# Into Math Grade 6 Module 7 Lesson 2 Answer Key Use Strategies to Find a Percent of a Quantity

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## HMH Into Math Grade 6 Module 7 Lesson 2 Answer Key Use Strategies to Find a Percent of a Quantity

I Can write a percent as a fraction or a decimal and use multiplication to find the percent of a number. In a school football game, Marcus completes 3 out of 4 pass attempts. Terry completes 7 out of 10 pass attempts. Who has the better record of successful pass attempts? Explain.  Marcus has the better record of successful pass attempts,

Explanation:
Given in a school football game, Marcus completes
3 out of 4 pass attempts. Terry completes 7 out of 10 pass
attempts. we caluculate 100% attempts as
Marcus completed $$\frac{3}{4}$$  X 100 = 75%,
Terry completed $$\frac{7}{10}$$  X 100 = 70%,
So the better record of successful pass attempts are done
by Marcus.

Turn and Talk Is there another way you could have solved this problem?
Comparing with decimals,

Explanation:
Yes, the another way I would solve the problem is
Marcus completed $$\frac{3}{4}$$ = 0.75,
Terry completed $$\frac{7}{10}$$ = 0.70,
comparing 0.75 and 0.70 as 0.75 > 0.70, so Marcus has
the better record of successful pass attempts.

Build Understanding

1. What is 32% of 25?
A. You can use equivalent ratios to find 32% of 25. The first ratio is the percent. How can you express 32% as a ratio?
_____________________
A. $$\frac{32}{100}$$,

Explanation:
32% as ratio is $$\frac{32}{100}$$,

B. The second ratio is a part-to-whole ratio. The whole is 25 and the part is unknown. Write the second ratio as a fraction. Use a question mark to represent the unknown part. Then set the ratios equal to each other to find the unknown part. $$\frac{32}{100}$$ : $$\frac{?}{25}$$
and 8,

Explanation:
The second ratio is a part-to-whole ratio.
The whole is 25 and the part is unknown.
Wrote the second ratio as a fraction. Using
a question mark to represent the unknown part.
Then set the ratios equal to each other to find the unknown part as
$$\frac{32}{100}$$ : $$\frac{?}{25}$$ =
$$\frac{32 X 25}{100}$$ = ?,
? = $$\frac{32 }{10}$$ = 8.

C. What multiplication fact will help you to find the unknown number? Explain how.
_______________________________
_______________________________
Multiplication fact :
x = $$\frac{32 X 25}{100}$$ = 8,

Explanation:
The multiplication fact that will help
me to find the unknown number x as
x = $$\frac{32 X 25}{100}$$ = 8.

D. Use the multiplication fact you wrote in Part C to find equivalent ratios.
32% of 25 is ____.  Explanation:
Used the multiplication fact that I wrote in Part C
to find equivalent ratios 32% of 25 is 8 as shown above.

2. Bree wants to save 40% of her weekly pay as a lifeguard. How much does she plan to save each week?
A. What number should you enter into the top bar of the model? What number should you enter into each section on the bottom bar? Explain your reasoning. 250 top bar ,10 on the bottom bar,

Explanation:
Given Bree wants to save 40% of her weekly pay as a lifeguard.
Bree earns $250 per week, Number should I enter into the top bar of the model is 250 and Number should I enter into each section on the bottom bar is 10. B. How much money does Bree plan to save each week? Explain. Answer:$100,

