Free Grade 6 Math Worksheets With Answers
Sixth grade is the bridge into algebra: ratios, negative numbers and letters standing for numbers all arrive at once. These free questions cover the whole bridge, with the working shown for each answer.
10 free questions · Answer keys included · No sign-up to practice
Skills covered in Grade 6
Aligned to Common Core Grade 6 domains: 6.RP ratios and proportional relationships, 6.NS the number system, 6.EE expressions and equations, 6.G geometry, and 6.SP statistics.
- Ratios and unit rates
- Percent of a quantity
- Operations with positive and negative integers
- Dividing fractions by fractions
- Writing and evaluating algebraic expressions
- Solving one-step equations
- Area of triangles and quadrilaterals
- Mean, median, mode and range
Free Grade 6 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 1easyRatios
Simplify the ratio 12 : 18
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Answer: 2 : 3
Divide both parts by their highest common factor, 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
- Question 2easyPercentages
What is 25% of 80?
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Answer: 20
25% is one quarter, so 80 ÷ 4 = 20.
- Question 3easyIntegers
Calculate −7 + 3
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Answer: −4
Start at −7 and move 3 to the right on the number line, landing on −4.
- Question 4easyExpressions
Evaluate 3x + 5 when x = 4
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Answer: 17
Substitute first: 3 × 4 = 12, then 12 + 5 = 17.
- Question 5easyArea
Find the area of a triangle with base 10 cm and height 6 cm.
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Answer: 30 square cm
Area = ½ × base × height = ½ × 10 × 6 = 30.
- Question 6mediumIntegers
Calculate −5 − (−8)
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Answer: 3
Subtracting a negative is adding: −5 + 8 = 3.
- Question 7mediumRatios
If 4 pens cost $6, what do 10 pens cost?
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Answer: $15
Unit rate is 6 ÷ 4 = $1.50 per pen, so 10 × 1.50 = $15.
- Question 8mediumExpressions
Solve: x + 12 = 30
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Answer: x = 18
Subtract 12 from both sides: x = 30 − 12 = 18.
- Question 9hardPercentages
A jacket costs $60 and is reduced by 15%. What is the sale price?
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Answer: $51
15% of 60 is 0.15 × 60 = $9, so the price becomes 60 − 9 = $51.
- Question 10hardStatistics
Find the median of 4, 9, 2, 7, 6
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Answer: 6
Order them: 2, 4, 6, 7, 9. With five values the middle one is the third, which is 6.
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What Grade 6 students are expected to master
Sixth grade asks students to accept three uncomfortable ideas at once: that numbers can be less than zero, that a letter can stand for a number, and that division can make a number bigger. Each of those contradicts something that was reliably true in elementary school, and students who are told to just follow the rule tend to lose confidence rather than gain it.
Ratios do most of the heavy lifting. A ratio is the first time students meet a relationship between two quantities rather than a quantity itself, and it underpins percentages, rates, scale and the proportional reasoning that Grade 7 is built on. Time spent on unit rates in Grade 6 pays back repeatedly over the next three years.
The negative number errors worth pre-empting
The most common Grade 6 error is treating subtraction of a negative as ordinary subtraction: writing −5 − (−8) = −13. It comes from reading the two minus signs as one operation. Making students rewrite the expression as −5 + 8 before evaluating removes almost all of these errors, because the rewriting step is visible and checkable.
The second is sign errors in multiplication once negatives meet algebra. A student who is confident that −3 × −4 = 12 in isolation will often get −3x when x = −4 wrong, because substitution hides the second negative. Insisting on brackets during substitution, writing −3 × (−4), makes the structure visible.