Percents

Percent Word Problems

Solve "part is what percent of base?" by forming the ratio part/base and multiplying by 100.

percent-word-problem To find what percent part is of base: - Form ratio part/base in lowest terms. - Multiply by 100 to get the percent.

Example

Turn the word relationship into a fraction and then a percent.

highlighted = computed this step

Step 1 — Set up

Set up the relationship.

18 is ?% of 2418 \text{ is ?\% of } 24
Start with 18 as the part and 24 as the whole.wholepart: 18whole: 24percent scale100%The shaded cells are the part; all cells together are the whole.

Step 2 — Write the fraction

Write part over base: 18/24.

1824\hlmath{\frac{18}{24}}
Write part over whole: 18/24.wholepart: 18whole: 24percent scale100%18/24The bar reads exactly 18 out of 24.

Step 3 — Simplify the fraction

Simplify with GCF 6: 18/24 = 3/4.

gcd⁡(18,24)=634\gcd( 18 , 24 )= \hl{6} \quad \hlmath{\frac{3}{4}}
Group by 6: 18/24 = 3/4.wholepart: 18whole: 24percent scale100%3/4groups of 63 of the 4 equal groups are shaded.

Step 4 — Convert to percent

Convert to percent: 3/4 x 100 = 75%.

34×100=75%\frac{3}{4} \times 100 = \hl{75\%}
Convert the rate: 3/4 x 100 = 75%.wholepart: 18whole: 24percent scale100%3/4groups of 675%3/4 x 100 = 75%3/4 of 100% is 75%.

Step 5 — Result

Read the final result.

75%75\%
The part is 75% of the whole.wholepart: 18whole: 24percent scale100%3/4groups of 675%3/4 x 100 = 75%So 18 is 75% of 24.