Texas Go Math

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 2 Answer Key Rates and Proportionality.

Texas Go Math Grade 7 Module 2 Answer Key Rates and Proportionality

Texas Go Math Grade 7 Module 2 Are You Ready? Answer Key

Divide.

Question 1.
\(\frac{3}{4}\) ÷ \(\frac{4}{5}\) _____________
Answer:
Multiply by the reciprocal of the divisor:
= \(\frac{3}{4}\) × \(\frac{5}{4}\)
= \(\frac{15}{16}\)

Grade 7 Module 2 Answer Key Texas Go Math Question 2.
\(\frac{5}{9}\) ÷ \(\frac{10}{11}\) _____________
Answer:
Multiply by the reciprocal of the divisor:
= \(\frac{5}{9}\) × \(\frac{11}{10}\)
= \(\frac{11}{18}\)

Question 3.
\(\frac{3}{8}\) ÷ \(\frac{1}{2}\) _____________
Answer:
Multiply by the reciprocal of the divisor:
= \(\frac{3}{8}\) × \(\frac{2}{1}\)
= \(\frac{3}{4}\)

Question 4.
\(\frac{16}{21}\) ÷ \(\frac{8}{9}\) _____________
Answer:
Multiply by the reciprocal of the divisor:
= \(\frac{16}{21}\) × \(\frac{9}{8}\)
= \(\frac{6}{7}\)

Write the ordered pair for each point.

Question 5.
B ____________
Answer:
B(-4, 1)

Question 6.
C ____________
Answer:
C(3, 0)

Question 7.
D _____________
Answer:
D(5, 4)

Question 8.
E _____________
Answer:
E(-2, -2)

Question 9.
F _____________
Answer:
F(0, 0)

Texas Go Math Module 2 Grade 7 Answer Key Question 10.
G _____________
Answer:
G(-4, 0)

Texas Go Math Grade 7 Module 2 Reading Start-Up Answer Key

Visualize Vocabulary

Use the ✓ words to complete the graphic. You can put more than one word in each bubble.

Understand Vocabulary

Match the term on the left to the definition on the right.

Answer:
1. rate of change ………. B. A rate that describes how one quantity changes in relation to another quantity.
2. proportion ………… A. Statement that two rates or ratios are equivalent
3. proportion ……….. C. Rate in which the second quantity is one unit

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 Lesson 1.4 Answer Key Subtracting Rational Numbers.

Texas Go Math Grade 7 Lesson 1.4 Answer Key Subtracting Rational Numbers

Example 1
The temperature on an outdoor thermometer on Monday was 5.5 °C. The temperature on Thursday was 7.25 degrees less than the temperature on Monday. What was the temperature on Thursday?
Answer:
Subtract to find the temperature on Thursday.
Step 1: Find 5.5 – 7.25
Step 2: Start at 5.5

Step 3: Move |7.25| = 7.25 units to the left because you are subtracting a positive number.
The result is -1.75
The temperature on Thursday was -1.75 °C.

Your Turn

Use a number line to find each difference.

Question 1.
-6.5 – 2 = __________

Answer:
Start at -6.5.
Move |2| = 2 units to the left because you are subtracting a positive number
The result is -8.5.

Go Math Lesson 1.4 7th Grade Answer Key Question 2.
1\(\frac{1}{2}\) – 2 = __________

Answer:
Start at 1\(\frac{1}{2}\).
Move |2| = 2 units to the left because you are subtracting a positive number
The result is -0.5.

Question 3.
-2.25 – 5.5 = __________

Answer:
Start at -2.25.
Move |5.5| = 5.5 units to the left because you are subtracting a positive number
The result is -7.75.

Example 2
During the hottest week of the summer, the water level of the Muskrat River was \(\frac{5}{6}\) foot below normal. The following week, the level was foot below normal. What is the overall change in the water level?
Answer:
Subtract to find the difference in water levels.
Step 1: Find –\(\frac{1}{3}\) – (-\(\frac{5}{6}\)).
Step 2: Start at –\(\frac{1}{3}\).

Step 3: Move |-\(\frac{5}{6}\)| = \(\frac{5}{6}\) to the right because you are subtracting a negative number.
The result is \(\frac{1}{2}\).
So, the water level increased \(\frac{1}{2}\) foot.

Reflect

Question 4.
Work with other students to compare addition of negative numbers on a number line to subtraction of negative numbers on a number line.
Answer:
We conclude that when it comes to addition of negative numbers we move to the left, while we move to the right in subtraction of negative numbers.

Question 5.
Compare the methods used to solve Example 1 and Example 2.
Answer:
Methods are the same, in both we use subtraction, the difference is in moving left (example 1) or right (example 2) on the number tine, and that depends on the subtrahend, whether it is positive or negative.

Your Turn

Use a number line to find each difference.

Question 6.
0.25 – (-1.50) = ___________

Answer:
Start at 0.25.
Move |-1.50| = 1.50 units to the right because you are subtracting a positive number
The result is 1.75.

Go Math Grade 7 Lesson 1.4 Answer Key Question 7.
– \(\frac{1}{2}\) – (-\(\frac{3}{4}\)) = ____________

Answer:
Step 1
Start at –\(\frac{1}{2}\)
Move |-\(\frac{3}{4}\)| = \(\frac{3}{4}\) units to the right because you are subtracting a negative number
The result is \(\frac{1}{4}\)

Explore Activity 1

Adding the Opposite
Joe is diving 2\(\frac{1}{2}\) feet below sea level. He decides to descend 7\(\frac{1}{2}\) more feet. How many feet below sea level is he?
Answer:
Step 1: Use negative numbers to represent the number of feet below sea level.
Step 2: Find -2\(\frac{1}{2}\) – 7\(\frac{1}{2}\).
Step 3: Start at -2\(\frac{1}{2}\).

Step 4: Move |7\(\frac{1}{2}\)| = 7\(\frac{1}{2}\) units to the _____________________
because you are subtracting a ____________________ number.
The result is -10.
Joe is ______________________ sea level.

Reflect

Question 8.
Use a number line to find each difference or sum.
a. -3 – 3 = __________

Answer:
Start at -3.
Move |3| = 3 units to the left because you are subtracting a positive number.
The result is -6.

b. -3 + (-3) = __________

Answer:
Start at -3.
Move |-3| = 3 units to the left because you are subtracting a positive number.
The result is -6.

Go Math Answer Key Grade 7 Subtracting Rational Numbers Question 9.
Make a Conjecture Work with other students to make a conjecture about how to change a subtraction problem into an addition problem.
Answer:
We conclude that we can substitute a subtraction problem with an addition problem. Minuend becomes the
first addend, while the second addend is a negative subtrahend
E.g.
5 – 3 = 5 + (-3)

Explore Activity 2

A cave explorer climbed from an elevation of -11 meters to an elevation of -5 meters. What vertical distance did the explorer climb?

There are two ways to find the vertical distance.
A.
Start at ________.
Count the number of units on the vertical number line up to -5.
The explorer climbed __________ meters.
This means that the vertical distance between
-11 meters and -5 meters is ________ meters.

B.
Find the difference between the two elevations and use the absolute value to find the distance.
11 – (-5) = __________
Take the absolute value of the difference because the distance traveled is always a non-negative number.
|-11 -(-5)| = __________
The vertical distance is _________meters.

Reflect

Question 10.
Does it matter which way you subtract the values when finding distance? Explain.
Answer:
It does not matter, because the difference in two ways is in the sign (+/-) Thus when we take the absolute values
of the results, it’s the same.
E.g.
5 – 3 = 2
|5 – 3| = 2
3 – 5 = -2
|3 – 5| = 2

7th Grade Go Math Lesson 1.4 Answer Key Question 11.
Would the same methods work if both the numbers were positive? What if one of the numbers were positive and the other negative?
Answer:
Yes, it would still work if both the numbers were positive.
It would not make a difference if one of the numbers were positive and the other negative. We would still use the same method.

Texas Go Math Grade 7 Lesson 1.4 Guided Practice Answer Key 

Use a number line to find each difference. (Example 1, Example 2 and Explore Activity 1)

Question 1.
5 – (-8) = ___________

Answer:
Start at 5.
Move |-8| = 8 units to the right because you are subtracting a negative number.
The result is 13.

Question 2.
-3\(\frac{1}{2}\) -4\(\frac{1}{2}\) = __________

Answer:
Start at -3\(\frac{1}{2}\).
Move |-4\(\frac{1}{2}\)| = 4\(\frac{1}{2}\) units to the left because you are subtracting a positive number
The result is -8

Question 3.
-7 – 4 = __________

Answer:
Start at -7.
Move |4| = 4 units to the left because you are subtracting a positive number
The result is -11.

Question 4.
-0.5 – 3.5 = __________

Answer:
Start at -0.5.
Move |3.5| = 3.5 units to the left because you are subtracting a positive number
The result is -4.

Find each difference. (Explore Activity 1)

Question 5.
-14 – 22 = ___________
Answer:
– 36

Question 6.
-12.5 – (-4.5) = ________
Answer:
Start by changing subtraction problem to addition problem.
= -12.5 + 4.8
= -7.7

Question 7.
\(\frac{1}{3}\) – (-\(\frac{2}{3}\)) = ___________
Answer:
Start by changing subtraction problem to addition problem.
= \(\frac{1}{3}\) + \(\frac{2}{3}\)
= \(\frac{3}{3}\)
= 1

Go Math Lesson 1.4 7th Grade Subtracting Rational Numbers Question 8.
65 – (-14) = ___________
Answer:
Start by changing subtraction problem to addition problem.
= 65 + 14
= 79

Question 9.
–\(\frac{2}{9}\) – (-3) = _________
Answer:
Start by changing subtraction problem to addition problem.
= –\(\frac{2}{9}\) + 3
= 2\(\frac{7}{9}\)

Question 10.
24\(\frac{3}{8}\) – (-54\(\frac{1}{8}\)) = ___________
Answer:
Start by changing subtraction problem to addition problem.
= 24\(\frac{3}{8}\) + 54\(\frac{1}{8}\)
= 78\(\frac{4}{8}\)
(1) = 78\(\frac{1}{2}\)
(1) Cancel fraction.

Question 11.
A girl is snorkeling 1 meter below sea level and then dives down another 0.5 meter. How far below sea level is the girl? (Explore Activity 1)
Answer:
Use negative numbers to represent the number of feet below sea level
Find -1 – 0.5.
Start at -1.
Move |0.5| = 0.5 units to the left because you are subtracting a positive number
The result is -1.5. The girl is now 1.5 meters below sea level.

Question 12.
The first play of a football game resulted in a loss of 1 yards. Then a penalty resulted in another loss of 5 yards. What is the total loss or gain? (Explore Activity 1)
Answer:
Use negative numbers to represent the number of yards lost
Find -12\(\frac{1}{2}\) – 5.
Start at -12\(\frac{1}{2}\).
Move |5| = 5 units to the left because you are subtracting apositive number
The result is-17\(\frac{1}{2}\). Total loss is -17\(\frac{1}{2}\) yards.

Question 13.
A climber starts descending from 533 feet above sea level and keeps going until she reaches 10 feet below sea level. How many feet did she descend? (Explore Activity 2)
Answer:
Find the difference between the two heights and use the absolute value to find the distance.
533 – (-10) = 533 + 10
= 543
Take the absolute value of the difference, because distance descended is always a positive number
|543| = 543
The climber descended 543 feet

Texas Go Math Grade 7 Answers Subtracting Rational Numbers Question 14.
Eleni withdrew $45.00 from her savings account. She then used her debit card to buy groceries for $30.15. What was the total amount Eleni took out of her account? (Explore Activity 1)
Answer:
Use negative numbers to represent the number of money withdrawn or spent.
Find -45 – 30,15.
Start at -45.
Move |30.15| = 30.15 units to the left because you are subtracting a positive number.
The result is -75.15. Eleni took total of $75.15 of her account.

Essential Question Check-In

Question 15.
Mandy is trying to subtract 4-12, and she has asked you for help. How would you explain the process of solving the problem to Mandy, using a number line?
Answer:
Start at 4
Move |12| = 12 units to the left because you are subtracting a positive number.
The resuLt is -8.

Texas Go Math Grade 7 Lesson 1.4 Independent Practice Answer Key 

Question 16.
Science At the beginning of a laboratory experiment, the temperature of a substance is -12.6°C. During the experiment, the temperature of the substance decreases 7.5 °C. What is the final temperature of the substance?
Answer:
Subtract temperatures to find the final temperature of the substance.
Find -12.6 – 7.5.
Start at -12.6.
Move |7.5| = 7.5 units to the left because you are subtracting a positive number
The result is -20.1. Final temperature of the substance is -20.1°C

Question 17.
A diver went 25.65 feet below the surface of the ocean, and then 16.5 feet further down, he then rose 12.45 feet. Write and solve an expression to find the diver’s new depth.
Answer:
Find -25.65 – 16.5 – 12.45.
First find -25.65 – 16.5.
Start at – 25.65.
Move |16.5| = 16.5 units to the left because you are subtracting a positive number.
The result is -42.15.
Now find -42.15 + 12.45.
Start at -42.15.
Move |12.45| = 12.45 units to the right because you are adding a positive number.
The result is -29.7. Diver’s new depth is -29.7 feet.

