Free Grade 7 Math Worksheets With Answers
Seventh grade turns proportional reasoning into a tool: percent change, scale, and two-step equations all rely on it. These free questions work through each area with the answer and reasoning attached.
10 free questions Β· Answer keys included Β· No sign-up to practice
Skills covered in Grade 7
Aligned to Common Core Grade 7 domains: 7.RP proportional relationships, 7.NS rational number operations, 7.EE expressions and equations, 7.G geometry, and 7.SP probability and statistics.
- Proportional relationships and constant of proportionality
- Percent increase, decrease and discount
- All four operations with rational numbers
- Solving two-step equations
- Expanding and factoring linear expressions
- Area, surface area and volume
- Circumference and area of circles
- Simple probability
Free Grade 7 practice questions with answers
Filter by topic or difficulty, or work straight through. Every answer opens to show the steps, so the page works as a worksheet and an answer key at the same time.
- Question 1easyProportions
If 3 notebooks cost $7.50, what is the unit price?
Show answer and worked solution
Answer: $2.50
Divide total by quantity: 7.50 Γ· 3 = 2.50 per notebook.
- Question 2easyIntegers
Calculate β6 Γ 4
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Answer: β24
A negative times a positive gives a negative: 6 Γ 4 = 24, so the answer is β24.
- Question 3easyEquations
Solve: 2x + 5 = 17
Show answer and worked solution
Answer: x = 6
Subtract 5: 2x = 12. Divide by 2: x = 6.
- Question 4easyPercent change
Increase 200 by 10%.
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Answer: 220
10% of 200 is 20, so 200 + 20 = 220.
- Question 5easyCircles
Find the circumference of a circle with radius 5 cm. Use Ο β 3.14.
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Answer: 31.4 cm
C = 2Οr = 2 Γ 3.14 Γ 5 = 31.4 cm.
- Question 6mediumPercent change
A price falls from $80 to $68. What is the percent decrease?
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Answer: 15%
Change is 80 β 68 = 12. Then 12 Γ· 80 = 0.15, which is 15%.
- Question 7mediumEquations
Solve: 3(x β 2) = 15
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Answer: x = 7
Divide both sides by 3: x β 2 = 5. Then add 2: x = 7.
- Question 8mediumIntegers
Calculate β18 Γ· (β3)
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Answer: 6
A negative divided by a negative gives a positive: 18 Γ· 3 = 6.
- Question 9hardProbability
A bag has 4 red and 6 blue marbles. What is the probability of drawing red?
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Answer: 2/5
There are 10 marbles total, so P(red) = 4/10, which simplifies to 2/5.
- Question 10hardCircles
A circle has circumference 62.8 cm. Find its radius. Use Ο β 3.14.
Show answer and worked solution
Answer: 10 cm
C = 2Οr, so 62.8 = 6.28r, giving r = 62.8 Γ· 6.28 = 10 cm.
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What Grade 7 students are expected to master
Seventh grade is where proportional reasoning stops being a topic and becomes a method. Percent change, scale drawings, unit rates and similar figures are all the same idea wearing different clothes, and students who see the connection carry far less to memorise than students who learn four separate procedures. Asking what stays constant in each situation is usually enough to expose the shared structure.
Two-step equations are the other milestone. The mechanics are simple, but they are the first time students must undo operations in reverse order, and that reversal is genuinely counter-intuitive. A student solving 2x + 5 = 17 has to see that the 5 was added last so it comes off first, which is the opposite of how they read the expression.
Percent change: the error that survives into high school
Ask a class what happens when a price rises 20% and then falls 20%, and most will say it returns to where it started. It does not: the rise is calculated on the original and the fall on the larger figure, so a $100 item becomes $120 and then $96. This misconception survives untouched into high school unless it is confronted directly in Grade 7.
The related error is dividing by the wrong base. A decrease from 80 to 68 is 15% because the change of 12 is compared to the original 80, not to the new 68. Writing the formula as change divided by original before substituting numbers prevents most of these mistakes.