Explanation:
As Bree earns $250 per week and Bree wants to save 40% of her weekly pay as a lifeguard. So Bree plan to save each week is $$\frac{40}{100}$$ X$250 = $100. Step It Out 3. Use multiplication to find 45% of 80. A. Write 45% as a fraction. B. I can _____ 80 by the fraction in Part A to find 45% percent of 80. C. Complete the multiplication to show how you can use the fraction from Part A to find 45% of 80. Answer: A. $$\frac{45}{100}$$, B. Use, C. Explanation: A. Wrote 45% as $$\frac{45}{100}$$, B. I can use80 by the fraction in Part A to find 45% percent of 80. C. Completed the multiplication to show how I can use the fraction from Part A to find 45% of 80 as $$\frac{45}{100}$$ X 80 = 36. Turn and Talk Is there another way to find 45% of 80? Explain. Answer: Yes, Decimal multiplication, Explanation: we can calculate another way to find 45% of 80 as $$\frac{45}{100}$$ X 80 = 0.45 X 80 = 36. 4. Alyssa has to make 250 invitations for a party. She has completed 72% of them. How many invitations has she completed? A. Write a ratio to represent the percent.  __________________ Answer: $$\frac{72}{100}$$, Explanation: Given Alyssa has to make 250 invitations for a party. She has completed 72% of them, The ratio to represent the percent is $$\frac{72}{100}$$. B. What operation does the word “of” indicate? __________________ Answer: “of” means times. Explanation: So if the question asks for 3/4 of 60, we want to work out 3/4 x 60 which is the same as working out (3 x 60) and then dividing the answer by 4. C. Write a multiplication problem to find the number of completed invitations. Answer: Explanation: Wrote a multiplication problem to find the number of completed invitations above as $$\frac{72}{100}$$ X 250 = 180. D. How many invitations has Alyssa completed? ______ Answer: 180 invitations, Explanation: Alyssa have completed 180 invitations. E. Check your answer using decimal multiplication. Write a decimal to represent 72%. _____ Answer: 0.72, Explanation: Checking my answer using decimal multiplication as 0.72 X 250 = 180 invitations, Decimal to represent 72% is 0.72. F. Write a decimal multiplication problem to find the number of completed invitations. Answer: , Explanation: The decimal multiplication problem to find the number of completed invitations are 0.72 X 250 = 180. Turn and Talk What is 100% of any amount? What is 50% of any amount? Answer: Amount itself, half of the amount, Explanation: The 100% of any amount is let x be the amount $$\frac{100}{100}$$ X x = x itself and 50% of any amount is $$\frac{50}{100}$$ X x = $$\frac{x}{2}$$ is half of the amount. 5. Scott planted 20% of a garden with roses. What is the area of the part of the garden planted with roses? A. How can you find the total area of the garden? What is the total area? _______________________________________________ Explanation: 50 square feet, Explanation: Given to find the total area of the garden length is 10 ft and width is 5 ft so area is 10 ft X 5 ft = 50 square ft. B. You know that the rose garden is 20% of the total garden. Write 20% as a ratio. Answer: $$\frac{20}{100}$$, Explanation: 20% as a ratio is $$\frac{20}{100}$$. C. Write a ratio to represent the unknown area of the garden planted with roses compared to the total area of the garden. Use a question mark for the unknown area. Answer: $$\frac{?}{100}$$, Explanation: A ratio to represent the unknown area of the garden planted with roses compared to the total area of the garden. Using a question mark for the unknown area D. Use equivalent ratios to find 20% of the rose gardens area is $$\frac{?}{100}$$. D. Use equivalent ratios to find 20% of the rose gardens area. Answer: $$\frac{20}{100}$$ = $$\frac{?}{50}$$, Explanation: The equivalent ratios to find 20% of the rose gardens are $$\frac{20}{100}$$ = $$\frac{?}{50}$$. E. What is the area of the rose garden? ____________ Answer: 10 square feet, Explanation: Calculating $$\frac{20}{100}$$ = $$\frac{?}{50}$$ we get the area of the rose garden as $$\frac{20}{100}$$ X 100 = 10 square feet. Turn and Talk What percent of the garden is not planted with roses? Explain how you know. Answer: 80% of the garden is not planted with roses, Explanation: Given 20% is planted with roses so percent of the garden is not planted with roses are 100% – 20% = 80%. Check Understanding Question 1. Shonda has$125. She spends 35% of the money she has on a concert ticket. How much did Shonda pay for the concert ticket?
_____________________
$43.75, Explanation: Given Shonda has$125. She spends 35% of the
money she has on a concert ticket. So much did
Shonda pay for the concert ticket is
$$\frac{35}{100}$$ X $125 =$43.75.

For Problems 2—5, find the percent of each number.