Go Math Grade 7 Answer Key Pdf Lesson 1.4 Question 18.
A city known for its temperature extremes started the day at -5 degrees Fahrenheit. The temperature increased by 78 degrees Fahrenheit by midday and then dropped 32 degrees by nightfall.
a. What expression can you write to find the temperature at nightfall?
Answer:
The temperature started the day at -5 degrees Fahrenheit, then it increased by 78 degrees That means we add 78 to -5. Lastly, the temperature dropped 32 degrees & Which means we subtract 32 from the result.
-5 + 78 – 32

b. What expression can you write to describe the overall change in temperature? Hint: Do not include the temperature at the beginning of the day since you only want to know about how much the temperature changed.
Answer:
Using the hint we see that we only need to use changes in temperatures. The first change is -r78 degrees, and the next is -32 degrees.
78 – 32

c. What is the final temperature at nightfall? What is the overall change in temperature?
Answer:
To get the final temperature we calculate expression from a).
-5 + 78 – 32 = 73 – 32
= 41
To get the overall change in temperature we calculate expression from b).
78 – 32 = 46

Question 19.
Financial Literacy On Monday, your bank account balance was -$12.58. Because you didn’t realize this, you wrote a check for $30.72 for groceries.
a. What is the new balance in your checking account?
Answer:
The balance was -$12.38. and a check was written on $30.72. That means we to subtract the amount written on the check from the balance.
– 12.58 – 30.72 = -43.3
The new balance is – $43.3.

b. The bank charges a $25 fee for paying a check on a negative balance. What is the balance in your checking account after this fee?
Answer:
We have to subtract the fee from the new balance.
-43.3 – 25 = -68.3
The balance after the fee is $68.3.

c. How much money do you need to deposit to bring your account balance back up to $0 after the fee?
Answer:
We have to deposit the opposite of the debt we have. That is $68.3.

Astronomy Use the table for problems 20-21.

Question 20.
How much deeper is the deepest canyon on Mars than the deepest canyon on Venus?
Answer:
Deepest canyon on Mars is at -26000 feet
Deepest canyon on Venus is at -9500 feet
To calculate the difference we have to subtract these 2 numbers, and then take the absolute value of the result.
-26000 – (-9500) = -26000 + 9500
= -16500
|-16500| = 16500
The deepest canyon on Mars is 16500 feet deeper that the deepest canyon on Venus.

Question 21.
Persevere in Problem Solving What is the difference between Earth’s highest mountain and its deepest ocean canyon? What is the difference between Mars’s highest mountain and its deepest canyon? Which difference is greater? How much greater is it?
Answer:
To find the difference between the highest mountain and the deepest ocean canyon, we have to subtract the mountain height from the ocean depth, and then take the absolute value of the result
Earth:
29035 – (-36198) = 29035 + 36198
= 65233
|65233| = 65233

Mars:
70000 – (-26000) = 70000 + 26000
= 96000
|96000| = 96000

We can see that 96000 > 65233. To calculate how much, subtract 65233 from 96000.
96000 – 65223 = 30777

Question 22.
Pamela wants to make some friendship bracelets for her friends. Each friendship bracelet needs 5.2 inches of string.
a. If Pamela has 20 inches of string, does she have enough to make bracelets for 4 of her friends?
Answer:
First we need to ca[cu[ate how much are 4 bracelets long. We need to add 5.2 inches 4 times.
5.2 + 5.2 + 5.2 + 5.2 = 10.4 + 5.2 + 5.2
= 15.6 + 5.2
= 20.8
Since, 20.8 is greater than 20, she will not have enough to make for all of her 4 friends.

b. If so, how much string would she have left over? If not, how much more string would she need?
Answer:
To calculate how much more string she would need, we need to substract the length of string she has from the
length of string she needs.
20.8 – 20 = 0.8
She needs 0.8 inches more.

Question 23.
Jeremy is practicing some tricks on his skateboard. One trick takes him forward 5 feet, then he flips around and moves backwards 7.2 feet, then he moves forward again for 2.2 feet.
a. What expression could be used to find how far Jeremy is from his starting position when he finishes the trick?
Answer:
If the first trick takes him forward 5 feet, that means he goes +5 feet forward. Second trick takes him 7.2 feet back, that means we subtract -7.2 from 5. Third trick moves him +2 feet forwards, that means we add 2 feet to
previous position.
5 – 7.2 + 2

b. How far from his starting point is he when he finishes the trick? Explain
Answer:
We have to calculate the expression from a), and then take its absolute value to find how far is he from his starting position after the trick.
5 – 7.2 + 2 = -2.2 + 2
= -0.2
|-0.2| = 0.2
He is 0.2 feet away from the starting position.

Question 24.
Esteban has $20 from his allowance. There is a comic book he wishes to buy that costs $4.25, a cereal bar that costs $0.89, and a small remote control car that costs $ 10.99.
a. Does Esteban have enough to buy everything?
Answer:
We have to add all of the expenses, and then check if they are greater than Esteban’s allowance to cheek if he has enough.
4.25 + 0.89 + 10.99 = 5.14 + 10.99
= 16.13
20 > 16.13
The allowance is greater than the expenses. Thus. Esteban has enough money to buy everything.

b. if so, how much will he have left over? If not, how much does he still need?
Answer:
To find out how much will he have leftover, we need to subtract the expenses from the allowance.
20 – 16.13 = 3.87
Esteban will have $3.87 leftover.

H.O.T. Focus on Higher Order Thinking

Question 25.
Look for a Pattern Show how you could use the Commutative Property to simplify the evaluation of the expression \(-\frac{7}{16}-\frac{1}{4}-\frac{5}{16}\)
Answer:
We can see that the first and the last member of the expression have the same denominator. Use the Commutative Property to switch second and third member. Now we have:
–\(\frac{7}{16}\) – \(\frac{5}{16}\) – \(\frac{1}{4}\)
Calculate the expression:

Go Math 7th Grade Answer Key Pdf Subtracting Rational Numbers Question 26.
Problem Solving The temperatures for five days in Kaktovik, Alaska, are given below.
-19.6 °F, -22.5 °F, -20.9 °F, -19.5 °F, -22.4 °F
Temperatures over the same 5-day period last year were 12 degrees lower. What were the highest and lowest temperatures over this period last year?
Answer:
If all temperatures were 12 degrees lower last year, then the highest/lowest temperature last year will be on the same day as the highest/Lowest temperature this year.
We can see that the lowest temperature this year is on the second day: -22.5° F, and that the highest temperature is on the fourth day: -19.5° F.
Since last year all temperatures were 12 degrees lower, we subtract 12 from the highest/lowest temperature this year.
-22.5 – 12 = -34.5
-19.5 – 12 = -31.5
The lowest temperature last year was -34.5° F.
The highest temperature last year was -31.5° F.

Question 27.
Make a Conjecture Must the difference between two rational numbers be a rational number? Explain.
Answer:
Yes, it must be a rational number.
We know that when we need to subtract one rational number from another, we need to find a common denominator, and then subtract numerators
Thus, our result will be a fraction.
Thus, a rational number

Question 28.
Look for a Pattern Evan said that the difference between two negative numbers must be negative. Was he right? Use examples to illustrate your answer.
Answer:
No, he was not right.
E.g.
–\(\frac{1}{4}\) – (-\(\frac{2}{4}\)) = –\(\frac{1}{4}\) + \(\frac{2}{4}\)
= \(\frac{1}{4}\)
If both numbers are negative, but minuend is greater than the subtracted, we will get a positive number as a result.

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 Unit 1 Study Guide Review Answer Key.

Texas Go Math Grade 7 Unit 1 Study Guide Review Answer Key

Texas Go Math Grade 7 Unit 1 Exercise Answer Key

Write each mixed number as a whole number or decimal. Classify each number by naming the set or sets to which it belongs: rational numbers, integers, or whole numbers. (Lessons 1.1, 1.2)

Question 1.
\(\frac{3}{4}\) _____________
Answer:

0.75 belongs to the set of rational numbers.

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

4 belongs to the set of integers. the set of whole numbers and the set of rational numbers.

Texas Go Math Grade 7 Unit 1 Answer Key Question 3.
\(\frac{11}{3}\) _______________
Answer:

\(3 . \overline{6}\) belongs to the set of rational numbers.

Question 4.
\(\frac{5}{2}\) _______________
Answer:

2.5 belongs to the set of rational numbers.

Find each sum or difference. (Lessons 1.3, 1.4)

Question 5.
-5 + 9.5 ____________
Answer:
= 9.5 – 5
= 4.5

Question 6.
\(\frac{1}{6}\) + (-\(\frac{5}{6}\)) ____________
Answer:
= \(\frac{1}{6}\) – \(\frac{5}{6}\)
= –\(\frac{4}{6}\)
= –\(\frac{2}{3}\)

Question 7.
-0.5 + (-8.5) _______________
Answer:
= -0.5 – 8.5
= -9

Question 8.
-3 – (-8) ___________
Answer:
= -3 + 8
= 5

Question 9.
5.6 – (-3.1) _________
Answer:
= 5.6 + 3.1
= 8.7

Unit 1 End of Unit Assessment Grade 7 Answer Key Question 10.
3\(\frac{1}{2}\) – 2\(\frac{1}{4}\) _____________
Answer:
Write mixed fractions as proper, then find a common denominator.
= \(\frac{7}{2}\) – \(\frac{9}{4}\)
= \(\frac{14-9}{4}\)
= \(\frac{5}{4}\)

Find each product or quotient. (Lessons 1.5, 1.6)

Question 11.
-9 × (-5) __________
Answer:
Product will be positive because signs are the same.
= 9 × 5
= 45

Question 12.
0 × (-7) ____________
Answer:
Any number multiplied by 0 is equal to 0.
= 0 × (-7)
= 0

Question 13.
-8 × 8 _____________
Answer:
The product will be negative because signs are different
= -(8 × 8)
= -64

Question 14.
– \(\frac{56}{8}\) _______________
Answer:
The quotient will be negative, because signs are different
= –\(\frac{56}{8}\)
= -7

Question 15.
\(\frac{-130}{-5}\) _____________
Answer:
The quotient will be positive, because signs are same.
= \(\frac{130}{5}\)
= 26

Unit 1 The Number System Answer Key 7th Grade Question 16.
\(\frac{34.5}{1.5}\) ______________
Answer:
Write decimal numbers as fractions:
\(\frac{\frac{345}{10}}{\frac{15}{10}}\)
Write complex fractions using division:
\(\frac{345}{10}\) ÷ \(\frac{15}{10}\)
Write using multiplication:
\(\frac{345}{10}\) × \(\frac{10}{15}\) = 23

Question 17.
–\(\frac{2}{5}\) (-\(\frac{1}{2}\)) (-\(\frac{5}{6}\)) ______________
Answer:
Find the product of first 2 factors. Both are negative, so the product is positive.
\(\frac{2}{5}\) (\(\frac{1}{2}\)) = \(\frac{1}{5}\)
Multiply the result by the third factor. One is negative, one is positive, so the product is negative.
–\(\frac{1}{5}\)(\(\frac{5}{6}\)) = –\(\frac{1}{6}\)

Question 18.
(\(\frac{1}{5}\)) (-\(\frac{5}{7}\)) (\(\frac{3}{4}\)) _____________
Answer:
Find the product of first 2 factors. One is negative, the other positive, so the product is negative.
–\(\frac{1}{5}\) (\(\frac{5}{7}\)) = –\(\frac{1}{7}\)
Multiply the result by the third factor. One is negative, one is positive, so the product is negative.
–\(\frac{1}{7}\) (\(\frac{3}{4}\)) = –\(\frac{3}{28}\)

Question 19.
Lei withdrew $50 from her bank account every day for a week. What was the change in her account in that week?
Answer:
Use negative number to represent withdrawal.
Find 7 × (-50):
7 × (-50) = -350
The change on Lei’s account that week was -$350.

Question 20.
In 5 minutes, a seal descended 24 feet. What was the average rate of change in the seal’s elevation per minute?
Answer:
Use negative number to represent descent in feet.
Find \(\frac{-24}{5}\):
\(\frac{-24}{5}\) = -4.8
Sears change in elevation is -4.8 feet per minute.

Texas Go Math Grade 7 Unit 1 Performance Task Answer Key

Question 1.
CAREERS IN MATH Urban Planner Armand is an urban planner, and he has proposed a site for a new town library. The site is between City Hall and the post office on Main Street.

The distance between City Hall and the post office is 6\(\frac{1}{2}\) miles. The library site is 1\(\frac{1}{4}\) miles closer to City Hall than it is to the post office.

a. Write 6\(\frac{1}{2}\) miles and 1\(\frac{1}{4}\) miles as decimals.
Answer:
First, write \(\frac{1}{2}\) and \(\frac{1}{4}\) as decimals.

Then, add 6 and 1 to the result respectively.
6\(\frac{1}{2}\) = 6 + 0.5 = 6.5 miles
1\(\frac{1}{4}\) = 1 + 0.25 = 1.25 miles

b. Let d represent the distance from City Hall to the library site. Write an expression for the distance from the library site to the post office.
Answer:
d* = distance from Library site to the Post Office
d* = d + 1.25

c. Write an equation that represents the following statement: The distance from City Hall to the library site plus the distance from the library site to the post office is equal to the distance from City Hall to the post office.
Answer:
d + d* = 6.5

d. Solve your equation from part c to determine the distance from City Hall to the library site, and the distance from the post office to the library site.
Answer:
d + d* = 6.5
d + d + 1.25 = 6.5
2d = 5.25
d = 2.625

d* = d + 1.25
d* = 2.625 + 1.25
d* = 3.875

Unit 1 End of Unit Assessment Grade 7 Answer Key Math Question 2.
Sumaya is reading a book with 240 pages. She has already read 90 pages. She plans to read 20 more pages each day until she finishes the book.
a. Sumaya writes the equation 330 = -20d to find the number of days she will need to finish the book. Identify the errors that Sumaya made.
Answer:
First, Sumaya added 90 to 240 instead of subtracting 90 from 240. This is a mistake because if she read 90 pages, that means she has 90 pages Less to read, not more.
Second mistake is the negative sign. If the equation results in how many days more she has to read, it can not be negative.

b. Write and solve an equation to determine how many days Sumaya will need to finish the book. In your answer, count part of a day as a full day.
Answer:
First, find out how many more pages she has to read:
240 – 90 = 150
Correct equation:
20d = 150
d = \(\frac{150}{20}\)
d = \(\frac{15}{2}\)
d = 7\(\frac{1}{2}\)
Sumaya will need 8 days to finish the book.

c. Estimate how many days you would need to read a book about the same length as Sumaya’s book. What information did you use to find the estimate?
Answer:
Let the book have the same number of pages. I would, for example, read 10 pages a day.
10d = 330
d = 33
It would take me 33 days to read the book.

