3}{8}\), \(\frac{5}{16}\), – 0.65, \(\frac{2}{4}\)
Answer:
First thing will be writing fractions as equivalent decimals!
Note that i will do division all the way down!
– \(\frac{3}{8}\) = – 0.375
\(\frac{5}{16}\) = 0.3125
\(\frac{2}{4}\) = \(\frac{1}{2}\) = 0.5

Now we know that number – 0.65 is smaLler than – 0.375 which is smaller than 0.3125 which is smaller than 0.5.
One last thing to do is to return decimals to given expressions and write it in order from least to greatest!
– 0.65, – \(\frac{3}{8}\), \(\frac{5}{16}\), \(\frac{2}{4}\)

Lesson 2.3 Comparing and Ordering Rational Numbers Question 17.
– 2.3, – 2\(\frac{4}{5}\), – 2.6
Answer:
First thing will be writing fractions as equivalent decimals!
– 2\(\frac{4}{5}\) = – 2 – \(\frac{4}{5}\) = – 2 – 0.8 = – 2.8

Now we know that number – 2.8 is smaller than – 2.6 which is smaller than – 2.3.
One last thing to do is to return decimals to given expressions and write it in order from greatest to least!
– 2\(\frac{4}{5}\), – 2.6, – 2.3

Question 18.
– 0.6, – \(\frac{5}{8}\), – \(\frac{7}{12}\), – 0.72
Answer:
First thing will be writing fractions as equivalent decimals!
Note that i will do division all the way down!
– \(\frac{5}{8}\) = – 0.625
– \(\frac{7}{12}\) = – 0.58\(\dot{3}\)

Now we know that number – 0.72 is smaller than – 0.625 which is smaller than – 0.6 which is smaller than – 0.58\(\dot{3}\).
One last thing to do is to return decimals to given expressions and write it in order from least to greatest!
– 0.72, –\(\frac{5}{8}\), – 0.6, – \(\frac{7}{12}\)

Question 19.
1.45, 1\(\frac{1}{2}\), 1\(\frac{1}{3}\), 1.2
Answer:
First thing will be writing fractions as equivalent decimals!
1\(\frac{1}{2}\) = 1 + \(\frac{1}{2}\) = 1 + 0.5 = 1.5
1\(\frac{1}{3}\) = 1 + \(\frac{1}{3}\) = 1 + 0.3 = 1.\(\dot{3}\)
Note that i will write division all the way down!

Now we know that number 1.2 is smaller than 1.\(\dot{3}\) which is smaller than 1.45 which is smaller than 1.5
One last thing to do is to return decimals to given expressions and write it in order from greatest to least!
1\(\frac{1}{2}\), 1\(\frac{1}{3}\), 1.45, 1.5

Question 20.
– 0.3, 0.5, 0.55, – 0.35
Answer:
First thing will be writing fractions as equivalent decimals!
Since all the numbers are written in appropriate form, we can proceed to next step!

Now we know that number – 0.35 is smaLler than – 0.3 which is smaller than 0.5 which is smaller than 0.55.
One last thing to do is to return decimals to given expressions and write it in order from least to greatest!
– 0.35, – 0.3,0.5, 0.55

Question 21.
Explain how to compare 0.7 and \(\frac{5}{8}\)
Answer:
we can solve this problem it two Ways.
As given, 0.7 is already written as decimal and therefore easiest way would include dividing number 5 with 8 to transform it into decimal.

Now, when we have both number as decimals, we can simply conclude that 0.7 is greater than 0.625.
So, we can write:
0.7 > \(\frac{5}{8}\)

Question 22.
Rosa and Albert receive the same amount of allowance each week. The table shows what part of their allowance they each spent on video games and pizza. Use a number line to help you compare.

a. Who spent more of their allowance on video games? Write an inequality to compare the portion spent on video games.
Answer:
We know that Rosa spent 0.4, and Albert \(\frac{1}{2}\) of their allowance on video games.
We can convert \(\frac{1}{2}\) into 0.5 by dividing 1 with 2.
Now, we can conclude that 0.5 is greater than 0.4, and we can write:
0.5 > 0.4
So Albert spent more of his allowance than Rosa on video games.

b. Who spent more of their allowance on pizza? Write an inequality to compare the portion spent on pizza.
Answer:
We know that Rosa spent \(\frac{2}{5}\), and Albert 0.25 of their allowance on pizza.
We can convert \(\frac{2}{5}\) into 0.4 by dividing 2 with 5.
Now, we can conclude that 0.4 is greater than 0.25, and we can write:
0.4 > 0.25
So Rosa spent more of her allowance than Albert on pizza.

c. Draw Conclusions Who spent the greater part of their total allowance? How do you know?
Answer:
All we need to do here is to add allowance values for each of kids, and compare them!
So we have:
0.4 + 0.4 = 0.8
0.5 + 0.25 = 0.75
Now we can conclude that 0.8 is greater than 0.75 and therefore we can say:
Rosa spent more of her allowance than Albert did!