Question 2.
10% of 70 ____
7,

Explanation:
10% of 70 is
$$\frac{10}{100}$$ X 70 = 7.

Question 3.
75% of 8 ____
6,

Explanation:
75% of 8 is
$$\frac{75}{100}$$ X 8 = 6.

Question 4.
55% of 55 ____
30.25,

Explanation:
55% of 55 is
$$\frac{55}{100}$$ X 55 = 30.25.

Question 5.
90% of 20 ____
18,

Explanation:
90% of 20 is
$$\frac{90}{100}$$ X 20 = 18.

Question 6.
A football team scored 70% of a total of 400 points in the first 11 games of the season.

A. Fill in the model to show 70% of 400.   Explanation:
Filled the model to show 70% of 400.

B. How many points did the football team score in the first 11 games of the season? Explain how you found your answer.
__________________________
280 points,

Explanation:
Given a football team scored 70% of a total of 400 points
in the first 11 games of the season. so number of
points did the football team score in the first 11 games
of the season is $$\frac{70}{100}$$ X 400 = 280 points.

Question 7.
Cassie is painting a rectangular wall in her bedroom. The wall is 12 feet by 15 feet. She plans on painting the top 20% of the wall green and the rest of the wall tan. What is the area of the part of the wall that she plans to paint green?
_____________________
36 square feet,

Explanation:
Given Cassie is painting a rectangular wall in her bedroom.
The wall is 12 feet by 15 feet. She plans on painting the
top 20% of the wall green and the rest of the wall tan.
The area of the part of the wall that she plans to paint green is
the area of the wall is 12 feet X 15 feet = 180 square feet,
As she palns 20% with green so the area with green is
$$\frac{20}{100}$$ X 180 square feet = 36 square feet.

Question 8.
Reason Stephon and Marcy are saving money to buy new bikes. If Stephon suddenly has to spend 12% of his savings and Marcy has to spend 8% of her savings, who spent more money? Explain how you found your answer. Marcy has spend more money,

Explanation:
Given Stephon and Marcy are saving money to buy new bikes.
If Stephon suddenly has to spend 12% of his savings and
Marcy has to spend 8% of her savings, who spent more money
Stephon has spend $$\frac{12}{100}$$ X $200 =$24,
Marcy has spend $$\frac{8}{100}$$ X $350 =$28,
Now compairing Marcy has spend more money.

Question 9.
The regular price of a pair of sneakers is $40. The sale price is 25% off the regular price. What is the sale price? Explain. __________________ Answer: The sale price is$30,

Explanation:
Given the regular price of a pair of sneakers is $40. The sale price is 25% off the regular price. So the sale price is$40 – $$\frac{25}{100}$$ X $40 =$ 40 – $10 =$30.

For Problems 10—15, find the percent of each number.

Question 10.
13% of 400 ____
52,

Explanation:
13% of 400 is
$$\frac{13}{100}$$ X 400 = 52.

Question 11.
80% of 14,236 _____
11,388.8,

Explanation:
80% of 14,236 is
$$\frac{80}{100}$$ X 14,236 = 11,388.8.

Question 12.
60% of 50 ____
30,

Explanation:
60% of 50 is
$$\frac{60}{100}$$ X 50 = 30.

Question 13.
30% of 70 ____
21,

Explanation:
30% of 70 is
$$\frac{30}{100}$$ X 70 = 21.

Question 14.
45% of 20 ________
9,

Explanation:
45% of 20 is
$$\frac{45}{100}$$ X 20 = 9.

Question 15.
75% of 804 ____
603,

Explanation:
75% of 60 is
$$\frac{75}{100}$$ X 804 = 603.

Question 16.
A quiz has 30 problems. Kamal answered 80% of the problems correctly.
A. How many problems did Kamal answer correctly? _____
24,

Explanation:
Given a quiz has 30 problems. Kamal answered 80% of
the problems correctly. number of problems did Kamal
answer correctly are $$\frac{80}{100}$$ X 30 = 24 problems.

B. How many problems did Kamal answer incorrectly? _____
6 problems,

Explanation:
If there are total 30 problems and 24 problems are correct then
incorrect problems are 30 – 24 = 6 problems or
$$\frac{20}{100}$$ X 30 = 6 problems.