Question 3.
Jackson works as a veterinary technician and earns $12.20 per hour.
a. Jackson normally works 40 hours a week. In a normal week, what is his total pay before taxes and other deductions?
Answer:
Find 40 × 12.20:
40 × 12.20 = 488
His total pay is $488.

b. Last week, Jackson was ill and missed some work. His total pay before deductions was $372.10. Write and solve an equation to find the number of hours Jackson worked.
Answer:
Find 372.10 ÷ 12.20
372.10 ÷ 12.20 = 30.5
Jackson worked 30.5 hours last week.

c. Jackson records his hours each day on a time sheet. Last week when he was ill, his time sheet was incomplete. How many hours are missing? Show your work.

Answer:
Find 40 – 30.5
40 – 30.5 = 9.5
Jackson missed 9.5 hours last week.

d. When Jackson works more than 40 hours in a week, he earns 1.5 times his normal hourly rate for each of the extra hours. Jackson worked 43 hours one week. What was his total pay before deductions? Justify your answer.
Answer:
His 40 hours pay is 488, as calculated iii a. He worked 43 – 40 = 3 hours overtime.
Find 3 × 12.20 × 1.5:
3 × 12.20 × 1.5 = 36.6 × 1.5
= 54.9
Now add 54.9 to his 10 hours pay.
Find 488 + 54.9:
488 + 54.9 = 5-12.9
Jackson’s pay that week was $542.9.

e. What is a reasonable range for Jackson’s expected yearly pay before deductions? Describe any assumptions you made in finding your answer.
Answer:
Let’s say that Jackson will be sick couple of days in a year, and he will work overtime couple of days in a year. When it all adds up, assumption is he will work 40 hours a week on average. There are 52 weeks in a year.
Find 488 × 52:
488 × 52 = 25376
Jackson will probably earn somewhere in between $25000 – $26000.

Texas Go Math Grade 7 Unit 1 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
What is -6\(\frac{9}{16}\) written as a decimal?
A. -6.625
B. -6.5625
C. -6.4375
D. -6.125
Answer:
B. -6.5625

First, write \(\frac{9}{16}\) as a decimal.

Then, add 6 to the result.
6 + 0.5625 = 6.5625
Now, since the starting number was negative, this one has to be negative too.
-6\(\frac{9}{16}\) = -6.5625

7th Grade Unit 1 Performance Task Answer Key Question 2.
Working together, 6 friends pick 14\(\frac{2}{5}\) pounds of pecans at a pecan farm. They divide the pecans equally among themselves. How many pounds does each friend get?
A. 20\(\frac{2}{5}\) pounds
B. 8\(\frac{2}{5}\) pounds
C. 4\(\frac{3}{5}\) pounds
D. 2\(\frac{2}{5}\) pounds
Answer:
D. 2\(\frac{2}{5}\) pounds

Start with dividing 14\(\frac{2}{5}\) by 6:
14\(\frac{2}{5}\) ÷ 6
Write mixed fraction as proper fraction:
\(\frac{72}{5}\) ÷ 6
Write using multiplication:
\(\frac{72}{5}\) × \(\frac{1}{6}\) = \(\frac{12}{5}\)
= 2\(\frac{2}{5}\)
Each friend gets 2\(\frac{2}{5}\) pounds.

Question 3.
What is the value of (-3.25)(-1.56)?
A. -5.85
B. -5.07
C. 5.07
D. 5.85
Answer:
C. 5.07

The product will, be positive, because both factors are negative:
= 3.25(1.56)
= 5.07

Question 4.
Ruby ate \(\frac{1}{3}\) of a pizza, and Angie ate \(\frac{1}{5}\) of the pizza. How much of the pizza did they eat in all?
A. \(\frac{1}{15}\) of the pizza
B. \(\frac{1}{8}\) of the pizza
C. \(\frac{3}{8}\) of the pizza
D. \(\frac{8}{15}\) of the pizza
Answer:
D. \(\frac{8}{15}\) of the pizza

We have to add how much Ruby ate, and how much Angie ate
\(\frac{1}{3}\) + \(\frac{1}{5}\) = \(\frac{5+3}{15}\)
= \(\frac{8}{15}\)
Ruby and Angie ate \(\frac{8}{15}\) of the pizza.

Question 5.
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime’s account after his deposit on Thursday?

A. $57.49
B. $59.65
C. $94.49
D. $138.93
Answer:
C. $94.49

Use positive numbers to represent the deposit. and negative numbers to represent withdrawal. Then, add it up to account balance before any deposits or withdrawals. 37.
37 + 17.42 – 12.60 – 9.62 + 62.29 = 54.42 – 12.60 – 9.62 + 62.29
= 41.82 – 9.62 + 62.29
= 32.2 + 62.29
= 94.49
The balance in Jaimes’s account on Friday was $94.49.

7th Grade Math Study Guide Answers Unit 1 Question 6.
A used motorcycle is on sale for $3,600. Erik makes an offer equal to of this price. How much does Erik offer for the motorcycle?
A. $4,800
B. $2,700
C. $2,400
D. $900
Answer:
B. $2,700

Start by multiplying 3600 and \(\frac{3}{4}\):
3600 × \(\frac{3}{4}\) = 2700
Erik offers $2700.

Question 7.
To which set or sets does the number -18 belong?
A. integers only
B. rational numbers only
C. integers and rational numbers only
D. whole numbers, integers, and rational numbers
Answer:
C. integers and rational numbers only

We can see that -18 does not belong in the set of whole numbers
Next, notice that -18 belongs to the set of integers. That implies it belongs in the set of rational numbers, since the set of integers is the subset of the set of rational numbers.

Question 8.
Mrs. Rodriguez is going to use 6\(\frac{1}{3}\) yards of material to make two dresses. The larger dress requires 3\(\frac{2}{3}\) yards of material. How much material will Mrs. Rodriguez have left to use on the smaller dress?
A. 1\(\frac{2}{3}\) yards
B. 2\(\frac{1}{3}\) yards
C. 2\(\frac{2}{3}\) yards
D. 3\(\frac{1}{3}\) yards
Answer:
C. 2\(\frac{2}{3}\) yards

Start by subtracting 3\(\frac{2}{3}\) = \(\frac{11}{3}\) from 6\(\frac{1}{3}\) = \(\frac{19}{3}\)
\(\frac{19}{3}\) – \(\frac{11}{3}\) = \(\frac{8}{3}\)
= 2\(\frac{2}{3}\)
Mrs. Rodriguez will have 2\(\frac{2}{3}\) yards of material to use on the smaller dress.

Grade 7 Unit 1 Practice Problems Answer Key Question 9.
Winslow buys 1.2 pounds of bananas. The bananas cost $1.29 per pound. To the nearest cent, how much does Winslow pay for the bananas?
A. $1.08
B. $1.20
C. $1.55
D. $2.49
Answer:
C. $1.55

Start by multiplying 1.2 by 1.29:
1.2 × 1.29 = 1.548
≈ 1.55
Vins1ow pays $1.55 for the bananas.

Gridded Response

Question 10.
Roberta earns $7.65 per hour. How many hours does Roberta need to work to earn $24.48?

Answer:
Given earning per hour = $7.65
Given total earning of Robert = $24.48

Hence, for the earning of $24.48, he needs to work for 3.2 hours
The table will be made as per the below instructions:
1st coLumn: mark * sign
2nd coLumn: mark 0
3rd coLumn: mark 0
4th column: mark 0
5th coLumn: mark 3
6th coLumn: mark 2
7th column: mark 0

7th Grade Math Unit 1 Test Study Guide Question 11.
What is the product of the following expression?
(-2.2)(1 .5)(-4.2)

Answer:
Given expression in problem: (-2.2)(1.5)(-4.2)
(-2.2)(1.5)(-4.2) = (-3.3)( 4.2)
= 13.86
The table will be made as per below instructions:
1st column: mark * sign
2nd column : mark 0
3rd column: mark 0
4th column : mark 1
5th column : mark 3
6th column: mark 8
7th column: mark 6

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

Question 12.
Victor is ordering pizzas for a party. He would like to have \(\frac{1}{4}\) of a pizza for each guest. He can only order whole pizzas, not part of a pizza. If he expects 27 guests, how many pizzas should he order?

Answer:
Portion of pizza for each guest = \(\frac{1}{4}\)
Total number of guest in party = 27
Number of guest in 1 pizza = \(\frac{1}{\frac{1}{4}}\) = 4
Required pizza for party = \(\frac{27}{4}\) = 6.75
But it is mentioned in question that we can onLy order whole pizza.The required amount of pizza for 27 guest is 6.75, So Victor will order 7 pizzas.
The table will be made as per below instructions:
1st coLumn: mark – sign
2nd column : mark 0
3rd column: mark 0
4th column : mark 0
5th column : mark 7
6th column: mark 0
7th column: mark 0

Texas Go Math Grade 7 Unit 1 Vocabulary Preview Answer Key

Use the puzzle to preview key vocabulary from this unit. Unscramble the circled letters within found words to answer the riddle at the bottom of the page.

1. Any number that can be written as a ratio of two integers. (Lesson 1-1)
2. A group of items. (Lesson 1-2)
3. A set that is contained within another set. (Lesson 1-2)
4. Decimals in which one or more digits repeat infinitely. (Lesson 1-1)
5. The opposite of any number. (Lesson 13)
6. Decimals that have a finite number of digits. (Lesson 1-1)

Question 1.
Why were the two fractions able to settle their differences peacefully?
Answer:
They were both ___ ___ ___ ___ ___ ___ ___ !

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 Lesson 2.1 Answer Key Unit Rates.

Texas Go Math Grade 7 Lesson 2.1 Answer Key Unit Rates

Texas Go Math Grade 7 Lesson 2.1 Explore Activity 1 Answer Key

Jeff hikes \(\frac{1}{2}\) mile every 15 minutes, or \(\frac{1}{4}\) hour. Lisa hikes \(\frac{1}{3}\) mile every 10 minutes, or \(\frac{1}{6}\) hour. How far do they each hike in 1 hour? 2 hours?

A. Use the bar diagram to help you determine how many miles Jeff hikes. How many \(\frac{1}{4}\)hours are in 1 hour? How far does Jeff hike in 1 hour?

B. Complete the table for Jeff’s hike.

C. Complete the bar diagram to help you determine how far Lisa hikes. How many miles does she hike in 1 hour?

D. Complete the table for Lisa’s hike.

Reflect

Question 1.
How did you find Jeff’s distance for \(\frac{3}{4}\) hour?
Answer:
I multiplied how many miles he walks in \(\frac{1}{4}\) by 3.

Unit Rates with Fractions 7th Grade Answer Key Question 2.
Which hiker walks farther in one hour? Which is faster?
Answer:
Both walkers walk 2 miles in 1 hour. Neither of them is faster than the other.

Your Turn

Question 3.
Paige mows \(\frac{1}{6}\) acre in \(\frac{1}{4}\) hour. How many acres does Paige mow per hour?
Answer:

Paige mows \(\frac{2}{3}\) acre per hour.

Question 4.
Greta uses 3 ounces of pasta to make \(\frac{3}{4}\) of a serving of pasta. How many ounces of pasta are there per serving?
Answer:

Greta uses 4 ounces of pasta per serving.

Question 5.
One tank is filling at a rate of \(\frac{3}{4}\) gallon per \(\frac{2}{3}\) minute. A second tank is filling at a rate of \(\frac{5}{8}\) gallon per \(\frac{1}{2}\) minute. Which tank is filling faster?
Answer:
First find rate in gallons per minute at which each tank is filling.

To find the unit rates, first rewrite the fractions.

To divide, multiply with the reciprocal.

Thus, Tank 2 is filling faster.

Texas Go Math Grade 7 Lesson 2.1 Guided Practice Answer Key

Question 1.
Brandon enters bike races. He bikes 8\(\frac{1}{2}\) miles every \(\frac{1}{2}\) hour. Complete the table to find how far Brandon bikes for each time interval. (Explore Activity)

Answer:

First, notice that every step of time is half an hour longer.
Thus. simply add the distance lie cross in half an hour to every successive distance box.
8\(\frac{1}{2}\) + 8\(\frac{1}{2}\) = 17
17 + 8\(\frac{1}{2}\) = 25\(\frac{1}{2}\)
25\(\frac{1}{2}\) + 8\(\frac{1}{2}\) = 34
34 + 8\(\frac{1}{2}\) = 42\(\frac{1}{2}\)

Find each unit rate. (Example 1)

Go Math Grade 7 Lesson 2.1 Answer Key Question 2.
Julio walks 3\(\frac{1}{2}\) miles in 1\(\frac{1}{4}\) hours.
Answer:
Determine the units of the rate.
The rate is the distance in mites per time in hours.
Find Julio’s rate of walking in distance walked per time.

Julio walks 2\(\frac{4}{5}\) miles per hour.

Question 3.
Kenny reads \(\frac{5}{8}\) page in \(\frac{2}{3}\) minute.
Answer:
Determine the units of the rate.
The rate is pages read per time in minutes.
Find Kenny’s rate of reading in pages read per time.

Kenny reads \(\frac{15}{16}\) pages per minute.

Question 4.
A garden snail moves \(\frac{1}{6}\) foot in \(\frac{1}{3}\) hour.
Answer:
Determine the units of the rate.
The rate is distance in feet per time in hours.
Find snails rate of moving in distance moved per time

Snail moves \(\frac{1}{2}\) foot per hour.

Question 5.
A fertilizer covers \(\frac{5}{8}\) square foot in \(\frac{1}{4}\) hour.
Answer:
Determine the units of the rate.
The rate is area covered in square feet per time in hours.
Find fertilizer’s rate of covering in area covered per time.

Fertilizer covers 2\(\frac{1}{2}\) square feet per hour.

Find each unit rate. Determine which is lower. (Example 2)

Lesson 2.1 Understand Unit Rate Answer Key Question 6.
Brand A: 240 mg sodium for \(\frac{1}{3}\) pickle or Brand B: 325 mg sodium for \(\frac{1}{2}\) pickle
Answer:
First find the rate in sodium per pickle at which each brand’s pickle contains sodium

To find the unit rates, first rewrite the fractions

To divide, multiply with the reciprocal

Thus, Brand 2’s pickles contain less sodium.

