Expressions and Equations Practice Questions

Common Core (US) · Common Core Math Grade 6 · 135 free MCQs with instant results and detailed explanations.

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Sample Questions from Expressions and Equations

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Easy

If 5y + 10 = 30, what is the value of y?

A. 4

B. 5

C. 10

D. 2

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Correct Answer: A

To solve for y, first subtract 10 from both sides: 5y = 20. Then, divide both sides by 5: y = 4.

Easy

Which expression represents the total cost, C, if a shirt costs $15 and a pair of pants costs $25?

A. C = 15 + 25

B. C = 15 * 25

C. C = 15 - 25

D. C = 15 / 25

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Correct Answer: A

To find the total cost of the shirt and pants, we need to add their prices: $15 + $25, which gives us the expression C = 15 + 25.

Easy

Which expression represents the total cost if a notebook costs $2 and a pen costs $3, buying x notebooks and y pens?

A. 2x + 3y

B. 5xy

C. 2 + 3

D. 3x + 2y

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Correct Answer: A

The total cost for x notebooks at $2 each is represented by 2x, and for y pens at $3 each by 3y. Combining these gives the total cost expression as 2x + 3y, making option A the correct choice.

Medium

If 5a + 3 = 2a + 21, what is the value of a?

A. 6

B. 5

C. 7

D. 8

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Correct Answer: A

To isolate a, first subtract 2a from both sides: 5a - 2a + 3 = 21. This simplifies to 3a + 3 = 21. Next, subtract 3 from both sides: 3a = 18, so a = 6 after dividing by 3.

Medium

Which expression represents the total cost C of buying x number of apples at $2 each and y number of bananas at $3 each?

A. 2x + 3y

B. 3x + 2y

C. 5xy

D. 2xy + 3

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Correct Answer: A

The total cost for apples is 2 dollars each, making it 2x, and for bananas, it's 3 dollars each, making it 3y. Therefore, the total cost is represented by the expression 2x + 3y.

Medium

Which expression represents the total cost if an item costs 'x' dollars and there is a sales tax of 5%?

A. 1.05x

B. 0.05x

C. x + 0.05

D. x + 1.05

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Correct Answer: A

1.05x accounts for the original price plus 5% sales tax, making it the correct expression for total cost.

Medium

If 3 times a number 'n' decreased by 7 equals 8, which equation can be used to solve for 'n'?

A. 3n - 7 = 8

B. 3n + 7 = 8

C. n - 7 = 8

D. 3n - 8 = 7

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Correct Answer: A

The equation 3n - 7 = 8 correctly represents the relationship given in the problem.

Hard

If 5x + 3 = 2x + 21, what is the value of x?

A. 6

B. 5

C. 4

D. 8

Show Answer & Explanation

Correct Answer: A

To solve for x, start by isolating x on one side. Subtract 2x from both sides to get 3x + 3 = 21. Then, subtract 3 from both sides to yield 3x = 18. Finally, divide both sides by 3 to find x = 6.

Hard

What is the expression for the total cost C of buying x notebooks at $3 each and y pens at $2 each?

A. C = 3x + 2y

B. C = 2x + 3y

C. C = x + y

D. C = 5(x + y)

Show Answer & Explanation

Correct Answer: A

The total cost C is calculated by multiplying the number of notebooks x by their cost of $3 and adding it to the cost of y pens at $2 each. Thus, the expression is C = 3x + 2y.

Q10

Hard

If 3(x + 5) = 2(x + 12), what is the value of x?

A. -3

B. 3

C. 0

D. 2

Show Answer & Explanation

Correct Answer: A

To solve for x, distribute on both sides: 3x + 15 = 2x + 24. Rearranging gives x = -3.

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Expressions and Equations — Common Core (US) Common Core Math Grade 6 Practice Questions Online

This page contains 135 practice MCQs for the chapter Expressions and Equations in Common Core (US) Common Core Math Grade 6. The questions are organized by difficulty — 42 easy, 71 medium, 22 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.