Question 23.
A group of friends is collecting aluminum for a recycling drive. Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon. The weight of each person’s donation is shown in the table.

a. Order the weights of the donations from greatest to least.
Answer:
Firstly, we will transform all fractions to decimals!
So, we have:
6\(\frac{1}{6}\) = 6 + \(\frac{1}{6}\) = \(\frac{37}{6}\) = 6.1\(\dot{6}\)
\(\frac{15}{4}\) = 3.75
4\(\frac{3}{8}\) = 4 + \(\frac{3}{8}\) = \(\frac{35}{8}\) = 4.375
Now, we can compare those donations!
Number 6.1\(\dot{6}\) is greater than 5.5 which is greater than 4.375 which is greater than 4.3 which is greater than 3.75
Now we can return numbers to its original forms and write them in order from greatest to least:
6\(\frac{1}{6}\), 5.5, 4\(\frac{3}{8}\), 4.3, \(\frac{15}{4}\)

b. Which of the friends will receive a free movie coupon? Which will not?
Answer:
We know that only students who donated more than 4.25 pounds of aluminum will receive a free movie coupon.
Therefore, we will compare given values with 4.25 and conclude which of students is not going to get a free
movie coupon.
We can compare each number with 4.25 but it is not necessary because we ordered them from greatest to least in
previous task!
Therefore, we go from right side and compare numbers until we reach one which is greater than 4.25.
\(\frac{15}{4}\) = 3.75
3.75 is smaller than 4.25, so Micah won’t receive the free movie coupon!
4.3 is greater than 4.25, so Brenda will receive free movie coupon!
Now we know that every other student will receive free movie coupon as their donations are higher!
So the following people will receive free movie coupon: Jim, Peter Brenda, Claire, and Micah won’t.

c. What If? Would the person with the smallest donation win a movie coupon if he or she had collected \(\frac{1}{2}\) pound more of aluminum? Explain.
Answer:
To find out would Micah receive free movie coupon if he had additional \(\frac{1}{2}\) pounds of aluminum, we will have to add these values and compare its sum to 4.25
\(\frac{15}{4}+\frac{1}{2}=\frac{15}{4}+\frac{1 \cdot 2}{2 \cdot 2}=\frac{15}{4}+\frac{2}{4}=\frac{17}{4}\)
Now we transform this into decimal number and get:
\(\frac{17}{4}\) = 4.25
Now we know that Micah’s new donation wilt be 4.25 pounds of aluminum
Since every person who donates at least 4.25 pounds of aluminum receives free movie coupon, Micah will receive it!

Division:

Go Math Lesson 2.3 Answer Key Grade 6 Question 24.
Last week, several gas stations in a neighborhood all charged the same price for a gallon of gas. The table below shows how much gas prices have changed from last week to this week.

a. Order the numbers in the table from least to greatest.
Answer:
Firstly, we will transform all fractions to decimals!
So, we have:

Now, we can compare those gas prices!
Number – 6.75 is smaller than – 6.6 which is smaller than – 5.625 which is smaller than 5.4 which is smaller than 5.8.
Now we can return numbers to its original forms and write them in order from greatest to least:
– 6\(\frac{3}{4}\), – 6.6, – 5\(\frac{5}{8}\), 5.4, 5.8

b. Which gas station has the cheapest gas this week?
Answer:
As we ordered them from least to greatest in last task, we know that the gas price is lowest in Gas and Go at a price change of – 6\(\frac{3}{4}\)

c. Critical Thinking Which gas station changed their price the least this week?
Answer:
To find out, which gas station changed their gas price the least this week we can calculate the absolute value of each price and figure which is the lowest.

As absolute value will give same result for positive numbers, We won’t include them in calculations.
We can draw these values on number line to see their relation, on simply compare them:
Number 6.75 is greater than 6.6 which is greater than 5.8 which is greater than 5.625 which is greater than 5.4.
Therefore, we can say that:
\(\frac{27}{5}\) or 5.4 is the smallest value!
So, least change is made in Corner Store

Division:

H.O.T. Focus on Higher Order Thinking

Question 25.
Analyze Relationships Explain how you would order from least to greatest three numbers that include a positive number, a negative number, and zero.
Answer:
It is actually very Simple. If we order them from least to greatest, negative number is always least, zero is in middle and positive number is greatest.
We can always draw them on number Line to convince our selves!