Question 7.
Ingredient C: \(\frac{1}{4}\) cup for \(\frac{2}{3}\) serving or Ingredient D: \(\frac{1}{3}\) cup for \(\frac{3}{4}\) serving
Answer:
First find rate in cup per serving at which each ingredient goes into the serving

To find the unit rates, first rewrite the fractions.

To divide, multiply with the reciprocal.

Thus, Ingredient C has a lower cup per serving rate.

Essential Question Check-In

Question 8.
How can you find a unit rate when given a rate?
Answer:
When we are given a rate, we need to divide one measurement with the other to get a unit rate.

Texas Go Math Grade 7 Lesson 2.1 Independent Practice Answer Key

Unit Rates with Fractions 7th Grade Answer Key Question 9.
The information for two pay-as-you-go cell phone companies is given.

a. What is the unit rate in dollars per hour for each company?
Answer:
First, find rate in dollars per hour at which each company bills phone calls

To find the unit rates, first rewrite the fractions

To divide, multiply with the reciprocal.

b. Analyze Relationships Which company offers the best deal? Explain your answer.
Answer:
Compare the unit rates.
On Cati \\\\Talk Time
2.84 \\\\\\\\> 2.5
Talk Time ¡s more affordable, because they charge Less for call.

c. What If? Another company offers a rate of $0.05 per minute. How would you find the unit rate per hour?
Answer:
We have to multiply the price by to 60 get dollars per hour.
0.05 × 60 = $3 per hour

d. Draw Conclusions Is the rate in part c a better deal than On Call or Talk Time? Explain.
Answer:
It is not, because they charge the most for a call, per hour.

Question 10.
Represent Real-World Problems Your teacher asks you to find a recipe that includes two ingredients with a rate of \(\frac{2 \text { units }}{3 \text { units }}\).
a. Give an example of two ingredients in a recipe that would meet this requirement.
Answer:
Corn flour and regular flour in unit of gram in a recipe for bread

b. If you needed to triple the recipe, would the rate change? Explain.
Answer:
The rate would not change. We would multiply both numerator and denominator by 3, that means the fraction would still have the same quotient.

Question 11.
A radio station requires DJs to play 2 commercials for every 10 songs they play. What is the unit rate of songs to commercials?
Answer:
First, divide number of songs by number of commercials.
10 ÷ 2 = 5
The unit rate of song to commercial is 5 songs for a commercial.

Go Math Book Grade 7 Answers How to find Unit Rate Question 12.
Multistep Terrance and Jesse are training for a long-distance race. Terrance trains at a rate of 6 miles every half hour, and Jesse trains at a rate of 2 miles every 15 minutes.
a. What is the unit rate in miles per hour for each runner?
Answer:
Find rate in miles per hour at which each runner trains.

To find the unit rates, first rewrite the fractions.

To divide, multiply with the reciprocal.

b. How long will each person take to run a total of 50 miles at the given rates?
Answer:
Divide each rate by 50.
Terrance:
\(\frac{50}{12}\) = \(\frac{25}{6}\)
= 4\(\frac{1}{6}\)
Jesse:
\(\frac{50}{8}\) = \(\frac{25}{4}\)
= 6\(\frac{1}{4}\)
Terrance would take 4\(\frac{1}{6}\) hours. Jesse would take 6\(\frac{1}{4}\) hours.

c. Sandra runs at a rate of 8 miles in 45 minutes. How does her unit rate compare to Terrance’s and to Jesse’s?
Answer:
Repeat as in a.

Sandra runs 10\(\frac{2}{3}\) miles per hour, which is faster than both Terrance and Jesse.

Go Math 7th Grade Lesson 2.1 Answer Key Pdf Question 13.
Analyze Relationships Eli takes a typing test and types all 300 words in an hour. He takes the test a second time and types the words in an hour. Was he faster or slower on the second attempt? Explain.
Answer:
He was faster the second time because he read the same number of words in less time.

H.O.T.S Focus On Higher Order Thinking

Question 14.
Justify Reasoning An online retailer sells two packages of protein bars.

a. Which package has the better price per bar?
Answer:
Divide the cost by the number of bars:
10-pack:
15.37 ÷ 10 = 1.537
≈ 1.54
12-pack:
15.35 ÷ 12 ≈ 1.28
12-pack has a better price per bar.

b. Which package has the better price per ounce?
Answer:
10-pack has 10 × 2.1 = 21 ounces
12-pack has 12 × 1.4 = 16.8 ounces
Without calculating we can see that the 10-pack has a better price per ounce, because the difference in cost is negligible, but the 10-pack has significantly more ounces.

c. Which package do you think is a better buy? Justify your reasoning.
Answer:
10-pack is a better buy. It does not matter which pack has a better price per bar, but the better price per ounce.

Question 15.
Check for Reasonableness A painter painted about half a room in half a day. Coley estimated the painter would paint 7 rooms in 7 days. Is Coley’s estimate reasonable? Explain.
Answer:
Coley’s estimate is reasonable. If the painter paints half a room in half a day, that means he paints a room in a day. Thus, he paints 7 rooms in 7 days.

Unit Rate Worksheet 7th Grade Answer Key Question 16.
Communicate Mathematical Ideas If you know the rate of a water leak in gallons per hour, how can you find the number of hours it takes for 1 gallon to leak out? Justify your answer.
Answer:
Divide 1 hour by the rate of a water leak.
E.g.
The rate of a water leak is 4 gallons per hour.
That means it will take \(\frac{1}{4}\) hour for 1 gallon to leak out.

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 Lesson 1.5 Answer Key Multiplying Rational Numbers.

Texas Go Math Grade 7 Lesson 1.5 Answer Key Multiplying Rational Numbers

Your Turn

Question 1.
Use a number line to find 2(-35). __________

Answer:
Start at 0 Move 3.5 units to the left 2 times.
The result is -7.

Go Math Grade 7 Lesson 1.5 Answer Key Question 2.
Find -3(-1.25). __________

Answer:
First, find the product 3(-1.25).
Start at 0. Move 1.25 units to the left two times.
The result is -3.75.
This shows that 3 groups of -1.25 equals -3.75.
So, -3 groups of -1.25 must equal the opposite of -3.75.
-3(-1.25) = 3.75

Reflect

Question 3.
Look for a Pattern You know that the product of two negative numbers is positive, and the product of three negative numbers is negative. Write a rule for finding the sign of the product of n negative numbers.
Answer:
The product of n negative numbers will be positive if n is even, or negative if n is odd.

Your Turn

Find each product.

Question 4.
(-\(\frac{3}{4}\)) (-\(\frac{4}{7}\)) (-\(\frac{2}{3}\))
Answer:
First, find the product of the first two factors. Both factors are negative, so their product will be positive.
(-\(\frac{3}{4}\)) (-\(\frac{4}{7}\)) = +(\(\frac{3}{4}\) . \(\frac{4}{7}\))
= \(\frac{3}{7}\)
Now, multiply the result, which is positive, by the third factor, which is negative. The product will be negative
\(\frac{3}{7}\) (-\(\frac{2}{3}\)) = \(\frac{3}{7}\) (-\(\frac{2}{3}\))
= –\(\frac{2}{7}\)

Question 5.
(-\(\frac{2}{3}\)) (-\(\frac{3}{4}\)) (\(\frac{4}{5}\))
Answer:
First, find the product of the first two factors Both factors are negative, so their product will be positive.
(-\(\frac{2}{3}\)) (-\(\frac{3}{4}\)) = + (\(\frac{2}{3}\) . \(\frac{3}{4}\))
= \(\frac{2}{4}\)
Now, multiply the result, which is positive, by the third factor, which is positive. The product will be positive.
\(\frac{2}{4}\) (\(\frac{4}{5}\)) = \(\frac{2}{4}\) (\(\frac{4}{5}\)) = \(\frac{2}{5}\)

Question 6.
(\(\frac{2}{3}\)) (-\(\frac{9}{10}\)) (\(\frac{5}{6}\))
Answer:
First, find the product of the first two factors. The first factor is positive, second is negative, so their product will be negative.
(\(\frac{2}{3}\)) (-\(\frac{9}{10}\)) = – (\(\frac{2}{3}\) . \(\frac{9}{10}\))
= –\(\frac{1}{2}\)
Now, multiply the result, which is negative, by the third factor, which is positive. The product will be negative.
–\(\frac{2}{5}\) (\(\frac{5}{6}\)) = –\(\frac{2}{5}\) (\(\frac{5}{6}\)) = –\(\frac{1}{3}\)

Texas Go Math Grade 7 Lesson 1.5 Guided Practice Answer Key 

Use a number line to find each product. (Example 1 and Example 2)

Question 1.
5(-\(\frac{2}{3}\)) = _____________

Answer:
Start at 0. Move \(\frac{2}{3}\) to the left 5 times.
The result is –\(\frac{10}{3}\).

Question 2.
3(-\(\frac{1}{4}\)) = ____________

Answer:
Start at 0. Move \(\frac{1}{4}\) to the left 5 times.
The result is –\(\frac{3}{4}\).

Go Math 7th Grade Lesson 1.5 Answer Key Question 3.
-3(-\(\frac{4}{7}\)) = ____________

Answer:
First find the product 3(-4\(\frac{4}{7}\)).
Start at 0. Move \(\frac{4}{7}\) units to the left 3 times.
The result is –\(\frac{12}{7}\).
This shows that 3 groups of –\(\frac{4}{7}\) equals –\(\frac{12}{7}\).
So, -3 groups of –\(\frac{4}{7}\) must equal to the opposite of –\(\frac{12}{7}\).
-3(-\(\frac{4}{7}\)) = \(\frac{12}{7}\)

Question 4.
–\(\frac{3}{4}\) (-4) = ______________

Answer:
Use the commutative property to swap multiplier and multiplicand.
-4(-\(\frac{3}{4}\))
First, find the product 4(-\(\frac{3}{4}\)).
Start at 0. Move \(\frac{3}{4}\) units to the left 4 times.
The result is -3.
This shows that 4 groups of –\(\frac{3}{4}\) equals -3.
So, -4 groups of –\(\frac{3}{4}\) must equal to the opposite of -3.
-4(-\(\frac{3}{4}\)) = 3

Question 5.
4 (-3) = ___________
Answer:
Start at 0. Move 3 to the left 4 times
The result is -12.

Question 6.
-1.8 (5) = __________
Answer:
Use commutative property to swap multiplier and multiplicand.
5(-1.8)
Start at 0. Move 1.8 to the left 5 times.
The result is -9.

Go Math Grade 7 Lesson 1.5 Multiplying Rational Numbers Question 7.
-2 (-3.4) = ____________
Answer:
First find the product 2(-3.4)
Start at 0. Move 3.4 units to the left 2 time&
The result is -6.8.
This shows that 2 groups of -3.4 equals -6.8.
So, -2 groups of -3.1 must equal to the opposite of -6.8.
-2(-3.4) = 6.8

Question 8.
0.54 (8) = ___________
Answer:
Given in problem : 0.54 (8) =
To find the product of 0.54 (8) on number line we will move 0.54 8 times on right of the number line because the product of 0.54 × 8 is positive.
The vaLue of: 0.54 × 8 = 4.32

Question 9.
-5 (- 1.2) = __________
Answer:
First, find the product 5(-1.2).
Start at 0. Move 1.2 units to the left 5 times.
The result is -6.
This shows that 5 groups of -1.2 equals -6.
So, -5 groups of -1.2 must equal to the opposite of -6.
-5(-1.2) = 6

Question 10.
-2.4 (3) = ____________
Answer:
Use commutative property to swap multiplier and multiplicand.
3(-2.4)
Start at 0. Move 2.4 to the left 3 times.
The result is -7.2.

Multiply. (Example 3)

Question 11.
\(\frac{1}{2}\) × \(\frac{2}{3}\) × \(\frac{3}{4}\) = _________ × \(\frac{3}{4}\) = __________
Answer:
First, find the product of the first two factors. Both factors are positive, so their product will be positive.
\(\frac{1}{2}\) × \(\frac{2}{3}\) = \(\frac{1}{3}\)
Now, muLtiply the result, which is positive, by the third factor, which is positive. The product will be positive.
\(\frac{1}{3}\) × \(\frac{3}{4}\) = \(\frac{1}{4}\)

Question 12.
–\(\frac{4}{7}\) (-\(\frac{3}{5}\)) (-\(\frac{7}{3}\)) = (__________) × (-\(\frac{7}{3}\)) = __________
Answer:
First, find the product of the first two factors. Both factors are negative, so their product wiLl be positive
-(\(\frac{4}{7}\)) (-\(\frac{3}{5}\)) = \(\frac{12}{35}\)
Now, muLtiply the resuLt, which is positive, by the third factor, which is negative. The product wilL be negative.
(\(\frac{12}{35}\)) (-\(\frac{7}{3}\)) = (\(\frac{12}{35}\)) × (-\(\frac{7}{3}\)) = –\(\frac{4}{5}\)

Question 13.
–\(\frac{1}{8}\) × 5 × \(\frac{2}{3}\) = __________
Answer:
First find the product of the first two factor & First factor is negative, second is positive, so their product will be negative.
–\(\frac{1}{8}\) × 5 × \(\frac{2}{3}\) = –\(\frac{5}{8}\)
Now, multiply the result, which is negative, by the third factor, which is positive. The product will be negative.
– \(\frac{5}{8}\) × \(\frac{2}{3}\) = –\(\frac{5}{12}\)

Go Math Grade 7 Lesson 1.5 Answer Key Rational Numbers Question 14.
–\(\frac{2}{3}\) (\(\frac{1}{2}\)) (-\(\frac{6}{7}\)) = ___________
Answer:
First, find the product of the first two factors. The first factor is negative, second is positive, so their product will be negative.
(-\(\frac{2}{3}\)) (\(\frac{1}{2}\)) = –\(\frac{1}{3}\)
Now, multiply the result, which is negative, by the third factor, which is negative. The product will be positive.
(-\(\frac{1}{3}\)) (-\(\frac{6}{7}\)) = \(\frac{2}{7}\)

Question 15.
The price of one share of Acme Company declined $3.50 per day for 4 days in a row. What is the overall change in the price of one share? (Example 1)
Answer:
Use negative number to represent the drop in price.
Find 4(-3.50).
Start at 0. Move 3.50 units to the left 4 times
The result is -14.
The overall change in the price of one share is -$14.

