Percent Proportion & Equation

Percent Proportion & Equation Objective: 7.1.01 Develop and use ratios, proportions, and percents to solve problems Essential Question: How can I use proportions and equations to solve problems involving percents?

Percent Proportion & Equation OLD Vocabulary: Percent: a special ratio comparing a number to 100. Proportion: a statement where one ratio is equal to another ratio. Equation: a sentence with an equal sign (=).

Percent Proportion & Equation NEW Vocabulary: Percent Proportion: a proportion that can be used to determine percents of numbers. Part: in a percent proportion, the number being compared to the whole quantity. Base: in a percent proportion, the whole quantity, or the number to which the part if being compared. IS % 100 OF

Percent Proportion & Equation Lets Remember: This concept is always going to be useful to us whenever we go shopping or are in any situation where tax, tip, or discounts are involved.

Percent Proportion & Equation We have already learned about how to solve proportions and equations. So the only thing we really have to learn how to do is set up the problem.

Percent Proportion & Equation Possible Algorithms Include: When you want to solve percent problems you can use either one of two algorithms: Method One: The Percent Proportion Method Two: The Percent Equation

Percent Proportion & Equation Method One: The Percent Proportion IS % OF 100

Percent Proportion & Equation Method One: The Percent Proportion Part Percent Base 100

Percent Proportion & Equation Method Two: The Percent Equation IS % IS % OF 100 OF Part % Base

Percent Proportion & Equation Real World Example: In a school band of 24 students, 9 students play a brass instrument. What percent of the band members play a brass instrument? 37.5%

Percents Proportion & Equation Example 1: How to find a Percent A) What percent of 150 is 45 30% 45 x The Percent Proportion IS % 100 150 OF 100

Percents Proportion & Equation Example 1: How to find a Percent B) What percent of 25 is 20 80% 20 x The Percent Proportion IS % 100 25 OF 100

Percents Proportion & Equation Example 1: How to find a Percent C) What percent of 400 is 8 2% 8 x The Percent Proportion IS % 100 400 OF 100

Percents Proportion & Equation Example 2: How to find a Part (IS) A) 30% of 150 is what number? 45 x 30 The Percent Proportion IS % 100 150 OF 100

Percents Proportion & Equation Example 2: How to find a Part (IS) B) 20% of 25 is what number? 5 x 20 The Percent Proportion IS % 100 25 OF 100

Percents Proportion & Equation Example 2: How to find a Part (IS) C) 2% of 400 is what number? 8 x 2 The Percent Proportion IS % 100 400 OF 100

Percents Proportion & Equation Example 3: How to find a Whole (OF) A) 30% of what number is 45? 150 45 30 The Percent Proportion IS % x 100 OF 100

Percents Proportion & Equation Example 3: How to find a Whole (OF) B) 20% of what number is 5? 25 5 20 The Percent Proportion IS % x 100 OF 100

Percents Proportion & Equation Example 3: How to find a Whole (OF) C) 2% of what number is 8? 400 8 2 The Percent Proportion IS % x 100 OF 100

Percent Proportion & Equation Method One: The Percent Proportion IS % We can use the percent proportion to find: 100 OF 1) Part (IS) – 60% OF 50 IS _?_ 2) Whole (OF) – 60% OF _?_ IS 30 3) Percent (%) – _?_ OF 50 IS 30

Percent Proportion & Equation Real World Example: The sale price of a new pair of Air Jordan basketball shoes is $120. This is 75% of the original price. What was the original price of the Air Jordan basketball shoes? IS % 100 OF $160

Percent Proportion & Equation Independent Practice: Solve the examples with a proportion or equation: 1. What is 80% of 12 2. 48 is 60% of what number 3. What percent of 90 is 50 4. What is 175% of 85 5. 96 is 160% of what number 6. What percent of 24 is 72 = 9.6 = 80 = 55.6% = 148.75 = 60 = 300%

Percent Proportion & Equation Summary: IS % We can use the percent proportion to find: 100 OF 1) Part (IS) – 60% OF 50 IS _?_ 2) Whole (OF) – 60% OF _?_ IS 30 3) Percent (%) – _?_ OF 50 IS 30

Percent Proportion & Equation Using the Percent Equation Not Discussed in class

Percent Proportion & Equation HOMEWORK

Solving Percent Problems Using Proportions COURSE 2 LESSON 6-5 117 is 45% of what number? The model shows the relationship. = 117 n 45 100 Write the proportion. Write the cross products. 45n = 117(100) Divide each side by 45. 45n 45 117(100) = n = 260 Simplify. 117 is 45% of 260. 6-5

Solving Percent Problems Using Proportions COURSE 2 LESSON 6-5 Use a proportion to solve: 96 is 15% of what number? Model the relationship. The model shows the relationship. = 96 n 15 100 Write the proportion. Write the cross products. 15n = 96(100) Divide each side by 15. 15n 15 96(100) = n = 640 Simplify. Check 15% of 640 = 0.15 • 640 = 96  6-5

Solving Percent Problems Using Proportions COURSE 2 LESSON 6-5 Use a proportion to solve. 1. What percent of 240 is 60? 2. 90 is what percent of 120? 3. 75% of what number is 66? 4. 24 is 96% of what number? 25% 75% 88 25 6-5