C. What percent of the problems did Kamal answer incorrectly? ____
20% of the problems Kamal answer were incorrect,

Explanation:
As Kamal answered 80% so percent of the problems did
Kamal answer incorrectly are 100% – 80% = 20%.

Question 17.
The regular price for swimming lessons for an hour is shown. The sale price for new students is 75% of $20 per hour the regular price. What is the sale price? Answer:$15,

Explanation:
Given the regular price for swimming lessons for
an hour is shown. The sale price for new students is
75% of $20 per hour the regular price. The sale price is $$\frac{75}{100}$$ X$20 = $15. Question 18. Maya has 200 songs on her cell phone. Of these songs, 48 are jazz songs. What percent of Maya’s songs are jazz songs? Answer: 24%, Explanation: Given Maya has 200 songs on her cell phone. Of these songs, 48 are jazz songs. Let x be the percent of Maya’s songs are jazz songs are So value of x is $$\frac{x}{100}$$ X 200 = 48, 200 x = 48 X 100, x = $$\frac{4800}{200}$$ = 24%. Question 19. Financial Literacy The sales tax in the town where Gina lives is 8%. Gina wants to buy a table saw that costs$300. How much sales tax will she pay?
__________________
$24, Explanation: Given the sales tax in the town where Gina lives is 8%. Gina wants to buy a table saw that costs$300.
the sales tax will she pay is
$$\frac{8}{100}$$ X $300 =$24.

Question 20.
Parson City Middle School has 1,340 students. About 38% of the students are in the seventh grade. About how many seventh-graders attend Parson City Middle School?
__________________
509 students,

Explanation:
Given Parson City Middle School has 1,340 students.
About 38% of the students are in the seventh grade.
Parson City Middle School are $$\frac{38}{100}$$ X 1,340 =
509.2 approximately 509 students.

For Problems 21—26, find the percent of each number.

Question 21.
25% of 500 ____
125,

Explanation:
25% of 500 is
$$\frac{25}{100}$$ X 500 = 125.

Question 22.
80% of 10 ____
8,

Explanation:
80% of 10 is
$$\frac{80}{100}$$ X 10 = 8.

Question 23.
10% of 100 ____
10,

Explanation:
10% of 100 is
$$\frac{10}{100}$$ X 100 = 10.

Question 24.
100% of 60 _____
60,

Explanation:
100% of 60 is
$$\frac{100}{100}$$ X 60 = 60.

Question 25.
105% of 220 ___
231,

Explanation:
105% of 220 is
$$\frac{105}{100}$$ X 220 = 231.

Question 26.
120% of 40 ____
48,

Explanation:
120% of 40 is
$$\frac{120}{100}$$ X 40 = 48.

I’m in a Learning Mindset!

What challenges do I face trying to master percent problems?
_____________________
_____________________
Finding percentage formula,
Calculating percent changes using decimal numbers,
Calculating Reverse Percentage Questions,
Preparing for Numerical Percentage Questions,
Percentages can be a tricky skill to master,
but it can be done with the right preparation and practice.

Explanation:
We use the following percentage formula: % = Fraction X 100,
To calculate percent changes using decimal numbers.
Since a percent is actually a fraction, 1% can be written as 0.01.
Therefore, increasing a number by 1% means multiplying
it by (1+0.01)= 1.01, and decreasing a number by 1% means
multiplying it by (1-0.01)=0.99.
Thus, a percent increase means multiplying by numbers
greater than one, and a percent decrease means multiplying by
numbers that are smaller than one.

Reverse Percentage Questions :
It is quite popular to present a quantity that has gone
through a percent change and ask its original value.
The fastest way to get these calculations is the following:
If a certain value is known to have been changed by a
certain percentage, its original value can be found by
dividing it by the decimal size it now comprises from the original:
[(Present value) / (Decimal size in relation to original value)] =
(Original value before change).
Preparing for Numerical Percentage Questions:
Percentages can be a tricky skill to master,
but it can be done with the right preparation and practice.

