Grade 6 Math · Topic 36

Understanding Percents

Percent means “per hundred.” The symbol % stands for 1/100. Saying 30% is the same as saying 30 out of every 100, or 0.30, or 30/100. Percents are simply another way to talk about parts of a whole when the whole is 100.

Lesson alignment: 6.RP.A.3.c · Take your time. You can return to this lesson whenever you need it.

Explore visually

See each percent as a rate per 100

The same shaded amount can be written as a percent, a fraction out of 100, and a decimal.

Think first: If 35 of 100 squares are shaded, how can you write that amount as a fraction and a decimal?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

What percent is shaded if 7 of 10 squares are shaded?

Set up the fraction: 7/10. Multiply numerator and denominator by 10 to get 70/100 = 70%.

Answer: 70%

Worked example 2

Write 45% as a fraction in simplest form.

Start by writing the calculation clearly: 45% = 45/100. Divide top and bottom by 5: 9/20.

Answer: 9/20

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. 20% =
    Check

    1/5, 0.2

  2. 50% =
    Check

    1/2, 0.5

  3. 75% =
    Check

    3/4, 0.75

  4. 10% =
    Check

    1/10, 0.1

  5. 60% =
    Check

    3/5, 0.6

  6. 35% =
    Check

    7/20, 0.35

  7. 8% =
    Check

    2/25, 0.08

  8. 125% =
    Check

    5/4, 1.25

Try this situation 1

Liam answered 17 out of 20 test questions correctly. What percent did he get right?

Show a worked solution

Answer: 85%.

Start by writing the calculation clearly: 17/20 = 85/100 = 85%.

Try this situation 2

A jar holds 40 marbles, of which 9 are red. What percent are red?

Show a worked solution

Answer: 22.5%.

Start by writing the calculation clearly: 9/40 = 22.5/100 = 22.5%.

Fresh questions · saved on this device

Practice this skill

51 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

Your practice results stay in this browser and appear in the course progress report.

Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. Express 50% as a fraction in simplest form.

2. Convert 1/4 to a percent.

3. A 10-by-10 grid is shaded to show a percent. If 40 squares are shaded, what percent is that?

4. Express 32% as a fraction in simplest form.

5. Which fraction is equivalent to 20%?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Factors, Multiples & Percents quiz ↗Try a full practice test ↗