Question 16.
In one day, 18 people each withdrew $100 from an ATM machine. What is the overall change in the amount of money in the ATM machine? (Example 1)
Answer:
Use a negative number to represent money withdrawn from an ATM machine.
Find 18(-100).
Start at 0. Move 100 units to the left 18 times
The result is -1800
The overall change in the amount of money in the ATM machine is -$1800

Essential Question Check-In

Go Math Lesson 1.5 Worksheet Answer Key 7th Grade Question 17.
Explain how you can find the sign of the product of two or more rational numbers.
Answer:
If we have an even number of factors with a negative sign, the product will be positive.
If we have an odd number of factors with a negative sign, the product will be negative.

Texas Go Math Grade 7 Lesson 1.5 Independent Practice Answer Key 

Question 18.
Financial Literacy Sandy has $200 in her bank account.
a. If she writes 6 checks for exactly $19.98, what expression describes the change in her bank account?
Answer:
Use a negative number to represent money lost with checks.
6(- 19.98)

b. What is her account balance after the checks are cashed?
Answer:
We need to calculate the expression from a. and then subtract it from 200.
6(-19.98) = -119.88
200 – 119.88 = 80.12
Her account balance after the checks are cashed is $80.12

Question 19.
Communicating Mathematical Ideas Explain, in words, how to find the product of -4(-1.5) using a number line. Where do you end up?
Answer:
First, find the product 4(-1.5).
Start at 0. Move 1.5 units to the left 4 times.
The result is -6.
This shows that 4 groups of -1.5 equal -6.
So, -4 groups of -1.5 must equal to the opposite of -6.
-4(-1.5) = 6

Question 20.
Greg sets his watch for the correct time on Wednesday. Exactly one week later, he finds that his watch has lost 3~ minutes. What is the overall change in time after 8 weeks?
Answer:
Time Lost by Greg’s watch in 1 week = 3\(\frac{1}{4}\) min
Time Lost by watch in 8 weeks = 8 × Time lest in 1 week
= 8 × 3\(\frac{1}{4}\)
= 8 × \(\frac{13}{4}\)
= 26 min
Hence, the time lost in 8 weeks will be 26 minutes.

Go Math 7th Grade Lesson 1.5 Multiplying Rational Numbers Answers Key Question 21.
A submarine dives below the surface, heading downward in three moves. If each move downward was 325 feet, where is the submarine after it is finished diving?
Answer:
Use a negative number to represent the drop ¡n depth.
Find 3(-325).
Start at 0. Move 325 units to the left 3 times.
The result is -975.
The submarine after finishing diving is at -975 feet.

Question 22.
Multistep For Home Economics class, Sandra has 5 cups of flour. She made 3 batches of cookies that each used 1.5 cups of flour. Write and solve an expression to find the amount of flour Sandra has left after making the 3 batches of cookies.
Answer:
We need to calculate how many cups of flour she used on 3 batches of cookies, and then subtract it from how many cups of flour she has, which is 5.
5 – 3(1.5)
First find 3(1.5).
Start at 0. Move 1.5 units to the right 3 times.
The result is 4.5.
Sandra used 4.5 cups of flour for 3 batches of cookies.
5 – 3(1.5) = 5 – 4.5
= 0.5
Sandra has 0.5 batches of flour left.

Question 23.
Critique Reasoning In class, Matthew stated, “I think that a negative is like an opposite. That is why multiplying a negative times a negative equals a positive. The opposite of negative is positive, so it is just like multiplying the opposite of a negative twice, which is two positives.” Do you agree or disagree with this statement? What would you say in response to him?
Answer:
I agree with his statement
Let p. q be rational Opposite of p is q if p = -q. So negative q is the opposite of p

Question 24.
Kaitlin is on a long car trip. Every time she stops to buy gas, she loses 15 minutes of travel time. If she has to stop 5 times, how late will she be getting to her destination?
Answer:
Use negative number to represent loss of minutes.
Find 5(-15).
Start at 0. Move 15 units to the left 5 times.
The result is -75.
Kaitlin lost 75 minutes, that means she will be 75 minutes late.

Question 25.
The table shows the scoring system for quarterbacks in Jeremy’s fantasy football league. In one game, Jeremy’s quarterback had 2 touchdown passes, 16 complete passes, 7 incomplete passes, and 2 interceptions. How many total points did Jeremy’s quarterback score?

Answer:
Start by writing the expression of Jeremy’s quarterback using the table.
2(6) + 16(0.5) + 7(-0.5) + 2(-1.5) = 12 + 8 – 3.5 – 3
= 20 – 3.5 – 3
= 16.5 – 3
= 13.5
Jeremy’s quarterback scored 13.5 points.

H.O.T. Focus on Higher Order Thinking.

Question 26.
Represent Real-World Problems The ground temperature at Brigham Airport is 12 °C. The temperature decreases by 6.8 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?
Answer:
Ground temperature of Brigham Airport = 12°
Height of the plane flying above ground = 5 Km
It is given in the problem that for every increase in 1 km above the ground the temperature decreases by 68°
So, the decrease in temperature will be 5 × 6.8 = 340
Temperature outside the plane = 12 – 34 = 220
Hence, the temperature outside the plane which is flying at an altitude of 5 kilometers will be -22°.

Multiplication Patterns Lesson 1.5 Go Math Answer Key Grade 7 Question 27.
Identify Patterns The product of four numbers, a, b, c, and d, is a negative number. The table shows one combination of positive and negative signs of the four numbers that could produce a negative product. Complete the table to show the seven other possible combinations.

Answer:
We need to have an odd number of negative signs in a row.
Put +/— accordingly.

Question 28.
Reason Abstractly Find two integers whose sum is -7 and whose product is 12. Explain how you found the numbers.
Answer:
Those numbers are 3 and 4.
3 +( – 4) = 7
3 (4) = 12
So, both integers need to be negative, because their sum needs to be negative, but their product needs to be positive.
Now, we cannot look at numbers less than, for example, 12, because their product needs to be equal to 12.
After some time, we find that our wanted numbers are -3 and -4.

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 Lesson 1.2 Answer Key Relationships Between Sets of Rational Numbers.

Texas Go Math Grade 7 Lesson 1.2 Answer Key Relationships Between Sets of Rational Numbers

Your Turn

Classify each number by naming the set or sets to which it belongs.

Question 1.
-8
Answer:
Integer, rational

Question 2.
-102.55 ……….
Answer:
Rational

Go Math Grade 7 Pdf Practice and Homework Lesson 1.2 Answer Key Question 3.
\(\frac{9}{2}\)
Answer:
Rational

Question 4.
3
Answer:
Whole, integer, rational.

Reflect

Question 5.
Make a Conjecture Jared said that every prime number is an integer. Do you agree or disagree? Explain.
Answer:
True. Every prime number is a whole number and every whole number is an integer. We can conclude that prime numbers are a subset of the set of integers.

Your Turn

Question 6.
Tell whether the statement “Some rational numbers are integers” is true or false. Explain your choice.
Answer:
True Integers are a subset of the set of rational numbers. Thus, some rational numbers are integers.

Question 7.
Describe a real-world situation that is best described by the set of rational numbers.
Answer:
A group of 5 friends go out and stop for a pizza. Pizza has 8 slices and there are 5 of you. Thus, every member of the crew gets \(\frac{8}{5}\) slices which is equal to 1\(\frac{3}{5}\) slices.
∴ Sharing a pizza with friends.

Texas Go Math Grade 7 Lesson 1.2 Guided Practice Answer Key 

Classify each number by naming the set or sets to which it belongs. (Example 1)

Question 1.
5
whole number, __________
Answer:
whole number, integer, rational number

Question 2.
– \(\frac{3}{14}\)
Answer:
rational number

Question 3.
-23
integer __________
Answer:
integer, rational number

Question 4.
4.5
Answer:
rational number

Tell whether the given statement is true or false. Explain your choice. (Example 2)

Question 5.
All rational numbers are integers. True / False
Answer:
False.
All, integers are rational numbers, but not all rational numbers are integers.
For E.g. 1.3 is a rational number, but not an integer.

Go Math Grade 7 Lesson 1.2 Answer Key Question 6.
Some integers are whole numbers. True / False
Answer:
True.
A Set of whole numbers is a subset of the set of integers, which implies that some integers are whole numbers.

Identify the set of numbers that best describes each situation. Explain your choice. (Example 3)

Question 7.
the number of students in a school
The set of best _____________ describes the situation because
Answer:
The set of whole numbers best describes the situation because the school contains a counting number of students. The possible outcomes are 0, 1, 2, 3, 4,… Since it’s impossible to have a negative number of students or a fraction of a student, the set of whole numbers is the most precise description.

Question 8.
possible points in a certain board game (…-3, -2, -1,0, 1, 2, 3,…….)
The set of ________________________ best describes the situation because
Answer:
The set of integers best describes the situation because all. possible points in a certain board game are integers.

Points are rational numbers also, but since points cannot be a fraction, the set of integers is the most precise description.

integers, alt possible points in a certain board game are integers Points are rational numbers aLso, but since any point cannot be a fraction, the set of integers is the most precise description.

Essential Question Check-In

Question 9.
How can you represent how the sets of whole numbers, integers, and rational numbers are related to each other?
Answer:
We can represent the relation using Venn’s diagram.

Texas Go Math Grade 7 Lesson 1.2 Independent Practice Answer Key 

Classify each number by naming the set or sets to which it belongs.

Question 10.
-9
Answer:
integer, rational number

Question 11.
7.5
Answer:
rational number

Go Math Grade 7 Answer Key Sets of Rational Number Question 12.
789
Answer:
whole number, integer, rational number

Question 13.
5\(\frac{3}{4}\)
Answer:
rational number

Fill in each Venn diagram with the whole numbers from 1 to 15. Remember that a composite number is a whole number greater than 1 that is not a prime number.

Question 14.
Whole Numbers from 1 to 15

Answer:

Venn’s diagram is solved.

Go Math Lesson 1.2 Relationships Between Sets of Rational Numbers Question 15.
Whole Numbers from 1 to 15

Answer:

Venn’s diagram is solved.

Tell whether the given statement is true or false. Explain your choice.

Question 16.
All rational numbers are whole numbers.
Answer:
False.
A set of whole numbers is a subset of a set of rational numbers, but not vice versa.
E.g. 3 is a rational number, but not a whole number.

Question 17.
All whole numbers are integers.
Answer:
True.
Every whole number is included in the set of integers.
A set of whole numbers is a subset of the set of integers.

Question 18.
Some whole numbers are negative.
Answer:
False
Whole numbers are greater or equal to zero, which means they are not negative.

Go Math 7th Grade Pdf Lesson 1.2 Understand Rational Numbers Answer Key Question 19.
No positive numbers are integers.
Answer:
False.
A set of whole numbers is a subset of integers. Thus, some integers are positive.

Identify the set of numbers that best describes each situation. Explain your choice.

Question 20.
possible number of miles you can walk in 1 hour
Answer:
The set of rational numbers best describes the situation.
You can walk any whole number of miles per hour, but you can also walk a fraction of a miLe per hour.

Question 21.
possible number of marbles in a jar
Answer:
The set of whole numbers best describes the situation.

The jar may contain no marbles or any counting number of marbLes.

The possible numbers of marbLes O, 1, 2, 3,… are whole numbers.

Whole numbers are also integers and rational numbers.

But since there cannot be a negative or a fractional number of bills, the set of whole numbers is the most precise description.

Question 22.
Represent Real-World Problems Using what you know of rational numbers, describe a real-world situation where a doctor might use the set of rational numbers on a daily basis.
Answer:
A doctor may prescribe 1\(\frac{1}{2}\) of some kind of pill to a patient

Daily intake of pills.

H.O.T.S Focus on Higher Order Thinking

Question 23.
Communicate Mathematical Ideas The letters in the Venn Divisible by 2 Divisible by 3 diagram represent whole numbers. Describe the numbers you would find in Section c, Section d, and Section e.

Answer:
Section c – Whole numbers divisible by 3, and not divisibLe by 2 or 5
Section d – WhoLe numbers divisible by 2 and 5, and not divisible by 3. Thus, divisible by 10.
Section e – Whole numbers divisible by 2, 3 and 5 Thus, divisible by 30

Go Math Answer Key 7th Grade Rational Numbers Answer Key Question 24.
Analyze Relationships Explain how the set of integers differs from the set of whole numbers.
Answer:
Set of whole numbers is a subset of the set of integers. Thus, set of integers contains set of whole numbers, but also contains negative numbers {…, 3, 2, 1, 0, 1, 2, 3, …}

Question 25.
Justify Reasoning Explain why a mixed number is not in the set of integers or whole numbers.
Answer:
Mixed number is not in the set of integers or whole numbers, because it contains a proper fraction. Thus, mixed fraction is in the set of rational 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 Lesson 1.3 Answer Key Adding Rational Numbers.

Texas Go Math Grade 7 Lesson 1.3 Answer Key Adding Rational Numbers

Reflect

Question 1.
Explain how to determine whether to move right or left on the number line when adding rational numbers.
Answer:
If the second addend is positive, we move to the right If not, we move to the left.

Your Turn

Use a number line to find each sum.

Question 2.
3 + 1\(\frac{1}{2}\) = ___________

Answer:
Start at 3
Move 1\(\frac{1}{2}\) units to the right because the second addend is positive
The result is 4.5

Go Math Lesson 1.3 Answer Key 7th Grade Question 3.
-2.5 + (-4.5) = ____________

Answer:
Start at 2.5.
Move |-4.5| = |4.5| units to the left because the second addend is negative.
The result is -7.

Reflect

Question 4.
Do -3 + 2 and 2 + (-3) have the same sum? Does it matter if the negative number is the first addend or the second addend?
Answer:
Yes, they have the same sum equal to 6. It doesn’t matter since adding is commutative.
(a + b = b + a)

Question 5.
Make a Conjecture Do you think the sum of a negative number and a positive number will always be negative? Explain your reasoning.
Answer:
No, it will not always be negative.
If the absolute value of a negative number is greater than the absolute value of a positive number, then the sum will be negative.
The sum will be positive ¡n other cases, expect when the absolute values are the same, then the sum will be equal to zero.