Lesson 7.2 More Practice/Homework

Use Strategies to Find a Percent of a Quantity

Question 1.
A football team scored 80% of a total of 500 points in the first 11 games of the season. Fill in the model to show 80% of 500 and then write the number. 80% of a total of 500 points is 400 points

Explanation:
Given afootball team scored 80% of a total of
500 points in the first 11 games of the season.
Filled in the model to show 80% of 500 shaded and
then wrote the number as 80% of a total of 500 points is
400 points as shown above.

Question 2.
STEM About 71% of Earth’s surface is covered in water. A. If the surface area of the Earth is about 196,900,000 square miles, about how many square miles are covered in water?
____________________
139,799,000 square miles is covered in water,

Explanation:
Given about 71% of Earth’s surface is covered in water,
If the surface area of the Earth is about 196,900,000 square miles,
about number of square miles are covered in water are
$$\frac{71}{100}$$ X 196,900,000 = 139,799,000 square miles.

B. About what percent of the Earth’s surface is not covered in water? How many square miles is this?
____________________
29% of the Earth’s surface is not covered in water,

Explanation:
Abount 100% – 71% = 29% of the Earth’s surface is not covered in water,
number of square miles is
$$\frac{29}{100}$$ X 196,900,000 = 57,101,000 square miles.

For Problems 3-4. use the following information.

The metal bar shown is an alloy of silver and other metals.

Question 3.
If the silver accounts for 84% of the bar’s weight, what is the weight of the silver? _____ 6.3 ounces,

Explanation:
Given if the silver accounts for 84% of the bar’s weight,
The weight of the silver is
$$\frac{84}{100}$$ X 7.5 ounces = 6.3 ounces.

Question 4.
Attend to Precision If 9% of the bar’s weight is iron, how much does the iron weigh? _______
0.675 ounces is iron weight,

Explanation:
If 9% of the bar’s weight is iron, The iron weigh is
$$\frac{9}{100}$$ X 7.5 ounces = 0.675 ounces.

Question 5.
Math on the Spot Find 30% of 180. _______
54,

Explanation:
30% of 180 is
$$\frac{30}{100}$$ X 180 = 54.

Question 6.
Use Repeated Reasoning Find 10% of each number. What pattern do you notice?
A. 10% of 30 is ___.
3,

Explanation:
10% of 30 is
$$\frac{10}{100}$$ X 30 = 3.

B. 10% of 47 is ____.
4.7,

Explanation:
10% of 47 is
$$\frac{10}{100}$$ X 47 = 4.7.

C. 10% of 240 is ___.
24,

Explanation:
10% of 240 is
$$\frac{10}{100}$$ X 240 = 24.

D. 10% of 10.8 is ___.
1.08,

Explanation:
10% of 10.8 is
$$\frac{10}{100}$$ X 10.8 = 1.08.

E. Describe the pattern that you notice.
10% of value of 0.1 of the number,

Explanation:
The pattern that I notice is it is asking for value of 10% or
the amount multiplied by 0.1 of the given number.

For Problems 7-10, find the percent of each number.

Question 7.
10% of 90
_______
9,

Explanation:
10% of 90 is
$$\frac{10}{100}$$ X 90 = 9.

Question 8.
50% of 14
_______
7,

Explanation:
50% of 14 is
$$\frac{50}{100}$$ X 14 = 7.

Question 9.
30% of 90
_______
27,

Explanation:
30% of 90 is
$$\frac{30}{100}$$ X 90 = 27.

Question 10.
80% of 40
_______
32,

Explanation:
80% of 40 is
$$\frac{80}{100}$$ X 40 = 32.

Test Prep

Question 11.
Of 140 people at a movie, 40% of the people bought popcorn, 30% of the people bought pretzels, and 10% of the people bought pizza. How many people bought each item?
Number of people who bought popcorn: _______
Number of people who bought pretzels: _______
Number of people who bought pizza: _______
Number of people who bought popcorn: 56 people,
Number of people who bought pretzels: 42 people,
Number of people who bought pizza: 14 people,

Explanation:
Given of 140 people at a movie, 40% of the people bought popcorn,
30% of the people bought pretzels and 10% of the
people bought pizza. Number of people bought each item are
Number of people who bought popcorn:
$$\frac{40}{100}$$ X 140 =  4 X 14 = 56 people,
Number of people who bought pretzels:
$$\frac{30}{100}$$ X 140 = 3 X 14 = 42 people,
Number of people who bought pizza:
$$\frac{10}{100}$$ X 140 = 1 X 14 = 14 people.

