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§ Arithmetic·Grades 6–7

Percentages Worksheets

Free PDF · Problems + answer key · Instant download

Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable percentages worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from common percentages (10%, 25%, 50%) at the easy level through to applied: discount, tax, successive, tip at the advanced level.

CCSS.6.RPCCSS.7.RP

What is percentages?

A percentage represents a part of 100, expressing fractions and ratios in a standardized form. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Converting between percentages, decimals, and fractions forms the foundation for solving proportion problems across mathematics.

Why it matters

Percentages appear throughout daily life in sales tax calculations, discount pricing, test scores, and statistical reporting. A 20% tip on a $45 meal equals $9, while a 15% discount on a $120 jacket saves $18. In finance, compound interest rates like 3.5% annually determine loan payments and investment returns. Medical statistics often report success rates as percentages, such as a 95% effectiveness rate for vaccines. Grade 6 students encounter percentages in CCSS.6.RP standards when finding percent of a quantity, while Grade 7 extends to multi-step problems under CCSS.7.RP. Advanced mathematics builds on percentage concepts in probability theory, where events are expressed as percentages of favorable outcomes. Economics relies heavily on percentage changes to track inflation, unemployment rates, and market performance indicators.

Common mistakes to watch for

  • ✗Confusing percent with decimal form leads to errors like calculating 25% of 80 as 25 × 80 = 2000 instead of 0.25 × 80 = 20.
  • ✗Adding percentages incorrectly produces results like claiming 30% + 40% = 70% of a number equals the sum of individual calculations, ignoring that percentages of different bases cannot be directly combined.
  • ✗Reversing the base and percentage in word problems creates errors such as finding 20% of 15 when the problem asks for 15% of 20, yielding 3 instead of the correct answer of 3.

Questions teachers ask

How do you convert a percentage to a decimal?+
Divide the percentage by 100 or move the decimal point two places to the left. For example, 45% becomes 0.45, and 7% becomes 0.07. This conversion enables multiplication with the base number to find the percentage amount.
What's the difference between finding a percent of a number and finding what percent one number is of another?+
Finding a percent of a number multiplies the decimal form by the base (20% of 50 = 0.2 × 50 = 10). Finding what percent involves division and multiplication by 100 (10 is what percent of 50? → 10 ÷ 50 × 100 = 20%).
How do you check if a percentage calculation is correct?+
Work backwards by dividing the result by the original number and multiplying by 100. If 30% of 60 equals 18, then 18 ÷ 60 × 100 should equal 30%. This reverse calculation confirms the accuracy of the original computation.
Why do some percentages have decimal places?+
Percentages can be more precise than whole numbers, like 12.5% or 33.3%. When 1 out of 8 items is selected, this equals 12.5%, not 12% or 13%. Decimal percentages provide exact representations of fractional relationships between quantities.
Can a percentage be greater than 100%?+
Yes, percentages above 100% indicate the part exceeds the whole. If a store's sales increased from $200 to $500, the increase is 150% of the original amount. Population growth, profit margins, and performance improvements often exceed 100%.
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Beginner

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Concepts
Common percentages (10%, 25%, 50%)
Range
10/25/50% of 10–100
Steps
1 step
Example
50% of 40

Easy

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Concepts
Percent-of calculation, decimal method
Range
10–90% of 20–200
Steps
1–2 steps
Example
80% of 50

Medium

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Concepts
Three forms: percent-of, what-percent, find-base
Range
10–80% of 40–250
Steps
2–3 steps
Example
48 is what % of 60?

Hard

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Concepts
Applied: discount, tax, successive, tip
Range
10–40% of 40–400
Steps
2–3 steps
Example
25% off 80, then 10% tax

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