Grade 7 Math Practice Test: Equivalent Expressions and the Distributive Property
- Equivalent Expressions
- 10 questions
- 15 minutes
This test covers simplifying linear expressions with the distributive property, combining like terms (including fractions and decimals) and factoring out a greatest common factor. Tip: a minus sign in front of parentheses changes the sign of every term inside.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Which expression is equivalent to 3(2x − 5) + 4x?
Correct answer: A
3(2x − 5) = 6x − 15, and 6x + 4x = 10x, so the result is 10x − 15. 10x − 5 comes from multiplying only the 2x by 3 and forgetting the −5.
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Question 2
Which expression is equivalent to −2(3a − 4) − (a + 1)?
Correct answer: C
−2(3a − 4) = −6a + 8 and −(a + 1) = −a − 1. Combining gives −7a + 7. −7a + 9 forgets to change the sign of the 1.
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Question 3
Which shows 12x + 18 factored using the greatest common factor?
Correct answer: D
The GCF of 12 and 18 is 6, and 12x ÷ 6 = 2x, 18 ÷ 6 = 3. 3(4x + 6) is equivalent, but 3 is not the greatest common factor because 4x + 6 can still be factored.
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Question 4
Simplify: 0.5n + 2.3 − 1.2n + 0.7
Correct answer: B
Combine the n-terms: 0.5n − 1.2n = −0.7n. Combine the constants: 2.3 + 0.7 = 3. 1.7n adds the coefficients instead of subtracting 1.2n.
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Question 5
A jacket costs p dollars. Which expression gives the price after a 15% discount?
Correct answer: C
p − 0.15p = (1 − 0.15)p = 0.85p. 0.15p is only the amount saved, and p − 0.15 subtracts 15 cents instead of 15%.
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Question 6
Which expression is equivalent to 23x − 16x?
Correct answer: B
Use a common denominator: 23 = 46, and 46 − 16 = 36 = 12. 56x adds the fractions instead of subtracting.
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Question 7
A rectangle has length 3x + 2 and width x − 1. Which expression gives its perimeter?
Correct answer: D
Perimeter = 2(3x + 2) + 2(x − 1) = 6x + 4 + 2x − 2 = 8x + 2. 4x + 1 only adds one length and one width.
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Question 8
The price of an item is a dollars. The expression a + 0.08a gives the price including an 8% sales tax. Which expression is equivalent?
Correct answer: D
a + 0.08a = 1a + 0.08a = 1.08a, which means 108% of the price. 1.8a would be an 80% increase.
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Question 9
Which expression is equivalent to 5 − 3(x − 2)?
Correct answer: A
Multiply first: −3(x − 2) = −3x + 6, so 5 − 3x + 6 = 11 − 3x. 2x − 4 comes from subtracting 5 − 3 before multiplying, which breaks the order of operations.
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Question 10
Which expression is equivalent to −12(4y − 10)?
Correct answer: A
−12 · 4y = −2y and −12 · (−10) = +5. A negative times a negative is positive, so −2y − 5 has a sign error.
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