Multi-Step Word Problems — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
Lily bought a jacket for $78 and a hat for $23. She paid with $120. Her change is $29 because 78 + 23 = 101 and 120 − 101 = 29.
Corrected: Lily bought a jacket for $78 and a hat for $23. She paid with $120. Her change is $19 because 78 + 23 = 101 and 120 − 101 = 19.
First find the total fish: 6 × 4 = 24. Then subtract the 9 sold: 24 − 9 = 15. The original got 33 by adding 24 + 9 instead of subtracting.
2. Fix the sentence:
A rope is 450 cm long. A worker cuts off 168 cm and then 195 cm. There are 97 cm left because 450 − 168 = 282 and 282 − 195 = 97.
Corrected: A rope is 450 cm long. A worker cuts off 168 cm and then 195 cm. There are 87 cm left because 450 − 168 = 282 and 282 − 195 = 87.
Ella has 45 + 15 = 60 marbles total. Dividing into 6 groups gives 60 ÷ 6 = 10 per group, not 8. The original used the wrong quotient.
3. Fix the sentence:
A store earned $935 on Saturday and $748 on Sunday. After paying $580 in expenses, the profit is $1,113 because 935 + 748 = 1,693 and 1,693 − 580 = 1,113.
Corrected: A store earned $935 on Saturday and $748 on Sunday. After paying $580 in expenses, the profit is $1,103 because 935 + 748 = 1,683 and 1,683 − 580 = 1,103.
The class starts with 5 × 7 = 35 desks. After removing 3, there are 35 − 3 = 32 desks, not 38. The original added 3 instead of subtracting.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A plumber has 750 cm of pipe. He uses 284 cm on one job and 195 cm on another. He has 271 cm left.
Start with 28, subtract the 9 who leave (28 − 9 = 19), then add the 5 who board (19 + 5 = 24). Two operations are needed because people both left and joined.
2. Maya saved $465 in January and $390 in February. She spent $275 on art supplies. She has $580 remaining.
First multiply to find the total cards: 3 × 8 = 24. Then subtract the 7 he gives away: 24 − 7 = 17 cards remaining.
3. A container holds 2,000 mL of juice. After pouring out 875 mL in the morning and 640 mL at lunch, there are 485 mL left.
Start with 4 × 6 = 24 plants already in the garden. Adding 11 more gives 24 + 11 = 35 plants total.
4. Ben earned $340 mowing lawns and $215 washing cars. He bought a game for $129. He has $426 left.
Subtract both amounts from 50: 50 − 18 = 32, then 32 − 14 = 18 stickers left. You can also add the amounts used first: 18 + 14 = 32, then 50 − 32 = 18.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A garden bed is 960 cm long. A gardener plants flowers along 385 cm and vegetables along 290 cm. How many centimeters are unused? Show your steps.
Sample answer: Step 1: 385 + 290 = 675 cm are used. Step 2: 960 − 675 = 285 cm are unused.
True. The shop sells 3 × 9 = 27 donuts from boxes plus 7 singles, and 27 + 7 = 34 donuts in all.
2. Why is it important to check whether your answer makes sense after solving a multi-step problem?
Sample answer: Checking your answer helps you catch mistakes like using the wrong operation or making an arithmetic error. If the answer seems too large or too small for the situation, you know to go back and fix a step.
False. Pablo starts with 40, spends 12 (40 − 12 = 28), then earns 8 (28 + 8 = 36). He has 36 coins, not 34.