Question 26.
Critique Reasoning Luke is making pancakes. The recipe calls for 0.5 quart of milk and 2.5 cups of flour. He has \(\frac{3}{8}\) quart of milk and \(\frac{18}{8}\) cups of flour. Luke makes the recipe with the milk and flour that he has. Explain his error.
Answer:
Luke hasn’t got enough milk and cups of flour
Let’s prove that!
Firstly, we transform given fractions into decimals.
\(\frac{3}{8}\) = 0.375
\(\frac{18}{8}\) = 2.25
Since 0.375 is less than 0.5 and 2.25 is less than 2.5.
We can conclude that Luke is missing both milk and cups of flour!

Division:

Question 27.
Communicate Mathematical Ideas If you know the order from least to greatest of 5 negative rational numbers, how can you use that information to order the absolute values of those numbers from least to greatest? Explain.
Answer:
If we know order of 5 negative rational numbers from least to greatest
That means their absolute values are actually vice versa.
Absolute value gives us distance from 0, so in this case, least number is farthest from 0.
So, order of numbers on which was used absolute value is actually from greatest to least

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 Answer Key Rational Numbers.

Texas Go Math Grade 6 Module 2 Answer Key Rational Numbers

Texas Go Math Grade 6 Module 2 Are you ready? Answer Key

Write each improper fraction as a mixed number.

Question 1.
\(\frac{7}{2}\)
Answer:
Firstly, we will write this improper fraction as a sum of proper fractions(ones) plus one which is not proper
SecondLy, we wilt exchange proper fractions with ones!
Thirdly, we will add them
Final soLution will be the mixed number.

\(\frac{7}{2}\) = \(\frac{2}{2}+\frac{2}{2}+\frac{2}{2}+\frac{1}{2}\)
= 1 + 1 + 1 + \(\frac{1}{2}\)
= 3 + \(\frac{1}{2}\)
= 3\(\frac{1}{2}\)

Grade 6 Module 2 Answer Key Go Math Question 2.
\(\frac{12}{5}\)
Answer:
Firstly, we will write this improper fraction as a sum of proper fractions(ones) plus one which is not proper
Secondly, we will exchange proper fractions with ones!
Thirdly, we will add them
Final solution will be: mixed number

\(\frac{12}{5}\) = \(\frac{5}{5}+\frac{5}{5}+\frac{2}{5}\)
= 1 + 1 + \(\frac{2}{5}\)
= 2 + \(\frac{2}{5}\)
= 2\(\frac{2}{5}\)

Question 3.
\(\frac{11}{7}\)
Answer:
Firstly, we will write this improper fraction as a sum of proper fractions(ones) plus one which is not proper
SecondLy, we wiLl exchange proper fractions with ones!
Thirdly, we will add them
Final solution will be: mixed number

\(\frac{11}{7}\) = \(\frac{7}{7}+\frac{4}{7}\)
= 1 + \(\frac{4}{7}\)
= 1\(\frac{4}{7}\)

Question 4.
\(\frac{15}{4}\)
Answer:
Firstly, we will write this improper fraction as a sum of proper fractions(ones) plus one which is not proper
Secondly, we will exchange proper fractions with ones!
Thirdly, we will add them.
Final solution will be: mixed number.

\(\frac{15}{4}\) = \(\frac{4}{4}+\frac{4}{4}+\frac{4}{4}+\frac{3}{4}\)
= 1 + 1 + 1 + \(\frac{3}{4}\)
= 3 + \(\frac{3}{4}\)
= 3\(\frac{3}{4}\)

Write each mixed number as an improper fraction.

Question 5.
2\(\frac{1}{2}\)
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.

2\(\frac{1}{2}\) = 1 + 1 + \(\frac{1}{2}\)
= \(\frac{2}{2}+\frac{2}{2}+\frac{1}{2}\)
= \(\frac{5}{2}\)

Go Math Grade 6 Module 2 Answer Key Pdf Question 6.
4\(\frac{3}{5}\)
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.

4\(\frac{3}{5}\) = 1 + 1 + 1 + 1 + \(\frac{3}{5}\)
= \(\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{3}{5}\)
= \(\frac{23}{5}\)

Question 7.
3\(\frac{4}{9}\)
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.