Your Turn

Use a number line to find each sum.

Question 6.
-8 + 5 = __________

Answer:
Start at -8.
Move 5 units to the right because the second addend is positive
The result is -3.

Question 7.
\(\frac{1}{2}\) + (-\(\frac{3}{4}\)) __________

Answer:
Start at \(\frac{1}{2}\).
Move |-\(\frac{3}{4}\)| = \(\frac{3}{4}\) units to the left because the second addend ¡s negative.
The result is –\(\frac{1}{4}\).

Go Math Grade 7 Lesson 1.3 Answer Key Question 8.
-1 + 7 = ____________

Answer:
Start at -1.
Move 7 units to the right because the second added is positive
The result is 6.

Your Turn

Use a number line to find each sum.

Question 9.
2\(\frac{1}{2}\) + (-2\(\frac{1}{2}\)) = ___________

Answer:
Start at 2\(\frac{1}{2}\).
Move |-2\(\frac{1}{2}\)| = 2\(\frac{1}{2}\) units to the left because the second addend is negative.
The result is 0.

Question 10.
-4.5 + 4.5 = _________

Answer:
Start at -4.5.
Move 4.5 units to the right because the second addend is positive.
The result is 0.

Your Turn

Find each sum.

Question 11.
-1.5 + 3.5 + 2 = ____________
Answer:
Start by grouping numbers with the same sign.
= -1.5 – (3.5 + 2) ………… (1)
= -1.5 – 5.5 …………. (2)
= 4 …………. (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Question 12.
3\(\frac{1}{4}\) + (-2) + (-2\(\frac{1}{4}\)) = __________
Answer:
Start by grouping numbers with the same sign.
= 3\(\frac{1}{4}\) + ((-2) + (-2\(\frac{1}{4}\))) …………. (1)
= 3\(\frac{1}{4}\) + (-4\(\frac{1}{4}\)) ………….. (2)
= -1 …………. (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Go Math Grade 7 Pdf Algebra Lesson 1.3 Properties Answer Key Question 13.
-2.75 + (-3.25) + 5 = _________
Answer:
Start by grouping numbers with the same sign.
= (-2.75 + (-3.25)) + 5 …………….. (1)
= -6 + 5 ………… (2)
= -1 ………… (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Question 14.
15 + 8 + (-3) = ___________
Answer:
Start by grouping numbers with the same sign.
= (15 + 8) + (-3) ……………. (1)
= 23 + (-3) ………… (2)
= 20 …………… (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Texas Go Math Grade 7 Lesson 1.3 Guided Practice Answer Key

Use a number line to find each sum. (Example 1 and Example 2)

Question 1.
-3 + (-1.5) = ___________

Answer:
Start at -3.
Move |-1.5| = 1.5 units to the left because the second addend is negative.
The result is -4.5.

Question 2.
1.5 + 3.5 = ___________

Answer:
Start at 1.5.
Move 3.5 units to the right because the second addend is positive.
The result is 5.

Question 3.
\(\frac{1}{4}\) + \(\frac{1}{2}\) = ___________

Answer:
Start at \(\frac{1}{4}\)
Move \(\frac{1}{2}\) units to the right because the second addend is positive.
The result is \(\frac{3}{4}\).

Question 4.
-1\(\frac{1}{2}\) + (-1\(\frac{1}{2}\)) = ____________

Answer:
Start at -1\(\frac{1}{2}\).
Move |-1\(\frac{1}{2}\)| = 1\(\frac{1}{2}\) units to the left because the second addend is negative.
The result is -3.

Go Math 7th Grade Lesson 1.3 Add Fractions Question 5.
3 + (-5) = __________

Answer:
Start at 3.
Move |-5 | = 5 units to the left because the second addend is negative.
The resuLt is -2.

Question 6.
-1.5 + 4 = ___________

Answer:
Start at -1.5
Move 4 units to the right because the second addend ¡s posit ive
The result is 2.5.

Question 7.
Victor borrowed $21.50 from his mother to go to the theater. A week later, he paid her $21.50 back. How much does he still owe her? (Example 3)
Answer:
Use a positive number to represent money Victor borrowed from his mother and a negative number to represent money Victor paid back.
Find 21.5 + (-21.5).
Start at 21.5.
Move |-21.5| = 21.5 units to the left because the second addend is negative.
The result is 0. That means he no longer owes her money.

Victor owes his mother $0.

Question 8.
Sandra used her debit card to buy lunch for $8.74 on Monday. On Tuesday, she deposited $8.74 back into her account. What is the overall increase or decrease in her bank account? (Example 3)
Answer:
We use a positive number to represent the money she deposited into her account, and a negative number to represent the money she spent to buy Lunch.
Find -8.74 + 8.74.
Start at – 8.74.
Move 8.74 units to the right because the second addend is positive.
The result is 0. That means there is no increase or decrease.

There is no increase or decrease.

Find each sum without using a number line. (Example 4)

Question 9.
2.75 + (-2) + (-5.25) = __________
Answer:
Start by grouping numbers with the same sign.
= 2.75 + ((-2) + (-5.25)) …………. (1)
= 2.75 + (-7.25) …………. (2)
= -4.5 ………… (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Question 10.
-3 + (1\(\frac{1}{2}\)) + (2\(\frac{1}{2}\)) = ____________
Answer:
Start by grouping numbers with the same sign.
= -3+ ((1\(\frac{1}{2}\)) + (2\(\frac{1}{2}\)) ………… (1)
= -3 + (4) ………….(2)
= 1 …………. (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Go Math Grade 7 Lesson 1.3 Rational Numbers Question 11.
-12.4 + 9.2 + 1 = ___________
Answer:
Start by grouping numbers with the same sign.
= -12.4 + (9.2 + 1) ………… (1)
= -12.4 + (10.2) ………….(2)
= -2.2 …………. (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Question 12.
-12 + 8 + 13 = ____________
Answer:
Start by grouping numbers with the same sign.
= -12 + (8 + 13) ………… (1)
= -12 + (21) ………….(2)
= 9 …………. (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Question 13.
4.5 + (-12) + (-4.5) = ____________
Answer:
Start by grouping numbers with the same sign.
= 4.5 + ((-12) + (-4.5)) ………… (1)
= 4.5 + (-16.5) ………….(2)
= -12 …………. (3)
(1) Associative property
(2) Add the numbers inside the parentheses.

Question 14.
\(\frac{1}{4}\) + (-\(\frac{3}{4}\)) = __________
Answer:
= – \(\frac{2}{4}\) …………… (1)
= – \(\frac{1}{2}\) …………… (2)
(1) Cancel fraction.

Question 15.
-4\(\frac{1}{2}\) + 2 = _____________
Answer:
= -2\(\frac{1}{2}\)

Question 16.
-8 + (-1\(\frac{1}{8}\)) = ___________
Answer:
= -9\(\frac{1}{8}\)

Essential Question Check-In

Question 17.
How can you use a number line to find the sum of -4 and 6?
Answer:
Start at the -4.
Move |6| = 6 units to the right because the second added is positive.
The result is 2.

Texas Go Math Grade 7 Lesson 1.3 Independent Practice Answer Key

Question 18.
Samuel walks forward 19 steps. He represents this movement with a positive 19. How would he represent the opposite of this number?
Answer:
He would represent the opposite of positive 19 with negative 19: -19

Go Math Lesson 1.3 7th Grade Add Fractions Question 19.
Julia spends $2.25 on gas for her lawn mower. She earns $15.00 mowing her neighbor’s yard. What is Julia’s profit?
Answer:
Julia earns $15.00 and spends/Loses $2.25. That means we have to add $15 to her gas expenses of $2.25.
-2.25 + 15 = 12.75
Julia’s profit is $12.75

Question 20.
A submarine submerged at a depth of -35.25 meters dives an additional 8.5 meters. What is the new depth of the submarine?
Answer:
If a submarine is at a depth of -35.25 meters, and dives an additional 8.5 meters, that means we have to add another -8.5 meters to original depth.
-35.25 + (-8.5) = -43.75
New depth of the submarine is -43.75 meters.

Question 21.
Renee hiked for 4\(\frac{3}{4}\) miles. After resting, Renee hiked back along the same route for 3\(\frac{1}{4}\) miles. How many more miles does Renee need to hike to return to the place where she started?
Answer:
We conclude that Renee has to hike 4\(\frac{3}{4}\) miles back. She already hiked 3\(\frac{1}{4}\) in opposite direction. To find out how many miles more Renee has to hike, we have to add negative 3\(\frac{1}{4}\) to 4\(\frac{3}{4}\).
4\(\frac{3}{4}\) + (-3\(\frac{1}{4}\)) = 1\(\frac{2}{4}\)
= 1\(\frac{1}{2}\) miles
(1) Cancel fraction.

Question 22.
Geography The average elevation of the city of New Orleans, Louisiana, is 0.5 m below sea level. The highest point in Louisiana is Driskill Mountain at about 163.5 m higher than New Orleans. How high is Driskill Mountain?
Answer:
The elevation of New Orleans is -0.5 meters. Driskill Mountain is at 163.5 m higher than New OrLeans To find out how high is Driskitl Mountain, we have to add -0.5 to 163.5.
163.5 + (-0.5) = 163
Driskill mountain is 163 m high.

Question 23.
Problem Solving A contestant on a game show has 30 points. She answers a question correctly to win 15 points. Then she answers a question incorrectly and loses 25 points. What is the contestant’s final score?
Answer:
If the contestant starts with 30 points, then wins 15 points and Lastly loses 25 points, or wins -25 points, we add 30, 15 and -25 together
30 + 15 + (-25) = 45 + (-25)
= 20
Contestant’s final score is 20 points.

Financial Literacy Use the table for 24-26. Kameh owns a bakery. He recorded the bakery income and expenses in a table.

Question 24.
In which months were the expenses greater than the income? Name the month and find how much money was lost.
Answer:
We can easily Look at the table and find where the expenses are greater than the income.
These months are January and February.
Calculate each month separately by adding expenses and negative income.
January:
1290.60 + (-1205) = 85.60
February:
1345.44 + (-1183) = 162.44

January: $85.60, February: $162.44

Question 25.
In which months was the income greater than the expenses? Name the months and find how much money was gained each of those months.
Answer:
We can easily Look at the table and find where the income is greater than the expenses.
These months are: June, July, August
Calculate each month separately by adding income and negative expenses.
June: 2413 + (-2106.23) = 309.77
July: 2260 + (-1958.50) = 301.50
August: 2183 + (-1845.12) = 337.88

June: $309.77, July: $301.50, August: $337.88

Question 26.
Communicate Mathematical Ideas If the bakery started with an extra $250 from the profits in December, describe how to use the information in the table to figure out the profit or loss of money at the bakery by the end of August. Then calculate the profit or loss.
Answer:
To determine the profit of these 6 months. we add how much has bakery gained/lost money per month.
-85.60 + (- 162.44) + 0+ 309.77 + 301.50 + 337.88 = 218.01 + 0 + 309.7 + 301.50 – 337.88
= -248.04 + 309.77 + 301.50 + 337.88
= 61.73 + 301.50 + 337.88
= 363.23 + 337.88
= 710.11
Finally, we add the profit from December ($250) and the profit/loss of these 6 months.
250 + 710.11 = 951.11
The bakery has a profit of $951.11.

Question 27.
Vocabulary -2 is the ______________ of 2.
Answer:
-2 is the opposite of 2.

Question 28.
The basketball coach made up a game to play where each player takes 10 shots at the basket. For every basket made, the player gains 10 points. For every basket missed, the player loses 15 points.
a. The player with the highest score sank 7 baskets and missed 3. What was the highest score?
Answer:
First, we have to add 10 points 7 times, then add -15 points 3 times.
10 + 10 + 10 + 10 + 10 + 10 + 10 + (-15) + (-15) + (-15) = ………. = 70 + (-35)
= 35

b. The player with the lowest score sank 2 baskets and missed 8. What was the lowest score?
Answer:
10 + 10 + (-15) + (-15) + (-15) + (-15) + (-15) + (-15) + (-15) + (-15) = ……. = 20 + (-120)
= -100

c. Write an expression using addition to find out what the score would be if a player sank 5 baskets and missed 5 baskets.
Answer:
First, we have to add 10 points 5 times, then add -15 points 5 times.
10 + 10 + 10 + 10 + 10 + (-15) + (-15) + (-15) + (-15) + (-15) = ….. = 50 + (-105)
= -65

H.O.T.S Focus on Higher Order Thinking

Question 29.
Communicate Mathematical Ideas Explain the different ways it is possible to add two rational numbers and get a negative number.
Answer:
We can get a negative number if both addends are negative. Also, if only one addend is negative, then its absolute value must be greater than the second addend’s absolute value.

Question 30.
Explain the Error A student evaluated -4 + x for x = -9\(\frac{1}{2}\) and got the answer of 5\(\frac{1}{2}\). What might the student have done wrong?
Answer:
The student might have overseen that the x is negative and calculated as the x was equal to 9\(\frac{1}{2}\).

Lesson 1.3 Add Fractions Go Math Grade 7 Question 31.
Draw Conclusions Can you find the sum [5.5 + (-2.3)] + (-5.5 + 2.3) without performing any additions?
Answer:
Yes, we can find the sum without performing any addition.
We can see that the square brackets don’t have any use in the expression.
Then, we can move -5.5 to its own bracket and separate it from 2.3, nothing will change.
Now we have:
5.5 + (-2.3) + (-5.5) + 2.3
Now, reorganize the expression by changing places of the 2 inner addends.
5.5 + (-5.5) + (-2.3) + 2.3
It’s easy to see that we are adding 2 pairs of opposite numbers. Since the sum of opposite numbers is equal to zero, the sum of our expression is equal to zero.

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 Lesson 1.1 Answer Key Rational Numbers and Decimals.

