GOZUNTA
Try it now
All courses Math Foundations · MF.PR.8 22 of 60
Use proportional reasoning to solve percent problems without relying on memorized templates alone.

Find a part from a percent and whole

Problem
Use a percent proportion to find 35% of 80.
Your answer
With a free account

Save the work you do.

Your session results stay with your account, so today’s practice can inform what you work on next.

Create a free account
With paid access

Follow one course all the way through.

A one-course subscription opens every objective, problem type, and variant in the course you choose.

Compare plans

Hint

Let x be the part you want, then write the proportion x/80 = 35/100.

Percent means "out of 100," so use part/whole = percent/100.

Solution walkthrough

01

Write the percent proportion

\[x/80~=~35/100\]

Let x be the part we are trying to find. Since percent means "out of 100," the part-to-whole ratio must match 35 to 100.

02

Cross-multiply to make an equation

\[100x~=~80~×~35\]

Cross-multiplying keeps the two ratios equivalent and turns the proportion into an equation with one unknown.

03

Compute and solve for the part

\[100x~=~2800,~\text{so}~x~=~2800/100~=~28\]

First multiply 80 by 35 to get 2800. Then divide both sides by 100 to isolate x.

04

Check and state the answer

\[28/80~=~35/100~=~0.35,~\text{so}~35\%~\text{of}~80~=~28\]

The ratio 28 to 80 really is 35 out of 100, so the proportion checks. That means the part represented by 35% of 80 is 28.

+

Another way

  1. Use decimal percent reasoning: 35% = 0.35, and 0.35 × 80 = 28.

  2. Break 35% into 30% and 5%: 30% of 80 is 24 and 5% of 80 is 4, so 24 + 4 = 28.

!

Common mistake

A common mistake is treating 35% as just 35 and doing 35 × 80 without thinking about the "out of 100" meaning. In a percent proportion, 35% must be written as 35/100, so the correct setup is x/80 = 35/100.