3\(\frac{4}{9}\) = 1 + 1 + 1 + \(\frac{4}{9}\)
= \(\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{4}{9}\)
= \(\frac{31}{9}\)

Question 8.
2\(\frac{5}{7}\)
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.

2\(\frac{5}{7}\) = 1 + 1 + \(\frac{5}{7}\)
= \(\frac{7}{7}+\frac{7}{7}+\frac{5}{7}\)
= \(\frac{19}{7}\)

Find the least common denominator.

Module 2 Rational Numbers Definition for 6th Grade Question 9.
\(\frac{1}{2}\) and \(\frac{3}{5}\) _________
Answer:
Firstly, we will list multiples of each denominator.
Secondly, we will highlight common multiples!
Thirdly, we will determine, which is the least common denominator!

Least Common denominator is 10

Question 10.
\(\frac{1}{6}\) and \(\frac{3}{8}\) _________
Answer:
Firstly, we will list multiples of each denominator.
Secondly, we will highlight common multiples!
Thirdly, we will determine, which is the least common denominator!

Least Common denominator is 24

Question 11.
\(\frac{9}{10}\) and \(\frac{7}{12}\) _________
Answer:
Firstly, we will list multiples of each denominator.
Secondly, we will highlight common multiples!
Thirdly, we will determine, which is the least common denominator!

Least Common denominator is 60

Grade 6 Module 2 Rational Numbers Graphic Organizer Question 12.
\(\frac{4}{9}\) and \(\frac{5}{12}\) _________
Answer:
Firstly, we will list multiples of each denominator.
Secondly, we will highlight common multiples!
Thirdly, we will determine, which is the least common denominator!

Least Common denominator is 36

Texas Go Math Grade 6 Module 2 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓ words to complete the web. You may put more than one word in each box.

Understand Vocabulary

Fill in each blank with the correct term from the preview words.

Question 1.
A _________________ is any number that can be written as a ratio of two integers.
Answer:
A rational is any number that can be written as a ratio of two integers!

Go Math Grade 6 Module 2 Rational Numbers Answer Key Question 2.
A _________________ is used to show the relationships between groups.
Answer:
A Venn diagram is used to show the relationships between groups.

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 1.1 Answer Key Identifying Integers and Their Opposites.

Texas Go Math Grade 6 Lesson 1.1 Answer Key Identifying Integers and Their Opposites

Texas Go Math Grade 6 Lesson 1.1 Explore Activity Answer Key

(A) The table shows the elevations of several locations in a state park.
Graph the locations on the number line according to their elevations.

(B) What point on the number line represents sea level?

(C) Which location is closest to sea level? How do you know?

(D) Which two locations are the same distance from sea level? Are these locations above or below sea level?

(E) Which location has the least elevation? How do you know?

Reflect

Question 1.
Analyze Relationships Morning Glory Stream is 7 feet below sea level. What number represents the elevation of Morning Glory Stream?
Answer:
Because Morning Glory Stream is 7 feet below sea level, the number which represents the elevation of Morning Glory wilt be – 7.
It is – 7 because Morning Glory Stream is 7 feet below sea level and we can let the sea level’s elevation be 0.

Result:
– 7

Integers and Their Opposites Go Math Grade 6 Lesson 1.1 Answer Key Question 2.
Multiple Representations Explain how to graph the elevation of Morning Glory Stream on a number line.
Answer:
Because the elevation of Morning Glory Stream is 7, it is a number that is Less than 0, so, it is a negative integer.
So, – 7 will be 7 units left from 0 on number Line.

Result:
It will be 7 units left from 0 on a number line.

Question 3.
Justify Reasoning Explain how your number line shows that 8 and -8 are opposites.
Answer:
From number Line we can notice that 8 and – 8 are the same distance from 0 but also, they are on different sides of 0.
So, according to previous, we can conclude that 8 and – 8 are opposites.

Result:
They are the same distance from 0 and on different sides of 0.

Question 4.
Multiple Representations Explain how to use your number line to find the opposite of the opposite of -6.
Answer:
First we need to find – 6 on number line. It is 6 units left of point 0. The opposite of – 6 is 6 units right from point 0, it is number 6.
And again, opposite of 6, which is opposite of – 6, is 6 units Left from 0 on number Line.
We get that it is number – 6.
So, conclusion is that the opposite of the opposite of – 6 is – 6.

Result:
The opposite of the opposite of – 6 is – 6.

Question 5.
Analyze Relationships Explain how you can find the opposite of the opposite of any number without using a number line.
Answer:
From all previous we can conclude that the opposite of the opposite of any number is that number always.