Texas Go Math Grade 7 Lesson 1.1 Answer Key Rational Numbers and Decimals

Texas Go Math Grade 7 Lesson 1.1 Explore Activity Answer Key

A. Use a calculator to find the equivalent decimal form of each fraction. Remember that numbers that repeat can be written as 0.333… or 0.\(\overline{3}\).

B. Now find the corresponding fraction of the decimal equivalents given in the last two columns in the table. Write the fractions in simplest form.

C. Conjecture What do you notice about the digits after the decimal point in the decimal forms of the fractions? Compare notes with your neighbor and refine your conjecture if necessary.

Reflect

Question 1.
Consider the decimal 0.101001000100001000001… Do you think this decimal represents a rational number? Why or why not?
Answer:
This decimal. number does not represent a rational number because it racks a repeating pattern.

Go Math Grade 7 Lesson 1.1 Rational Number Answers Question 2.
Do you think a negative sign affects whether or not a number is a rational number? Use –\(\frac{8}{5}\) as an example.
Answer:
No, a negative sign does not affect whether or not a number is a rational number.
– \(\frac{8}{5}\) = \(\frac{-8}{5}\)
No, – \(\frac{8}{5}\) = \(\frac{-8}{5}\)

EXPLORE ACTIVITY (cont’d)

Question 3.
Do you think a mixed number is a rational number? Explain.
Answer:
Yes, a mixed number is a rational number because it can be written as a simpLe fraction.
For exampLe,
2 \(\frac{1}{4}\) = \(\frac{9}{4}\)

Your Turn

Write each rational number as a decimal.

Question 4.
\(\frac{4}{7}\) ___________
Answer:
Complete the long division.
Stop when you discover a pattern.

= \(0 . \overline{571428}\)

Question 5.
\(\frac{1}{3}\) ___________
Answer:
Complete the long division.
Stop when you discover a pattern.

= \(0 . \overline{3}\)

Rational Numbers Test Grade 7 Pdf Go Math Question 6.
\(\frac{9}{20}\) __________
Answer:
Complete the long division.

= 0.45

Question 7.
Yvonne made 2\(\frac{3}{4}\) quarts of punch. Write 2\(\frac{3}{4}\) as a decimal. 2\(\frac{3}{4}\) = _________ Is the decimal equivalent a terminating or repeating decimal
Answer:
First, write \(\frac{3}{4}\) as a decimal.

Then, add 2 to the result.
2 + 0.75 = 2.75
The decimal equivalent is a terminating decimal.
2.75, The decimal equivalent is a terminating decimal.

Question 8.
Yvonne bought a watermelon that weighed 7\(\frac{1}{3}\) pounds. Write 7\(\frac{1}{3}\) as a decimal. 7\(\frac{1}{3}\) = __________
Is the decimal equivalent a terminating or repeating decimal?
Answer:
First, write \(\frac{1}{3}\) as a decimal.

Then, add 7 to the result.
7 + \(0 . \overline{3}\) = \(7 . \overline{3}\)
The decimal equivalent is a terminating decimal.
\(7 . \overline{3}\) , The decimal equivalent is a repeating decimal.

Texas Go Math Grade 7 Lesson 1.1 Guided Practice Answer Key

Write each rational number as a decimal. Then tell whether each decimal is a terminating or a repeating decimal. (Explore Activity and Example 1)

Question 1.
\(\frac{3}{5}\) = ____________
Answer:
Complete the long division.

The decimal equivalent is a terminating decimal.
0.6; Terminating decimal.

Question 2.
\(\frac{89}{100}\) = _____________
Answer:
Complete the long division.

The decimal equivalent is a terminating decimal.
0.89; Terminating decimal.

Go Math Workbook Grade 7 Answer Key Rational Numbers Question 3.
\(\frac{4}{12}\) = ______________
Answer:
Complete the long division.
Stop when you discover a pattern.

The decimal equivalent is a repeating decimal.
\(0 . \overline{3}\) ; Repeating decimal.

Question 4.
\(\frac{25}{99}\) = ______________
Answer:
Complete the long division.
Stop when you discover a pattern.

The decimal equivalent is a repeating decimal.
\(0 . \overline{25}\) ; Repeating decimal.

Question 5.
\(\frac{7}{9}\) = ____________
Answer:
Complete the long division.
Stop when you discover a pattern.

The decimal equivalent is a repeating decimal.
\(0 . \overline{7}\) ; Repeating decimal.

Question 6.
\(\frac{9}{25}\) = ____________
Answer:
Complete the long division.

The decimal equivalent is a terminating decimal.
0.36; Terminating decimal.

Question 7.
\(\frac{1}{25}\) = ___________
Answer:
Complete the long division.

The decimal equivalent is a terminating decimal.
0.04; Terminating decimal.

Question 8.
\(\frac{25}{176}\) = ____________
Answer:
Complete long division.
Stop when you discover a pattern.
This case is special because the first. four decimals are not a part of the pattern that occurs after them.

The decimal equivalent is a repeating decimal.
\(0.1420 \overline{45}\) ; Repeating decimal.

Go Math Answer Key Grade 7 Lesson 1.1 Rational Numbers As Decimals Question 9.
\(\frac{12}{1,000}\) = _____________
Answer:
Complete the long division.

The decimal equivalent is a terminating decimal.
0.012; Terminating decimal.

Write each mixed number as a decimal. (Example 2)

Question 10.
11\(\frac{1}{6}\) = ___________
Answer:
First, write \(\frac{1}{6}\) as a decimal.

Then, add 11 to the result.
11 + \(0.1 \overline{6}\) = \(11.1 \overline{6}\)
= \(11.1 \overline{6}\)

Question 11.
2\(\frac{9}{10}\) = ____________
Answer:
First, write \(\frac{9}{10}\) as a decimal.

Then, add 2 to the result.
2 + 0.9 = 2.9
= 2.9

Question 12.
8\(\frac{23}{100}\) = _____________
Answer:
First, write \(\frac{23}{100}\) as a decimal.

Then, add 8 to the result.
8 + 0.23 = 8.23
8.23

Question 13.
7\(\frac{3}{15}\) = ___________
Answer:
First, write \(\frac{3}{15}\) as a decimal.

Then, add 7 to the result.
7 + 0.2 = 7.2
= 7.2

Question 14.
54\(\frac{3}{11}\) = ____________
Answer:
First, write \(\frac{3}{11}\) as a decimal.

Then, add 54 to the result.
54 + \(0 . \overline{27}\) = \(54 . \overline{27}\)
= \(54 . \overline{27}\)

Question 15.
3\(\frac{1}{18}\) = _________
Answer:
First, write \(\frac{1}{18}\) as a decimal.

Then, add 3 to the result.
3 + \(0.0 \overline{5}\) = \(3.0 \overline{5}\)
= \(3.0 \overline{5}\)

Question 16.
Maggie bought 3\(\frac{2}{3}\) lb of apples to make some apple pies. What is the weight of the apples written as a decimal? (Example 2)
3\(\frac{2}{3}\) = ______________
Answer:
First, write \(\frac{2}{3}\) as a decimal.

Then, add 3 to the result.
3 + \(0 . \overline{6}\) = \(3 . \overline{6}\)
Maggie bought \(3 . \overline{6}\) lb of apples.

Rational Numbers Answer Key Go Math Grade 7 Question 17.
Harry’s dog weighs 12\(\frac{7}{8}\) pounds. What is the weight of Harry’s dog written as a decimal? (Example 2)
12 \(\frac{7}{8}\) = _____________
Answer:
First, write \(\frac{7}{8}\) as a decimal.

Then, add 12 to the result.
12 + 0.875 = 12.875
Harry’s dog weighs 12.875 pounds.

Essential Question Check-In

Question 18.
Tom is trying to write \(\frac{3}{47}\) as a decimal. He used long division and divided until he got the quotient 0.0638297872, at which point he stopped. Since the decimal doesn’t seem to terminate or repeat, he concluded that \(\frac{3}{47}\) is not rational. Do you agree or disagree? Why?
Answer:
Tom was wrong to conclude that \(\frac{3}{47}\) is not rational. First of all. \(\frac{3}{47}\) is a fraction. Thus, \(\frac{3}{47}\) is a rational number. After some time of long division, the patter would appear.
I disagree. \(\frac{3}{47}\) is a rational number.

Texas Go Math Grade 7 Lesson 1.1 Independent Practice Answer Key

Use the table for 19-23. Write each ratio in the form \(\frac{a}{b}\) and then as a decimal. Tell whether each decimal is a terminating or a repeating decimal.

Question 19.
basketball players to football players
Answer:
\(\frac{5}{11}\) is the ratio of basketball players to football players.

The equivalent decimal is a repeating decimal.
\(\frac{5}{11}\) = \(0 . \overline{45}\); repeating decimal

Question 20.
hockey players to lacrosse players
Answer:
\(\frac{6}{10}\) is the ratio of basketball players to football players.

The equivalent decimal is a terminating decimal.
\(\frac{6}{10}\) = 0.6; terminating decimal.

Question 21.
polo players to football players
Answer:
\(\frac{4}{11}\) is the ratio of polo players to football players.

The equivalent decimal is a repeating decimal.
\(\frac{4}{11}\) = \(0 . \overline{36}\); repeating decimal.

Question 22.
lacrosse players to rugby players
Answer:
\(\frac{10}{15}\) is the ratio of basketball lacrosse players to football players.

The equivalent decimal is a repeating decimal.
\(\frac{10}{15}\) = \(0 . \overline{6}\); repeating decimal.

Question 23.
football players to soccer players
Answer:
\(\frac{11}{11}\) is the ratio of football players to soccer players.

The equivalent decimal is a terminating decimal (.0).
\(\frac{11}{11}\) = 1; terminatimg decimal.

Question 24.
Look for a Pattern Beth said that the ratio of the number of players in any sport to the number of players on a lacrosse team must always be a terminating decimal. Do you agree or disagree? Why?
Answer:
I agree. The number of lacrosse players on a team is equal to 10. Since in any other sport the number of players on a team must be a whole number. Thus, by dividing any whole number by 10. you just “ move” the decimal point one spot to the left.
Example: Number of soccer players on a team is 11.
The ratio of soccer players on a team to lacrosse players on a team is \(\frac{11}{10}\)

The ratio will always have a terminating decimal.

Go Math Grade 7 Lesson 1.1 Answer Key Grade 7 Question 25.
Yvonne bought 4\(\frac{7}{8}\) yards of material to make a dress.
a. What is 4\(\frac{7}{8}\) written as an improper fraction?
Answer:
4 × 8 + 7 = 39
4\(\frac{7}{8}\) = \(\frac{39}{8}\)

b. What is 4\(\frac{7}{8}\) written as a decimal?
Answer:
First, write \(\frac{7}{8}\) as a decimal.

Then, add 4 to the result
4 + 0.875 = 4.875

c. Communicate Mathematical Ideas If Yvonne wanted to make 3 dresses that use 4\(\frac{7}{8}\) yd of fabric each, explain how she could use estimation to make sure she has enough fabric for all of them.
Answer:
Yvonne could multiply 4\(\frac{7}{8}\) by 3 and then buy some more yards (1 or 2) of fabric to ensure she would have enough to make 3 dresses.

Question 26.
Vocabulary A rational number can be written as the ratio of one _________ to another and can be represented by a repeating or ________ decimal.
Answer:
A rational number can be written as the ratio of one integer to another and can be represented by a repeating or a terminating decimal.

Question 27.
Problem Solving Marcus is 5\(\frac{7}{24}\) feet tall. Ben is 5\(\frac{5}{16}\) feet tall. Which of the two boys is taller? Justify your answer.
Answer:
Since both boys are 5 and something feet tall, we can just compare the fractions in the mixed numbers to find out which boy is taller.
Compare it by reducing to a common denominator or converting it to a decimal number.
Since it is not so easy to convert those fractions to decimal numbers we will reduce to a common denominator.

Ben is taller than Marcus.

Question 28.
Represent Real-World Problems If one store is selling \(\frac{3}{4}\) of a bushel of apples for $9, and another store is selling \(\frac{2}{3}\) of a bushel of apples for $9, which store has the better deal? Explain your answer.
Answer:
They both offer some amount of apples for the same price of $9.
The store which offers a greater amount of tipples for the price of $9 has the better deal.
Convert fractions to decimal numbers.

The first store has a better offer.

Question 29.
Analyze Relationships You are given a fraction in simplest form. The numerator is not zero. When you write the fraction as a decimal, it is a repeating decimal. Which numbers from 1 to 10 could be the denominator?
Answer:
The denominator could be a prime number (except 2 and 5) or a number that has a prime number in its factored form (again except 2 and 5).
These numbers from 1 to 10 are: 3, 6 = 2 × 3, 7, 9 = 3 × 3

Question 30.
Communicate Mathematical Ideas Julie got 21 of the 23 questions on her math test correct. She got 29 of the 32 questions on her science test correct. On which test did she get a higher score? Can you compare the fractions \(\frac{21}{23}\) and \(\frac{29}{32}\) by comparing 29 and 21 ? Explain. How can Julie compare her scores?.
Answer:
Divide the number of correct answers to the number of alt questions on both tests (round to 3 decimal digits).
Compare those decimaL numbers to see on which test she scored better
21 ÷ 23 = 0.913
29 ÷ 32 = 0.906
0.913 > 0.906
She got a higher score on the first test.
You can not compare those fractions by comparing 29 and 21 because the denominators are not equal. You could do that if they were equal.

Question 31.
Look for a Pattern Look at the decimal 0.121122111222…. If the pattern continues, is this a repeating decimal? Explain.
Answer:
It is not a repeating decimal if the pattern continues
This is not a repeating pattern. This pattern is created by adding 1 and 2 after 1 and 2 respectively.
The pattern of a repeating decimal has to repeat without adding any other decimal in the pattern
Example:
0.567567567… = \(0 . \overline{567}\) Is a repeating decimal.
0.56556555655556… IS NOT a repeating decimal because the pattern has an additional 5 at every repetition.
This is not a repeating decimal if the pattern continues.

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 3 Answer Key Proportions and Percent.

Texas Go Math Grade 7 Module 3 Answer Key Proportions and Percent

Texas Go Math Grade 7 Module 3 Are You Ready? Answer Key

Write each percent as a decimal.

