Solving Percent Problems Study Guide: GED Math

Finding a Part of a Whole

Often you will be asked to find a part of a whole. In these problems, you are given a whole and a percent and asked to find the part represented by the percent of the whole. Let's go through an example.

Example

What is 30% of 60?

Begin by figuring out what you know from the problem and what you're looking for.

You have the percent: 30%.

You have the whole: 60.

You are looking for the part.

Then, use the equation to solve the problem: whole × percent = part.

Plug in the pieces of the equation that you know: 60 × 30% = part.

Convert the percent to a decimal to make your multiplication easier: 60 × 0.30 = part.

Solve: 60 × 0.30 = 18.

So, 30% of 60 is 18.

Finding a Percent

In the following types of problems, you will be given the part and the whole. Your task is to determine what percent the part is of the whole. Remember that a percent is just a fraction written over 100. You can solve these types of problems by writing the part over the whole and converting the fraction to a percent.

Examples

1. 10 is what percent of 200?

Begin by figuring out what you know from the problem and what you're looking for.

You have the part: 10.

You have the whole: 200.

You are looking for the percent.

Write a fraction of the part over the whole: .

Convert the fraction to a percent. Remember there are two methods for converting fractions to percents. Use either method. Method 1 is shown: 10 ÷ 200 = 0.05; 0.05 × 100 = 5.

Therefore, 10 is 5% of 200.

2. There are 500 people in Sandra's travel club. Fifty people were chosen to go to Washington, D.C., for a trip. What percent of Sandra's travel club was chosen to go on the trip?

Begin by figuring out what you know from the problem and what you're looking for.

You have the part: 50.

You have the whole: 500.

You are looking for the percent.

Write a fraction of the part over the whole: .

Convert the fraction to a percent. Remember there are two methods for converting fractions to percents. Use either method. Method 1 is shown:

50 ÷ 500 = 0.1

0.1 × 100 = 10 or 10%

Therefore, 50 is 10% of 500; 10% of Sandra's travel club was chosen to go on the trip.

Sometimes problems will ask you to find a percentage change. The problem will give you one part of the whole. Your task is to calculate the part of the whole represented by the percentage difference between the whole and the part given.

Example

Last year, Sasha could run one mile in 12 minutes.

This year, he can run a mile in 8 minutes.

By what percentage did his timing improve?

Begin by figuring out what you know from the problem and what you're looking for.

You have the part: 10 minutes – 8 minutes = 2 minutes.

You also have the whole: 10 minutes.

You are looking for the percent.

Write a fraction of the part over the whole:

Convert the fraction to a percent:

2 ÷ 10 = 0.2

0.2 × 100 = 20 or 20%

Therefore, 2 minutes is 20% of 10 minutes. Sasha's running time improved by 20% since last year.

When you see the following types of phrases, you are probably being asked to calculate the part of the whole represented by the difference between the whole and the part given.

• Find the percent change.
• Find the percent increase.
• Find the percent decrease.
• By what percent did it improve?
• By what percent did it go down?
• By what percent did it go up?

Sometimes the problem will not directly tell you the whole amount. Instead, you will be given enough information to calculate the whole on your own. Here's an example.

Example

Priyanka made a beaded bracelet using 10 red beads, 5 turquoise beads, 8 yellow beads, and 2 white beads. What percent of the bracelet do the red beads make up?

Begin by figuring out what you know from the problem and what you're looking for.

You have the parts:

10 red beads

5 turquoise beads

8 yellow beads

2 white beads

You also have the whole: 10 + 5 + 8 + 2 = 25 beads.

You are looking for the percent.

Write a fraction of the part over the whole:

Convert the fraction to a percent:

10 ÷ 25 = 0.4

0.4 × 100 = 40 or 40%

Therefore, 40% of the beads are red.

Finding the Whole

In the following types of problems, you will be given the part and the percent. Your task is to determine the whole. You can solve these types of problems by writing the part over the percent and dividing.

Examples

1. 45 is 75% of what number?

Begin by figuring out what you know from the problem and what you're looking for.

You have the part: 45.

You also have the percent: 75%.

You are looking for the whole.

Write the part over the percent: .

Convert the percent to a fraction to make your division easier: 45 ÷ = whole.

Solve:



Therefore, 45 is 75% of 60.

2. Five people on a track team qualified to go to the state competition. This represents 20% of the track team. How many people are on the track team?

Begin by figuring out what you know from the problem and what you're looking for.

You have the part: 5 people.

You also have the percent: 20%.

You are looking for the whole.

Write the part over the percent: .

Convert the percent to a fraction to make your division easier: 5 ÷ = whole.

Solve:



So, there are 25 people on the track team.

Practice problems for these concepts can be found at:

Percentages Practice Problems: GED Math