Result:
The opposite of the opposite of any number is that number.

Your Turn

Graph the opposite of the number shown on each number line.

Question 6.

Answer:
Here we need to find the opposite of the number – 1. It is 1 unit from 0 to the right We can conclude that it is number 1.

Result:
1

Go Math 6th Grade Lesson 1.1 Identifying Integers Question 7.

Answer:
Here we need to find the opposite of the number 7.
It is 7 units from 0 to the left. We can conclude that it is number -7.

Result:
– 7

Write the opposite of each number.

Question 8.
10 ___________
Answer:
The opposite of 10 is – 10, because – 10 is number on number line with the same distance from 0 as 10 and on the opposite side of 0.

Result:
– 10

Question 9.
– 5 ___________
Answer:
The opposite of – 5 is 5 because 5 is number on number tine with the same distance from 0 as – 5 and on the opposite side of 0.

Result:
5

Question 10.
0 ____________
Answer:
Here, conclusion is that 0 is its own opposite.

Result:
0

Question 11.
What is the opposite of the opposite of 6?
Answer:
Like we explain in some previous tasks, the opposite of the opposite of any number is that number.
So, here, the opposite of the opposite of 6 is 6.

Result:
6

Texas Go Math Grade 6 Lesson 1.1 Guided Practice Answer Key

Question 1.
Graph and label the following points on the number line.
a. -2
b. 9
c. -8
d. -9
e. 5
f. 8

Answer:

Graph the opposite of the number shown on each number line. (Explore Activity 2 and Example 1)

Go Math Grade 6 Practice and Homework Lesson 1.1 Answer Key Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:
Note that opposite of 0 is actually 0

Write the opposite of each number. (Explore Activity 2 and Example 1)

Question 5.
4
Answer:
Opposite of 4 is – 4.
Therefore, we write – 4 on a line.

Question 6.
– 11
Answer:
Opposite of – 11 is 11.
Therefore, we write 11 on a line.

Question 7.
3
Answer:
Opposite of 3 is – 3.
Therefore, we write – 3 on a line.

Question 8.
– 3
Answer:
Opposite of – 3 is 3.
Therefore, we write 3 on a line.

Lesson 1.1 Relate Integers and Their Opposites Go Math 6th Grade Question 9.
0
Answer:
Opposite of 0 is 0.
Therefore, we write 0 on a line.

Question 10.
22
Answer:
Opposite of 22 is – 22.
Therefore, we write – 22 on a line.

Essential Question Check-In

Question 11.
Given an integer, how do you find its opposite?
Answer:
We will get opposite of integer if we add “—” sign in front of a number(from Left side).

Question 12.
Chemistry Atoms normally have an electric charge of 0. Certain conditions, such as static, can cause atoms to have a positive or a negative charge. Atoms with a positive or negative charge are called ions.

a. Which ions have a negative change?
Answer:
Ions with a negative charge are: A, C, E

b. Which ions have charges that are opposites?
Answer:
Ions that have charges which are opposite are: B, D, A, E

c. Which ions charge is not the opposite of another ion’s charge?
Answer:
Ion charge which is not opposite of another ion charge is C

Name the integer that meets the given description.

Question 13.
the opposite of -17 ____________
Answer:
Opposite number of – 17 is 17.
Therefore, our final solution is: 17

Question 14.
4 units left of 0 _________
Answer:
Number that is 4 units left from 0 is: – 4
Actually, we could have just drawn a number line for ourselves and have shown the solution through it!
Let’s do it:

Question 15.
the opposite of the opposite of 2 ____________
Answer:
Opposite of the opposite of some number is actuaLLy that same number!
So, in our case the integer that meets the given description is: 2
That is our final solution!

Question 16.
15 units right of 0 ____________
Answer:
Number that is 15 units right of 0 is: 15
Actually, we could have just drawn a number line for ourselves and have shown the solution through it!

Let’s do it:

Question 17.
12 units right of 0 ____________
Answer:
Number that is 15 units right of 0 is: 15
We can use addition while finding number placed right of another number!
Actually, we could have just drawn a number line for ourselves and have shown the solution through it!