Question 1.
22% ______
Answer:
Write the percent as fractions. Then, write the fraction as a decimal.
= \(\frac{22}{100}\)
= 0.22

Question 2.
75% _____________
Answer:
Write the percent as fractions. Then, write the fraction as a decimal.
= \(\frac{75}{100}\)
= 0.75

Grade 7 Module 3 Answer Key Proportions and Percent Question 3.
6% _____________
Answer:
Write the percent as fractions. Then, write the fraction as a decimal.
= \(\frac{6}{100}\)
= 0.06

Question 4.
189% _____________
Answer:
Write the percent as the sum of 1 whole and a percent remainder
= 100% + 89%
Write the percent as fractions.
= \(\frac{100}{100}\) + \(\frac{89}{100}\)
Write the fractions as decimals.
= 1 + 0.89
= 1.89

Write each decimal as a percent.

Question 5.
0.59 ______________
Answer:
Multiply the decimal by 100 to get the percentage.
0.59 × 100 = 59%

Question 6.
0.98 ____________
Answer:
Multiply the decimal by 100 to get the percentage.
0.98 × 100 = 98%

Question 7.
0.02 _____________
Answer:
Multiply the decimal by 100 to get the percentage.
0.02 × 100 = 2%

Proportions and Percent Module 3 Grade 7 Answer Key Question 8.
1.33 ________________
Answer:
Multiply the decimal by 100 to get the percentage.
1.33 × 100 = 133%

Find the percent of each number.

Question 9.
50% of 64 ___________
Answer:
50% = 0.5
\opmul[displayshiftintermediary=all]{64}{0.5}
= 32.

Question 10.
7% of 30 ___________
Answer:
7% = 0.07
\opmul[displayshiftintermediary=all]{30}{0.07}
= 2.1

Question 11.
15% of 160 ____________
Answer:
15% = 0.15
\opmul[displayshiftintermediary=all]{160}{0.15}
= 24

7th Grade Proportions Answer Key Module 3 Question 12.
32% of 62 _____________
Answer:
32% = 0.32
\opmul[displayshiftintermediary=all]{62}{0.32}
= 19.84

Question 13.
120% of 4 ____________
Answer:
120% = 1.2
\opmul[displayshiftintermediary=all]{4}{1.2}
= 4.8

Question 14.
6% of 1,000 ______________
Answer:
6% = 0.06
\opmul[displayshiftintermediary=all]{1000}{0.06}
= 60

Texas Go Math Grade 7 Module 3 Reading Start-Up Answer Key

Visualize Vocabulary

Use the ✓ words to complete the graphic. You can put more than one word in each bubble.

Understand Vocabulary

Complete the sentences using the preview words.

Question 1.
A fixed percent of the principal is _______________.
Answer:
A fixed percent of the principal is simple interest.

Go Math Grade 7 Module 3 Answer Key Pdf Question 2.
The original amount of money deposited or borrowed is the __________________
Answer:
The original amount of money deposited or borrowed is the principal.

Question 3.
A _____________ _______ is a ratio of two equivalent measurements.
Answer:
A conversion factor is a ratio of two equivalent measurements.

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 16.4 Answer Key Estimating College Costs and Payments.

Texas Go Math Grade 8 Lesson 16.4 Answer Key Estimating College Costs and Payments

Example 1

June wants to attend Texas A&M University-Kingsville, near Corpus Christi, Texas. She is 18, single, does not have any dependents, and lives in Dallas. She was raised by her single father, a contractor who makes $81,000 per year and pays roughly 12% income tax. For the past 4 years, June has worked part time at the local bookstore, earning a taxable annual income of $15,000, which is taxed at roughly 8%. June has 2 brothers, both of whom are in middle school.

How much should June expect to spend if she plans on completing a four-year degree program at A&M University-Kingsville while living in on-campus housing?
STEP 1: Find the cost of attending Texas A&M University-Kingsville for 1 year using the values in the table.

STEP 2: Compute the cost of attending the university for 4 years.
$20,496 × 4 = $81,984
The estimated cost of June attending for 4 years is $81,984.

Reflect

Question 1.
How can June help to pay for her education?
Answer: June has worked part time at the local bookstore, earning a taxable annual income of $15,000. It is taxed at roughly 8%.

Your Turn

Question 2.
June is also considering attending Del Mar College in Corpus Christi to get a 2-year associate’s degree. Estimate the cost of June attending Del Mar College. Use the college’s website or another online tool to find the figures for an out-of-district student.

Answer:
The total amount of June tuition and fees at the Del Mar College for one year = is $5738.
The total amount of June tuition and fees at the Del Mar College for two years = $5738 × 2 = $11,476
The total amount of June’s room and board fee for one year = is $6013.
The total amount of June room and board fee for two years = $6013 × 2 = $12,026
The total amount for June books for one year = $3820.
The total amount for June books for two year = $3820 × 2 = $7640
The total amount for June and other purposes for one year = $1000.
The total amount for June and other purposes for two years = $1000 × 2 = $2000
The total cost of June attending Del Mar College for two years = $11,476 + $12,026 + $7640 + $2000 = $33,142.

Texas Go Math Grade 8 Pdf Paying for College Answer Key Question 3.
Suppose June earns an associate’s degree from Del Mar and then transfers to Texas A&M University-Kingsville for two more years to complete a bachelor’s degree. Estimate the total amount that the 4 years of school will cost.
Answer:
The total amount of June tuition and fees at the Del Mar College for one year = $5738.
The total amount of June tuition and fees at the Del Mar College for two years = $5738 × 2 = $11,476
The total amount of June room and board fee for one year = $6013.
The total amount of June room and board fee for two years = $6013 × 2 = $12,026
The total amount for June books for one year = $3820.
The total amount for June books for two year = $3820 × 2 = $7640
The total amount for June and other purposes for one year = $1000.
The total amount for June and other purposes for two years = $1000 × 2 = $2000.
The total cost of June attending Del Mar College for two years = $11,476 + $12,026 + $7640 + $2000 = $33,142.
June wants to attend Texas A&M University-Kingsville college for one year = $20,494.
June wants to attend Texas A&M University-Kingsville college for two years = $20,494 × 2 = 40,988
The total amount that the 4 years of school will cost = $33,142 + $40,988 = $74,130

Question 4.
Approximately how much less would it cost June to attend Del Mar for two years and A&M Kingsville for two years than to attend A&M Kingsville for four years?
Answer:
Compute the cost of attending the university for 4 years.
$20,496 × 4 = $81,984
The cost June to attend Del Mar for two years = (11,445 × 2) + ($20,496 × 2) = $63,882
$81,984 – $63,882 = $18,102
Thus it costs around $18,102 less.

Texas Go Math Grade 8 Lesson 16.4 Explore Activity Answer Key

As we saw in Example 1, it will cost June an estimated $81,984 to attend Texas A&M University-Kingsville for 4 years. Let’s apply the savings from June’s scholarship, the money her father can contribute to her education, and the funds from her college savings account, to find a more accurate estimated total remaining cost.

A. June received a scholarship and has been awarded $2,000 each year for 4 years. Find the new estimated total cost of June’s college education.
After subtracting the funds from the scholarship from the total cost of her college education, what estimated amount will June pay?
Answer:
Given,
June received a scholarship and has been awarded $2,000 each year for 4 years.
It will cost June an estimated $81,984 to attend Texas A&M University-Kingsville for 4 years.
2000× 4 = 8000
$81,984 – $8000 = $73,984
Thus the estimated amount June will pay is $73,984.

B. June’s father has put aside $11,000 for June’s college expenses. Find the new estimated total remaining cost of June’s education.
After applying her father’s contribution to her education expenses, what estimated remaining amount will June pay?
Answer:
June’s father has put aside $11,000 for June’s college expenses.
The estimated amount June will pay is $73,984.
By subtracting the father’s contribution to her educational expenses and the estimated amount June will pay we can find the remaining amount that June pays.
$73,984 – $11,000 = $62,984

C. At the beginning of each of the 4 years of high school, June put $4500 of her bookstore income into a savings account. The account earns interest at a rate of 2.5%, compounded annually. Complete the table to find how much June has in her college savings account at the beginning of her freshman year of college.

After applying June’s savings to her education expenses, what estimated remaining amount will June pay?
Answer:
2. The beginning balance is $4612.50
The amount deposited = $4500
Total = $4612.50 + $4500 = $9112.50
The account earns interest at a rate of 2.5% = 9112.50 × 0.025 = $227.81
3. The beginning balance is $9340.31
The amount deposited = $4500
Total = $9340.31 + $4500 = $13,840.31
The account earns interest at a rate of 2.5% = 13,840.31 × 0.025 = $346.01
4. The beginning balance is $14,186.32
The amount deposited = $4500
Total = $14,186.32 + $4500 = $18686.32
The account earns interest at a rate of 2.5% = 18686.32 × 0.025 = $467.16

Reflect

Question 5.
Does June have enough in her savings account to cover her first year at Texas A&M University-Kingsville without help from her father or a scholarship? What about the scholarship?
Answer:
As per Example 1, one year will cost an estimated $20,496 and she has only $19,153, hence she cannot cover her first year with her savings account alone.
The scholarship fees of $21,153 will be able to pay for her first year.

Texas Go Math Answer Key Grade 8 Lesson 16.4 Workbook Answers Question 6.
If June had been able to deposit $5,000 a year instead of $4,500, earning the same annual interest rate of 2.5%, would she have enough saved to pay for her first year?
Answer:
Given,
June had deposited $5000 instead of $4500 for a year.
Interest rate = 2.5%
The formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $5000
T = time = 1 year
R = interest rate = 2.5%
Simple interest for 1 years = $5000 × 1 × 2.5/100 = $125.
June fee for one year = $5738
Now he has = $5000 + $125 = $5125.
Therefore after the deposit of $5000 also he had less money than the college fee.

Texas Go Math Grade 8 Lesson 16.4 Guided Practice Answer Key

Ronan, a 19-year-old male from Texas, has been accepted at the University of Texas at Austin. If he attends the University of Texas, he plans to live at home with his mother, a single parent. His mother is a nurse who makes roughly $60,000 a year and pays roughly 13% in taxes annually. Ronan has never had a job. (Example 1, Explore Activity)

Question 1.
Use the table and an online tool to estimate the cost of Ronan attending the University of Texas for 1 year.
Answer:
The cost of Ronan attending the University of Texas for one-year Tuition and fees = $9794
The cost of books for one year = $904
The cost other for one year = $3752
The total cost of Ronan attending the university of texas for one year = $9794 + $904 + $3752 = $14,450.

Question 2.
Estimate the cost of Ronan getting a 4-year degree from the University of Texas.
Answer:
The total cost of Ronan attending the university of texas for one year = $14,450
The total cost of Ronan attending the university of texas for four years = $14,450 × 4 = $57,800

Question 3.
Ronan has been granted a scholarship for $1,500 per year. His mother has saved $21,000 for Ronan’s college education. Recalculate the estimated remaining cost of Ronan’s degree.
Answer:
Given that,
Ronan has been granted a scholarship for one year = $1,500
For four years = $1500 × 4 = $6000.
Mother saved for Ronan’s college education = $21,000.
The total money at Ronan = $6000 + $21000 = $27000
The total cost of Ronan attending the university of texas for four years = $57800.
Remaining cost of Ronan’s degree = $57800 – $27,000 = $30,800

Essential Question Check-In

Question 4.
What are some things to consider when estimating the cost of college?
Answer:
1. Will you attend in/out state school?
2. Do you plan on living at home?
3. Do you have any savings or not to pay the fees?
4. Are you eligible for scholarships?

Texas Go Math Grade 8 Lesson 16.4 Independent Practice Answer Key

Question 5.
At the beginning of each of the last two years, Laura put $4800 from her earnings as a part-time cashier during high school into a college savings account earning 1.2% interest compounded annually. Now she is applying for school and needs to know how much she has in her account. Complete the table to determine how much money Laura has saved.

Answer:

Laura saved from her earnings as a part-time cashier during high school into a college savings account earning = $4800.
Interest = 1.2%

Go Math Answer Key Grade 8 The Cost of College Homework 4 Answer Key Question 6.
At the beginning of each of the last three years, Lucas put $7000 from his earnings as a waiter into a college savings account that earned 1.5% interest compounded annually. Now he wants to attend community college for 2 years without taking out a loan. The cost of college will be about $18,000. Complete the table to determine whether Lucas has saved enough money to attend a community college.

Answer:
Lucas saved from his earnings as a waiter into a college savings account that earned = $1800.
Interest = 1.5%

Question 7.
Find a college grant online.
a. Grant Name:
Answer: College grants online are Federal Pell Grants.

b. Describe the application process.
Answer: To apply for Federal Pell Grants. First, you should fill out the FAFSA form and submit it. Then you will have to fill out the FAFSA form every year you are in school and demonstrate financial need to stay eligible for federal students.

c. How much money does the grant award?
Answer: The money for the grant award is $6995.

Question 8.
Find a college scholarship,
a. Name of Scholarship:
Answer: The name of the scholarship is the Tennessee HOPE scholarship.

b. Describe the application process.
Answer:

• First login to the student’s login.
• Filling in the scholarship application.
• Upload all the documents related to education.
• Submit the form to the respective educational institution.

c. How much money does the scholarship award?
Answer: The money award for the scholarship is $2000. It is not available for the summer semester.

H.O.T. Focus on Higher Order Thinking

Question 9.
Critical Thinking Having a savings plan is important even if you are not currently planning on attending college. Describe your savings plan, including stating a goal, how much you plan to save, and how you plan to save your money.
Answer:
Having a savings plan is important even if there is no plan for attending college. Saving money helps in the emergency purpose and it is also used for enjoying a quality life. I can save 30% of my salary every month

Question 10.
Make a Conjecture A CD, or certificate of deposit, is similar to a savings account, but it requires the depositor to leave the money in the account for a fixed period of time. There is a penalty for withdrawing money from the CD before the time period is over. The interest rates on CDs are generally higher than those for savings accounts. When would it be a good idea to put money in a CD to save for college? Would you put all of your savings into a CD? Explain your answer.
Answer: