Percentages Worksheets

What is a percentage?

"Percent" means "per hundred": 25% is $\tfrac{25}{100}$, or 0.25. Every percentage problem links three numbers, the part, the percent and the whole:

Each worksheet asks for one of the three:

• Find the part — "What is 25% of 80?"
• Find the percent — "12 is what % of 48?"
• Find the whole — "18 is 30% of what number?"

The percents are common ones (10%, 15%, 20%, 25%, 30%, 40%, 50%, 60%, 75% and 80%), and the numbers are chosen so that every answer is a whole number.

Worked examples

Find the part: What is 25% of 80?

Find the percent: 12 is what % of 48?

Find the whole: 18 is 30% of what number?

30% of the whole is 18, so divide: $18 \div 0.30 = 60$. Check: 30% of 60 is $0.3 \times 60 = 18$.

Check your answers

Put the answer back into the sentence. "12 is 25% of 48": $0.25 \times 48 = 12$, so the answer fits.

Common mistakes

• Forgetting to convert the percent. 25% of 80 is $0.25 \times 80 = 20$, not $25 \times 80 = 2000$.
• Dividing the wrong way when finding the percent. The part goes on top: $\tfrac{12}{48} = 25\%$, while $\tfrac{48}{12}$ would give 400%.
• Multiplying when finding the whole. "18 is 30% of what number?" is not $0.3 \times 18 = 5.4$. The whole must be larger than the part here, so divide.
• Leaving off the % sign. In "find the percent" questions the answer is 25%, not 25 or 0.25.

A practice path through the question types

1. Find the part. Start here: it is a single multiplication. Begin with 10%, 25% and 50%, which can be done mentally, then build the others from them: 75% of 40 is three lots of 25% of 40, so $3 \times 10 = 30$.
2. Find the percent. Write the part over the whole and simplify before converting: $\tfrac{36}{48} = \tfrac{3}{4} = 75\%$. The percents on the worksheets all come from the same short list, so the fractions soon become familiar.
3. Find the whole. Usually the hardest, because students must divide by the percent instead of multiplying. Working through 10% helps: if 12 is 20% of a number, then 10% of it is 6, so the whole is $6 \times 10 = 60$.

Mixing the three types is the real test of understanding, so once each type is secure, alternate them from one worksheet to the next.

Sample problems

These problems come from the same generator as the worksheet above. Press Generate for a fresh set.

Find the part

1. What is 75% of 80?
2. What is 80% of 60?

Find the percent

3. 8 is what % of 20?
4. 64 is what % of 80?

Find the whole

5. 20 is 20% of what number?
6. 40 is 20% of what number?

Tips for teachers and parents

• Teach the benchmarks first: 50% is half, 25% is a quarter, 10% is one tenth. Many problems can then be done mentally, such as 15% = 10% + 5%.
• A double number line (0 to 100% above, 0 to the whole below) works for all three question types.
• Everyday contexts such as discounts and test scores make the three question types easy to tell apart.

Related topics

• Fractions Basic Math 2
• Decimals Basic Math 2
• Ratios & Proportions Pre-Algebra