Let’s do it:

Go Math Grade 6 Lesson 1.1 Integers on the Number Line Answer Key Question 18.
the opposite of – 19 __________
Answer:
Opposite number of – 19 is 19
Therefore, our final solution is 19

Question 19.
Analyze Relationships Several wrestlers are trying to lose weight for a competition. Their change in weight since last week is shown in the chart.

a. Did Victor lose or gain weight since last week?
Answer:
Victor gained weight since last week.

b. Which wrestlers weight change is the opposite of Ramsey’s?
Answer:
Opposite of Ramsey’s weight change is Tino.

c. Which wrestlers have lost weight since last week?
Answer:
Wrestlers who lost weight since last week are: Tino, Luis.

d. Frankie’s weight change since last week was the opposite of Victor’s.
What was Frankie’s weight change? ____________
Answer:
Firstly, we conclude that Victor gained 6 pounds!
Now, we can say that Frankie lost 6 pounds
So, Frankie’s weight change from last week is – 6 pounds!

e. Frankie’s goal last week was to gain weight. Did he meet his goal? Explain.
Answer:
Frankie didn’t meet his goat because he gained 6 pounds since last week and he was supposed to loose weight.

Find the distance between the given number and its opposite on a number line.

Question 20.
6 ____________
Answer:

Question 21.
– 2 ____________
Answer:

Question 22.
0 ____________
Answer:
Please not that the opposite of 0 is 0.

Question 23.
– 7 ____________
Answer:

Go Math 6th Grade Lesson 1.1 Answers Question 24.
What If? Three contestants are competing in a trivia game show.
The table shows their scores before the final question.

a. How many points must Shawna earn for her score to be the opposite of Timothy’s score before the final question?
Answer:
We know that the opposite of 18 is – 18
So we calculate the distance between – 25 and – 18.
Here is how we do it:
|- 25| – |-17| = 25 – 17 = 8
So, amount of points that Shawna has to earn is: 8

b. Which person’s score is closest to 0?
Answer:
Here, we calculate lowest absolute value!
|- 25| > |18| >| – 14| = – 14
Absolute value of – 14 is lowest
and therefore closest to 0

c. Who do you think is winning the game before the final question? Explain.
Answer:
Shawna is in lead before final question since her score is greatest!

H.O.T. Focus on Higher Order Thinking

Question 25.
Communicate Mathematical Ideas Which number is farther from 0 on a number line: – 9 or 6? Explain your reasoning.
Answer:
Here we can conclude that – 9 is farther from 0 than 6.
That works because the absolute value of – 9 is greater than 6 and therefore it’s distance from 0.

Question 26.
Analyze Relationships A number is k units to the left of 0 on the number line. Describe the location of its opposite.
Answer:
Since a number is to the Left of 0, that means that it’s opposite
is to the right of O, and aLso means that it starting value is negative
Therefore, its opposite will have value of: – k

Question 27.
Critique Reasoning Roberto says that the opposite of a certain integer is – 5. Cindy concludes that the opposite of an integer is always negative. Explain Cindy’s error.
Answer:
Cindy basically said that – 5 has negative opposite, which is absurd.
Opposite of some number has different sign, only 0 remains same!

Question 28.
Multiple Representations Explain how to use a number line to find the opposites of the integers 3 units away from – 7.
Answer:
Firstly, we locate number – 7.
Then we find values of 3 units to the left of – 7 and to the right of – 7.
Now we know that – 10 and – 4 are the values!
The next step is finding their opposites!
Opposite of – 10 is 10 land opposite of – 4 is 4

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 Answer Key Integers.

Texas Go Math Grade 6 Module 1 Answer Key Integers

Texas Go Math Grade 6 Module 1 Are you ready? Answer Key

Compare. Write <, >, or =.

Question 1.
471 __________ 468
Answer:
Number 471 is greater than 168
Therefore, we write:
471 > 468

Question 2.
5,005 __________ 5,050
Answer:
Number 5,005 is smaller than 5,050
Therefore, we write:
5. 005 < 5,050

Go Math Grade 6 Module 1 Answer Key Pdf Question 3.
398 __________ 389
Answer:
Number 398 is greater than 389
Therefore, we write:
398 > 389

Question 4.
10,973 __________ 1099
Answer:
Number 10, 973 is smaller than 10,999
Therefore, we write:
10, 973 < 10,999

Question 5.
8,471 __________ 9,001
Answer:
Number 8,471 is smaller than 9,001
Therefore, we write:
8, 471 < 9,001

Question 6.
108 __________ 95
Answer:
Number 108 is greater than 95
Therefore, we write:
108 > 95

Order the numbers from greatest to least.

