Percent Proportions & Equations (SOL 7.4)

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Math 6/7 NOTES (7.4)

Name ________________________

Percent Proportions & Equations

^{(SOL 7.4)}

• Percent Proportions

𝐏𝐀𝐑𝐓 (𝐢𝐬)

𝐖𝐇𝐎𝐋𝐄 (𝒐𝒇)

=

𝐏𝐄𝐑𝐂𝐄𝐍𝐓 (%) 𝟏𝟎𝟎

What is 75% of 240? Find 60% of 264. 29 is what percent of 50

=

𝟏𝟎𝟎

=

𝟏𝟎𝟎

=

𝟏𝟎𝟎

1. 1 is what percent of 5?

=

𝟏𝟎𝟎

2. What number is 25% of 40?

=

𝟏𝟎𝟎

3. 30 is 60% of what number?

=

𝟏𝟎𝟎

4. What percent of 8 is 6? 5. Find 15% of 20. 6. 33 is 33% of what number?

7. 15 is what percent of 150? 8. What number is 30% of 140? 9. 90 is 60% of what number?

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•

Percent Equations:

We can write an equation using direct translation.

“is” or “are” means =

“What” means a variable

“of” means multiplication

Example 1 - Question:

Five is what percent of 8?... (5 = x • 8) or (5 = 8x)

Equation:

5 = x • 8

• Use Percent Proportions or Percent Equations to solve practical problems.

What percent of this class are boys?

^{𝒃𝒐𝒚𝒔}

𝒄𝒍𝒂𝒔𝒔

=

_𝟏𝟎𝟎^% The boys represent the part (is)

Equation: Proportion: The class represents the whole (of)

X% • ________ = _________

class boys

=

_𝟏𝟎𝟎^𝒙

Example 1. There are 435 students total and 55 of them like the color purple the best. What percent of them like the color purple?

Example 2. Yolanda's club has 40 members. Its rules state that 80% of them must be present in order to vote. At least how many members must be present to have a vote?

1. On his trip across town, Mark was stopped by a red light at 9 out of 15 intersections. At what percent of intersections was Mark stopped by a red light?

2. In Las Vegas, Nevada, the skies are clear on 92%

of the days. How many days in the month of June would you expect the skies to be clear in Las Vegas? Round the answer to the nearest day.

3. A recent poll shows that 65% of adults are in favor of increased funding for education. The number of adults surveyed for the poll was 140.

How many of the adults surveyed were in favor of increased funding for education?

4. Mika’s rosebush had 24 blooms in the first week of May. This was 80% as many blooms as Tammy’s rosebush had during the same period. How many blooms did Tammy’s rosebush have?

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HOMEWORK (7.4) Name ________________________

4. 46 is what percent of 69? 5. Find 55% of 120. 6. 11 is 44% of what number?

10. In a recent season, the San Francisco Giants won 75 out of 162 games. What percent of their games did they win? Round to the nearest tenth if necessary.

11. On a recent round of golf, Shana made par on 15 out of 18 holes. On what percent of holes did Shana make par? Round to the nearest tenth if necessary.

12. On the written portion of her driving test, Sara answered 84% of the questions correctly. If Sara answered 42 questions correctly, how many questions were on the driving test?

13. In a certain small town, 65% of the adults are college graduates. How many of the 240 adults living in the town are college graduates?

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NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems

The Percent Proportion

1. DRIVING David installed a device on his car that guaranteed to increase his gas mileage by 15%. He currently gets 22 miles per gallon. How much will the gas mileage increase after installing the device?

2. POPULATION The number of students at Marita’s school decreased to 98% of last year’s number. Currently, there are 1,170 students. How many students were there last year? Round to the nearest whole number.

3. VOTING Yolanda’s club has

35 members. Its rules require that 60%

of them must be present for any vote.

At least how many members must be present to have a vote?

4. GARBAGE This month, Chun’s office produced 690 pounds of garbage. Chun wants to reduce the weight of garbage produced to 85% of the weight

produced this month. What is the target weight for the garbage produced next month?

5. SALARIES Alma just received a 6% raise in salary. Before the raise, she was making $52,000 per year. How much more will Alma earn next year?

6. SPORTS Sally’s soccer team played 25 games and won 17 of them. What percent did the team win?

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AR Remediation Plan – Practical Applications-Rational Number and Proportional Reasoning

Solving Percent Problems Using Proportional Reasoning

STRAND: Computation and Estimation

STRAND CONCEPT: Practical Applications-Rational Number and Proportional Reasoning SOL 7.3

Remediation Plan Summary

Students apply proportions to solve problems that involve percents.

