Grade 7 Math Practice Test: Operations with Integers and Rational Numbers
- Integers and Rational Numbers
- 12 questions
- 15 minutes
This test covers adding, subtracting, multiplying and dividing positive and negative numbers, absolute value as distance, repeating decimals, and word problems with temperatures, elevations and money. Tip: subtracting a number is the same as adding its opposite, so 2 − (−5) = 2 + 5.
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
On a number line, Theo starts at −3 and moves 8 units to the right. On which number does he stop?
Correct answer: A
Moving to the right means adding: −3 + 8 = 5. −11 is where he would stop if he moved 8 units to the left (−3 − 8).
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Question 2
What is 4 − (−9)?
Correct answer: D
Subtracting −9 is the same as adding its opposite, 9: 4 + 9 = 13. −5 is the answer to 4 + (−9), not 4 − (−9).
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Question 3
At 6 a.m. the temperature in a town was −7°F. By noon it had risen 15 degrees. What was the temperature at noon?
Correct answer: B
A rise of 15 degrees means adding 15: −7 + 15 = 8°F. −22°F subtracts 15, as if the temperature had dropped.
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Question 4
A diver is 35 feet below sea level. A pelican is flying 20 feet above sea level, directly above the diver. How far apart are they?
Correct answer: C
Write the positions as −35 and 20. The distance between them is the absolute value of their difference: |20 − (−35)| = |20 + 35| = 55 feet. 15 feet would be right only if both were on the same side of sea level.
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Question 5
Which expression gives the distance between −6 and 4 on a number line?
Correct answer: D
The distance between two numbers is the absolute value of their difference: |−6 − 4| = |−10| = 10. −6 − 4 equals −10, but a distance cannot be negative, and |−6 + 4| = 2 adds the numbers instead of subtracting them.
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Question 6
What is (−6) × (−4) × (−2)?
Correct answer: A
(−6) × (−4) = 24, and 24 × (−2) = −48. A product with three negative factors is negative, so 48 has the wrong sign.
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Question 7
Which expression is NOT equal to −34?
Correct answer: D
A quotient of two numbers with different signs is negative, so −34 and 3−4 both equal −34, and −0.75 is the same number written as a decimal. In −3−4 both numbers are negative, so the quotient is positive 34.
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Question 8
Which fraction has a decimal form that repeats forever instead of terminating?
Correct answer: C
Divide each numerator by its denominator: 38 = 0.375, 720 = 0.35 and 916 = 0.5625 all stop. 512 = 0.41666…, where the 6 repeats forever.
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Question 9
Jada has $35 in her bank account. She makes three purchases of $12.50 each with her debit card. What is her account balance after the purchases?
Correct answer: B
The purchases total 3 × $12.50 = $37.50, and $35 − $37.50 = −$2.50. The balance is negative because she spent $2.50 more than she had, so $2.50 has the wrong sign.
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Question 10
What is −34 ÷ 12?
Correct answer: A
Dividing by 12 is the same as multiplying by 2: −34 × 2 = −64 = −112. −38 multiplies by 12 instead of dividing.
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Question 11
A submarine is at −120 meters, which means 120 meters below the surface. It rises 15 meters each minute for 6 minutes. What is its new position?
Correct answer: C
Rising 15 meters a minute for 6 minutes is a change of 6 × 15 = +90 meters: −120 + 90 = −30 meters, so it is still 30 meters below the surface. −210 meters treats rising as going deeper.
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Question 12
Over 6 hours, the temperature fell a total of 18°F at a steady rate. Which number shows the change in temperature per hour?
Correct answer: B
A fall is a negative change, so divide −18 by 6: −18 ÷ 6 = −3°F per hour. 3°F has the wrong sign, because the temperature went down.
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