Question 12.
The circle graph shows the percent of votes the winning candidate received in a local election. About how many votes did the winning candidate receive? Explanation:
Given the circle graph shows the percent of votes
the winning candidate received in a local election.
Number of many votes did the winning candidate receive are
$$\frac{63}{100}$$ X 6,350 = 4,000.5,
so about 4,000 votes which matches with bit C.

Question 13.
There are 80 marbles in a bag. If 30% of the marbles are green, how many marbles are not green?
56 marbles are not green,

Explanation:
Given there are 80 marbles in a bag. If 30% of the marbles are green,
Number marbles are not green are as not green is 100% – 30% = 70%,
so number is $$\frac{70}{100}$$ X 80 = 56 marbles.

Question 14.
Lamar earns 40% of his money moving furniture. If he earns $150 in total, how much money did he earn moving furniture? A.$110
B. $60 C.$40
D. $90 Answer: B.$60,

Explanation:
Given Lamar earns 40% of his money moving furniture.
If he earns $150 in total, Much money did he earn moving furniture is $$\frac{40}{100}$$ X$150  = \$60 which matches with bit B.

Question 15.
Barry entered a singing competition. Three of 15 judges voted for him to go on to the semi-finals. What percent of the judges voted for him?
__________________
20% of judges voted for him,

Explanation:
Given Barry entered a singing competition.
Three of 15 judges voted for him to go on to the semi-finals.
So percent of the judges voted for him let it be x so
$$\frac{x}{100}$$ X 15 = 3,
x = 3 X $$\frac{100}{15}$$ = 20%.

Spiral Review

Question 16.
A bakery packages 868 muffins into 31 boxes. The same number of muffins are put into each box. How many muffins are in each box?
__________________
28 muffins,

Explanation:
Given a bakery packages 868 muffins into 31 boxes.
The same number of muffins are put into each box.
Number of muffins are in each box $$\frac{868}{31}$$ = 28 muffins.

Question 17.
Order the numbers 0, 3, -12, and -1 from least to greatest.
__________________
-12, -1, 0 3,

Explanation:
Given to find ordering the numbers 0, 3, -12 and -1 from
least to greatest are as – 12 is the least next least is -1 and the 0
then 3 so the order is -12 < -1 < 0 < 3 or -12, -1, 0, 3.

Find the quotient. If necessary, round to the nearest thousandth.

Question 18.
560 ÷ 1.4 ____
400,

Explanation:
Given to find the quotient of 560 ÷ 1.4 is
1.4)560(400
560
0, So it is 400.

Question 19.
9.5 ÷ 500
0.02,

Explanation:
Given to find the quotient of 9.5 ÷ 500 is
500)9.5(0.019
5
4.5
4.5
0
0.019 approximately equal to 0.02, So it is 0.02.

Question 20.
0.80 ÷ 46 _____
0.02,

Explanation:
Given to find the quotient of 0.80 ÷ 46 is
46)0.80(0.017
0.46
0.340
0.322
0.018
0.017 approximately equal to 0.02, So it is 0.02.

Question 21.
10.2 ÷ 100 ____
0.1,

Explanation:
Given to find the quotient of 10.2 ÷ 100 is
100)10.2(0.102
10.0
0.2
0.2
0
0.102  approximately equal to 0.1, So it is 0.1.

Question 22.
0.72 ÷ 0.09 ____
8,

Explanation:
Given to find the quotient of 0.72 ÷ 0.09 is
0.09)0.72(8
0.72
8
So it is 8.

Question 23.
13 ÷ 0.04 ____
325,

Explanation:
Given to find the quotient of 9.5 ÷ 500 is
0.04)13(325
12
1.00
0.08
0.02
0.02
0
So it is 325.

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