Common Misconceptions

 Students will incorrectly set up the proportions by always putting the variable as the numerator in the second ratio or over 100.

 Students may multiply numerators and then multiply denominators instead of using cross products to solve the proportion.

Materials

 Percents as Ratios handout

Introductory Activity

Begin a class discussion to find out what kind of number sense the students have about percents.

Ask them:

Where have you seen or used percents?

What does 50 percent mean?

What is the definition of percent?

What does 50 percent look like as a ratio?

What would a picture of 50 percent look like?

An example of what 50 percent looks like is a grid of 100 squares with 50 (or half) of the squares shaded or a circle with one half shaded.

Plan for Instruction

1. Discuss percent as a ratio, reminding students that a ratio is a comparison of two numbers and that with percents, one of the numbers is always 100. Therefore, the ratio for 25% is 25 to 100, or 25:100, or ²⁵

100. Have the students write 30% as a ratio. (30 to 100, 30:100, ³⁰ 100) Have them write 80% as a ratio. Tell students that they will be using the fraction form of the ratio for solving percent problems.

2. Distribute the “Percents as Ratios” handout. Have students do problems 1 through 5, and check their answers. It is not important for students to simplify the ratios.

3. Have the students apply the concept of percent to solve some simple problems. Ask them what the grade for a test means, reminding them that 100% is the basis for most test grades.

Show students that a grade of 90% that means that ⁹⁰

100points were scored.

4. Give students the following problem: “Your friend tells you that he made a 90% on a test that had 20 questions. How many questions did your friend answer correctly?” Tell students that we know that if he had answered all 20 questions correctly, he would have made 100 percent.

Have them use that information to set up a proportion, keeping in mind that a proportion

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Virginia Department of Education 2018 2

means that two ratios are equal. Hence, 90% is ⁹⁰

100, and all 20 correct is 100%. Since the 20 corresponds to 100 and we do not know how many questions were correct, the proportion will be ⁹⁰

100 20

 n . Make sure students understand that the total number on the test always corresponds to the 100 and that the number of correct answers always corresponds to the grade. Have students solve the proportion:

Original problem: ⁹⁰ 100 20

 n

Step 1: 90 20 100 n   Step 2: 1800 100n

Step 3: 1800 100 100  n100 Solution: 18n

5. Ask students to determine how many questions a student got correct if the test had 25 questions and the students got a grade of 76%. Help them set up the proportion, if necessary:

76 100 25

 n

6. Have students do problems 6 through 9 on the worksheet. Review the answers with the class.

7. Ask students how a teacher uses proportions to determine grades on the test. For example, Mrs. Jones gives a test with 25 questions. If Sarah answers 20 questions correctly, what grade does she earn on the test? Help students set up the proportion, if necessary:

20 100 25

n  Sarah’s grade is 80%.

8. Point out that the only difference from the proportion in step 5 is the location of the missing number (n) in the ratio.

9. Ask students to solve this problem: “Mrs. Jones gave a test with 20 problems, and Marcie got 15 correct. What is Marcie’s grade?”

15 100 20

n  Marcie’s grade is 75%.

10. Assign problems 10 through12 on the worksheet. Review the answers with the class.

Pulling It All Together

Exit Ticket: Explain what the 100 in the ratio for a percent corresponds to on a test. Write how you can use this information to solve problems about test grades, using proportions

Note: The following pages are intended for classroom use for students as a visual aid to learning.

Virginia Department of Education 2018

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Virginia Department of Education 2018 3

Percents as Ratios

Write each percent as a ratio in fraction form. Remember the definition of percent. If you need a picture, use the grids provided.

1. 40% _________________ 4. 33% _________________

2. 75% _________________ 5. 20% _________________

3. 15% _________________

Set up a proportion for each problem below, and determine the number of test questions each student got correct for each test.

6. Sue receives a score of 75% on a test with 20 questions. How many did she get correct?

7. John received a score of 68% on a test with 50 questions. How many did he get correct?

8. Anne received a score of 84% on a test with 25 questions. How many did she get correct?

9. Adam received a score of 90% on a test with 40 questions. How many did he get correct?

Set up a proportion for each problem below, and determine the score earned by the student on each test.

10. Ms. Smith gave a test with 25 questions, and John got 22 correct. What is John’s score?

11. Ms. Smith gave a test with 30 questions, and Jim got 21 correct. What is Jim’s score?

12. Ms. Smith gave a test with 40 questions, and Mark got 32 correct. What is Mark’s score?