Question 7.
156; 87; 177; 99
Answer:
Number 177 is greater than 156 which is greater than 99 which is greater than 87
Therefore, we write:
177 > 156 > 99 > 87

Question 8.
591; 589; 603; 600
Answer:
Number 603 is greater than 600 which is greater than 591 which is greater than 589
Therefore, we write:
603 > 600 > 591 > 589

Question 9.
2,650; 2,605; 3,056; 2,088
Answer:
Number 3,056 is greater than 2,650 which is greater than 2,605 which is greater than 2,088
Therefore, we write:
3, 056 > 2. 650 > 2.605 > 2. 088

Grade 6 Module 1 Answer Key Pdf Go Math Question 10.
1,037; 995; 10,415; 1,029
Answer:
Number 10,415 is greater than 1,037 which is greater than 1,029 which is greater than 995
Therefore, we write:
10,115 > 1,037 > 1, 029 > 995

Graph each number on the number line.

Question 11.
12
Answer:

Question 12.
20
Answer:
Here, we know the weight of 1 hamburger’s meat needs.
If we want to know the weight of 1000 hamburgers’s meat needs, we need to multiply it!

Question 13.
2
Answer:
Firstly, we know that the building has 4 floors with 12 apartments on each!
That means that the building has:
4 ∙ 12 = 48 apartments.
If we know that each floor has 3 apartments which are not one-bedroom ones, that implies
There are:
4 ∙ 3 = 12 apartments.
which are not one-bedroom ones! Now we subtract values and get:
48 – 12 = 36
apartments with one bedroom!
Now, we know that every expression that does not give 48, when evaluated, is wrong!
Therefore, final solution for this task is

Integers Test Grade 6 Pdf with Answers Question 14.
9
Answer:
Here, we calculate the content of parenthesis first!
So. we get:
900 + 60000 + 200000 + 80 = 260980
Note that I automatically calculated that because when we multiply with such numbers.
all we do is add a certain number of 0 to the time right of the last digit!

Texas Go Math Grade 6 Module 1 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓ words to complete the chart. Write the correct vocabulary word next to the symbol.

Understand Vocabulary

Complete the sentences using the preview words.

Question 1.
An ___________ is a statement that two quantities are not equal.
Answer:
inequality

Go Math Grade 6 Volume 1 Answer Key Question 2.
The set of all whole numbers and their opposites are _____________.
Answer:
integers

Question 3.
Numbers greater than 0 are _____________. Numbers less than 0 are _____________.
Answer:
positive numbers and negative numbers

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Module 14 Quiz Answer Key.

Texas Go Math Grade 7 Module 14 Quiz Answer Key

Texas Go Math Grade 7 Module 14 Ready to Go On? Answer Key

14.1 Personal Budgets

For 1-3, use the following information on the Plimpton family’s monthly budget.

Their net monthly income is $4,500. They have an emergency fund that is 6% of their monthly budget and they have a savings of 7% per month. Medical costs are $675 per month, housing is $1,485, and transportation costs $450. Food accounts for 17% of the monthly budget and they spend 5% on entertainment. They also spend 7% of the budget on clothing each month.

Question 1.
How much does the Plimpton family spend on clothing each month? ____
Answer:
Net monthly income of Plimpton family = $4, 500
Percentage of budget used for clothing 7%
Amount spent on clothing = \(\frac{\text { Percentage }}{100}\) × Net monthly income
Amount spent on clothing = \(\frac{7}{100}\) × 4,500
= 0.07 × 4,500
= $315
Hence, Plimpton family spend $315 monthly on cLothing.

Question 2.
How much does the Plimpton family spend on entertainment each year? ____
Answer:
Net monthly income of Plimpton family = $4, 500
Percentage of budget used for Entertainment = 5%
Amount spent on Entertainment = \(\frac{\text { Percentage }}{100}\) × Net monthly income
Amount spent on Entertainment = \(\frac{5}{100}\) × 4, 500
= 0.05 × 4, 500
= $225
Hence, the Plimpton family spends $225 monthly on Entertainment.

Go Math Grade 7 Answer Key Module 14 Quiz Question 3.
How much more does the Plimpton family spend on food than on savings each month? ____
Answer:
Net monthly income of Plimpton family = $4, 500
Percentage of budget used for food = 17%
Percentage of budget used for saving = 7%
Amount spent on food = \(\frac{\text { Percentage }}{100}\) × Net monthly income
Amount spent on food = \(\frac{17}{100}\) × 4, 500
= 0.17 × 4,500
= $765
Amount spent on saving = \(\frac{7}{100}\) × 4, 500
= 0.07 × 4,500
= $ 315
Hence, Plimpton family spend $765 monthly on food and $315 is saving.

