Grade 7 Math Practice Test: Multi-Step Word Problems with Fractions, Decimals and Negative Numbers
- Multi-Step Word Problems with Rational Numbers
- 10 questions
- 15 minutes
This test covers real-life problems that need two or more steps with positive and negative fractions and decimals. Tip: before you calculate, estimate with rounded numbers, then check that your final answer is close to the estimate.
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
Kara earns $14.50 per hour. She works 612 hours on Saturday and 4 hours on Sunday. How much does she earn in all?
Correct answer: A
She works 6.5 + 4 = 10.5 hours, and 10.5 × $14.50 = $152.25. $94.25 is only Saturday's pay.
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Question 2
A board is 12 feet long. Sam cuts off 3 pieces that are each 234 feet long. How much of the board is left?
Correct answer: C
The pieces use 3 × 2 3/4 = 8 1/4 feet, and 12 − 8 1/4 = 3 3/4 feet. 9 1/4 feet subtracts only one piece.
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Question 3
At 5 a.m. the temperature was −8.5°C. It rose 2.25°C every hour for 6 hours. What was the temperature at 11 a.m.?
Correct answer: B
The total rise is 6 × 2.25 = 13.5°C, and −8.5 + 13.5 = 5°C. −22°C subtracts the rise instead of adding it, and 13.5°C forgets the starting temperature.
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Question 4
Ben buys 4 shirts at $19.85 each and pays with a $100 bill. How much change should he get?
Correct answer: B
4 × $19.85 = $79.40, and $100 − $79.40 = $20.60. Estimate: 4 shirts at about $20 cost about $80, so the change is about $20. $79.40 is the cost, not the change.
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Question 5
Lena says that 3.9 × 21.2 = 826.8. Which estimate best shows that her answer is not reasonable?
Correct answer: D
Rounding gives 4 × 20 = 80, so the product should be near 80 (it is 82.68). Lena's answer is about 10 times too big, likely from a misplaced decimal point. Rounding 21.2 to 200 or 2 changes its size by a factor of 10.
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Question 6
A water tank holds 240 gallons when full. It is 34 full. A farm uses 18 gallons each day and adds no water. How many gallons are left after 4 days?
Correct answer: B
The tank starts with 3/4 × 240 = 180 gallons. In 4 days the farm uses 4 × 18 = 72 gallons, so 180 − 72 = 108 gallons remain. 168 starts from the full 240 gallons.
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Question 7
A diver is at −30 meters. She rises 13 of the way to the surface and then dives down 6 meters. What is her new position?
Correct answer: C
One third of the way to the surface is 30 ÷ 3 = 10 meters up, so she reaches −20. Diving 6 meters down gives −20 − 6 = −26 meters. −14 treats the dive as a move upward.
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Question 8
Sam has $60. He spends 14 of it on a concert ticket and then 15% of the money that is left on snacks. How much money does he have now?
Correct answer: D
The ticket costs 60 ÷ 4 = $15, leaving $45. Snacks cost 15% of $45 = $6.75, so $45 − $6.75 = $38.25. $36.00 takes 15% of the original $60 instead of the remaining $45.
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Question 9
On a hike, Ari's elevation changes by −120.5 ft, +85 ft, −40.25 ft and +30 ft. What is the total change in elevation?
Correct answer: A
Add the gains: 85 + 30 = 115. Add the losses: −120.5 + (−40.25) = −160.75. Then 115 + (−160.75) = −45.75 ft, a net drop. 34.75 ft treats the −40.25 as a gain.
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Question 10
A phone costs $249. Mia has saved $87.50 and saves $13.50 more each week. After how many weeks will she first have enough money?
Correct answer: D
She still needs $249 − $87.50 = $161.50, and 161.50 ÷ 13.50 ≈ 11.96. After 11 weeks she is a little short, so she needs 12 weeks. 19 weeks ignores the money she already saved.
Questions you leave blank are not counted as wrong.
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