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6.6: Proportions to Find Part a

Difficulty Level: At Grade Created by: CK-12

Let’s Think About It

License: CC BY-NC 3.0

Jamal works at a local store after school that sells pumpkin lanterns for $12. The day after Halloween, the store manager wants Jamal to mark down the lanterns by 75%. What new price sticker does Jamal put on them?

In this concept, you will learn to use a proportion to find part a, the amount.

Guidance

Sometimes you will be given the base and the percent, and you will need to find the amount. You can use the same proportion to figure out this missing value, a. You just need to fill in the numbers in the correct places and solve.

Let’s look at an example.

What is 25% of 75?

To figure this out, let’s look at what you have been given for information. First, you know the percent so you can fill in that half of the proportion.

25100

Next, you have been given the base. “Of 75” lets you know that this number is the base. The amount is missing. That is our unknown. So the second half of the proportion is:

a75

Now let’s put it together as a proportion and use cross products to solve for a.

a75100a100aa====2510075(25)187518.75

Notice that you moved the decimal point two places to the left when you divided by 100.

The answer is 18.75 or 1834 is 25% of 75.

Notice that there isn’t a percent sign here because you were looking for an amount not a percent. Remember to note what you are looking for.

Let’s take a look at another example.

What number is 15% of 60?

First, set up a proportion. Remember, the missing part is variable a, the amount.

a60=15100

Next, cross-multiply and solve.

100aa==9009

The answer is 9 is 15% of 60.

Guided Practice

Mr. Green bought both vegetable and flowering plants for his garden. He bought 40 plants and 35% were flowering plants. How many flowering plants did he buy?

You can think of this problem as “What is 35% of 40?”

40 is the base (b) and 35 is the percent (p). You need to find the amount (a).

First, set up the proportion.

a40=35100

Then, use cross products to solve for the amount.

100a100aa===35(40)1,40014

The answer is Mr. Green bought 14 flowering plants.

Examples

Example 1

What is 20% of 30?

First, let’s set up the proportion.

a30=20100

Now you can use cross products to solve for the amount.

100a100aa===20(30)6006

The answer is 6 is 20% of 30.

Example 2

What is 16% of 50?

First, let’s set up the proportion.

a50=16100

Now you can use cross products to solve for the amount.

100a100aa===16(50)808

The answer is 8 is 16% of 50.

Example 3

What is 22% of 80?

First, let’s set up the proportion.

a80=22100

Now you can use cross products to solve for the amount.

100a100aa===22(80)1,76017.6

The answer is 17.6 is 22% of 80.

Follow Up

License: CC BY-NC 3.0

Remember Jamal and his job at the store? He needs to put discounted price stickers on the Halloween lanterns. The lanterns, which originally cost $12, are now going to be reduced by 75%. What new price sticker does Jamal put on them?

First, if the lanterns are discounted by 75%, their new price is 100%75% or 25% of the original price.

Next, let’s setup the proportion.

a12=25100

Now you can use cross products to solve for the amount.

100a100aa===25(12)3003

The answer is the discounted sticker price Jamal should put on the lanterns is $3.

Video Review

https://www.youtube.com/watch?v=cApv0GeF2XM&feature=youtu.be

Explore More

Find each missing amount.

  1. What number is 25% of 18?
  2. What number is 10% of 20?
  3. What number is 45% of 16?
  4. What number is 20% of 44?
  5. What number is 30% of 100?
  6. What number is 25% of 60?
  7. What number is 40% of 80?
  8. What number is 40% of 60?
  9. What number is 50% of 120?
  10. What number is 5% of 12?
  11. What number is 5% of 20?
  12. What number is 16% of 80?
  13. What number is 25% of 23?
  14. What number is 50% of 17?
  15. What number is 30% of 33?

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 6.6. 

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0

Description

Difficulty Level:

At Grade

Grades:

Date Created:

Dec 02, 2015

Last Modified:

Dec 02, 2015
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