The Percent Proportion

Unit Objective

● Use the percent Proportion to find missing quantities

Key Vocabulary

· Words You can represent “a as p percent of w” with the proportion

where a is part of the whole w, and p% or , is the percent.

· Numbers 3 out of 4 is 75%.

In percent problems, the word of is usually followed by the whole.

Let's Practice

Write the percent proportion for the following.

9 out of 20 is 45%

The following video will stop at points. You will need to answer the questions and click continue for the video to proceed.

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Finding a Percent

Example: What percent of 15 is 12?

	Write the proportion.
	Substitute 12 for a and 15 for w.
	Multiplication Property of Equality
80 = p	Simplify.

So, 80% of 15 is 12.

Check Use a model to check your answer.

You can also use cross products(multiplication) to solve

15p = 1200	cross products
	divide by 15
80 = p

Let's Practice.

Write and solve a proportion to answer the question.

1) What percent of 5 is 3?

2) 24 is what percent of 20?

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Finding a Part
Example: What number is 0.5% of 200?

	Write the percent proportion.
	Substitute 200 for w and 0.5 for p.
a = 1	Multiply each side by 200.

So, 1 is 0.5% of 200.

Let's practice.

1) What number is 80% of 60?

2) 10% of 40.5 is what number?

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Finding a Whole

Example: 150% of what number is 30?

	Write the percent proportion.
	Substitute 30 for a and 150 for p.
3000 = 150w	Cross Products Property
20 = w	Multiply each side by 150.

So, 150% of 20 is 30.

Let's practice.

1) 0.1% of what number is 4?

2) ½ is 25% of what number?

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Applying the Percent Proportion
Example: The bar graph shows the strengths of tornadoes that occurred in a state in a recent year. What percent of the tornadoes were EF1s?

Understand the Problem.
You are given a bar graph that shows the number of tornadoes in each strength category. You are asked to find the percent of tornadoes that were EF1s.

Make a Plan.
The total number of tornadoes, 145, is the whole, and the number of EF1 tornadoes, 58, is the part. Use the percent proportion to find the percent of tornadoes that were EF1s.

Solve and Check.

	Write the percent proportion.
	Substitute 58 for a and 145 for w.
	Multiplication Property of Equality
40 = p	Simplify.

So, 40% of the tornadoes were EF1s.

Check Reasonableness
The number of EF1 tornadoes, 58, is less than half the total number of tornadoes, 145.So, the percent of tornadoes that were EF1s should be less than 50%. Because 40% < 50%, the answer is reasonable.

Let’s practice.

An arctic woolly-bear caterpillar lives for 7 years and spends 90% of its life frozen. How many days of its life is the arctic woolly-bear frozen?