Percentages: learn and practice

Who this lesson is for

This percentages lesson is for grades 5–8. Grades 5 and 6 find a percent of a number, including 10% and 25%. Grades 7 and 8 also describe a change as a percent increase. The practice link opens percent of a number at grade 6. One page serves all four grade hubs.

Percent means out of 100

Percent means hundredths. 15% is 15/100, which is 0.15. To find 15% of 80, multiply 0.15 × 80. You can also take 15 hundredths of 80 by finding 1% first: 80 ÷ 100 = 0.8, then 15 × 0.8 = 12. Both paths are the same multiplication. The word of, here as in fractions, means multiply.

A friendly percent is a fraction you know

10% is 10/100 = 1/10, so 10% of a number is that number divided by 10. 25% is 25/100 = 1/4, so 25% of a number is that number divided by 4. 50% is one half. These three are the quick cases. A percent increase is a different question: the change divided by the original amount, written as a percent. Going from 40 to 50 is a change of 10, and 10/40 = 25%.

Worked example 1: 15% of 80

Find 15% of 80. Write 15% as 0.15. Then 0.15 × 80 = 12. The hundredths path agrees: 1% of 80 is 0.8, and 15 × 0.8 = 12. A third path uses the hint from the catalog. 10% of 80 is 8. Half of that 10% is 5%, which is 4. Add them: 8 + 4 = 12. All three paths land on 12. 15% of 80 is not 15, and it is not 80 − 15.

Worked example 2: 10% and 25%

Find 10% of 50, and find 25% of 80. 10% of 50 is 50 ÷ 10 = 5. 25% of 80 is 80 ÷ 4 = 20, because 25% is one quarter. You can also take 10% of 80, which is 8, and add another 10% and a half of 10%: 8 + 8 + 4 = 20. The quarter path is shorter. These are the grade 6 cases the catalog asks for beside the general percent-of skill.

Worked example 3: a price from 40 to 50

A price rises from 40 to 50. The change is 50 − 40 = 10. The percent increase uses the original price as the base: 10/40 = 1/4 = 25%. The new price is not the base. 10/50 = 20% would answer a different question, what part of the new price the change is. The catalog exercise asks for the increase compared with the starting price, which is 25%.

Checks before you leave the problem

For a percent of a number, convert the percent to hundredths and multiply. For 10% or 25%, dividing by 10 or by 4 is enough. For a percent increase, divide the change by the original amount. Then practice percent of a number on the board.

Common questions about percentages

Is 15% of 80 equal to 15?

No. 15% of 80 is 12. The 15 names hundredths, not an amount to subtract from 80 or to copy as the answer.

Why divide a percent increase by the original price?

The original price is the whole that the change is compared with. A rise of 10 from 40 is one quarter of the starting price. A rise of 10 from a different start is a different percent.

Which grades share this page?

Grades 5 through 8. The button opens percent of a number at grade 6. Percent increase is the grades 7–8 extension of the same idea, explained in the third example.