Question 4.
What percent of the net monthly income goes to housing? ____
Answer:
Net monthly income of Plimpton family = $4, 500
Amount from budget that goes to housing = $1,485

Percentage of budget on housing = \(\frac{1,485}{4500}\) × 100
= 0.33 × 4,500
= 33%
Hence, Plimpton family spend 33% of monthly budget on housing.

14.2 Planning a Budget

Question 5.
Ms. Wofford and her two sons live in Lubbock, Texas, where she makes $3,200 a month. She is thinking of transferring to Abilene and uses an online family budget estimator to see her potential monthly expenses. Use the table below. Is a transfer to Abilene a good financial move for the Woffords? Explain.

Answer:
Minimum monthly saving of Ms. Wofford in Lubbock = 3,111 – 2, 951 = $160
Minimum monthly saving of Ms. Wofford in Abilene = 2,812 – 2,775 = $37
Now on comparing the minimum monthly saving in both the city, we can see that saving in the Lubbock is more as
compared to the saving in Abilene. So for Ms. Wofford transfer to Abilene will, be not a good financial move.
Hence, transfer to Abilene will be not good move for Ms. Wofford.

14.3 Constructing a Net Worth Statement

Question 6.
Calvin lives in a home with a value of $185,000 and has a mortgage of $ 145,000. He has a stock portfolio worth $ 11,700. He owns his car, which is valued at $10,500. He has $15,300 in student loans to repay. He has a credit card balance of $6,228. He also has $3,400 in a bank account. What is Calvin’s net worth? ____
Answer:
Net worth = Value of assets – Value of Liabilities
= $210,600 – $166,528
= $44,072
Hence, Calvin’s net worth is $44 072

Texas Go Math Grade 7 Module 14 Mixed Review Texas Test Prep Answer Key 

Selected Response

Question 1.
Which of the following is an example of income?
(A) insurance
(B) emergency savings
(C) wages
(D) taxes
Answer:
(C) wages
Wages are the amount which anyone receives when he/she completes the work. So wages is an income for any anyone.

Grade 7 Math Module 14 Answer Key Question 2.
Which of the following is an example of a variable expense?
(A) weekly martial arts lesson
(B) rent
(C) entertainment
(D) monthly bus pass
Answer:
(C) entertainment
Variable expenses are the expense that varies over the time. Variable expanse is never fixed and depends on the daily life of persons. Examples of variable expenses are snacks, entertainment, etc.

Question 3.
A boating company on the lake charges a $10 equipment fee and $5.50 per hour to rent a canoe. Write the equation of the linear relationship.
(A) y = 10x + 5.5
(B) y = 10x + 55
(C) y = 55x + 10
(D) y = 5.5x + 10
Answer:
(D) y = 5.5x + 10
Equipment fee of boating company = $10
Per hour charge for renting canoe = $5.50
Renting charge of canoe for x hours = 5.5 × x
Total cost of renting canoe for x hours = Equipment fee + Renting fee for x hours.
In linear equation form : y = 10 + 5.5x
Hence, Option D is correct answers.

Question 4.
Barry owns a home with a value of $170,000. He owes $4,400 on his cat, which is valued at $11,500. He has $9,500 in student loans to repay. He owns $3,300 worth of musical equipment. He has a credit card balance of $2,117. He also has $2,900 in a bank account. What is Barry’s net worth?
(A) $157,483
(B) $171,683
(C) $165,883
(D) $175,917
Answer:
(B) $171,683


Net worth = Value of assets – Value of Liabilities
= $187,700 – $16,017
= $171,683

Module 14 Quiz Answer Sheet Go Math Grade 7 Question 5.
Which of the following is an example of an asset?
(A) car loan
(B) credit card bill
(C) savings bond
(D) rent
Answer:
(C) savings bond
Assets are something that we own and it has some positive cash value which means we will get some money when we sell it. Savings bonds are issued by the government and when we sell them back to the government after a certain duration of time we will get money back with an additional amount of interest.

Gridded Response

Question 6.
The Garza family consists of two adults and two children. Their current monthly income is $4,800. The circle graph shows their monthly budget. How much money in dollars do the Garzas spend on housing each month?


Answer:
Current monthly income of Garza family = $4, 800
Percentage of budget used for housing = 30%
Amount spent on housing = \(\frac{\text { Percentage }}{100}\) × Net monthly income
Amount spent on housing = \(\frac{30}{100}\) × 4, 800
= 0.3 × 4,800
= $1440
Hence, the Garza family spends $1440 monthly on housing.