How to Solve Multi-Step Word Problems

To solve a multi-step word problem, find exactly what the question asks, list the facts you are given, plan the steps in order, solve one step at a time and label each result, then check that the final answer fits the question and its units. Most mistakes come from stopping after an intermediate step, so always reread the question before you write the answer.

Multi-step word problems need more than one operation: you might multiply to find a cost, then subtract to find the change. Below is a five-step method, a planning template, worked examples from grade 3 to grade 7 level, the most common traps, and practice problems with answers.

A 5-step method for any multi-step word problem

1. Find the question. Underline the last sentence. What exactly is being asked: a total, a difference, how much each, how much is left?
2. List the facts. Write every number with its label (4 shirts, $12 each, $10 coupon). Cross out numbers you don’t need.
3. Plan the steps. Decide what you need to know first. Often you have to answer a hidden question before the asked one.
4. Solve one step at a time. Label each result (cost of shirts = $48) so you know what it means.
5. Check. Does the answer answer the question? Is it a reasonable size? Are the units right?

Planning template

Worked examples

1. Shopping (grade 3-4). Maya buys 4 shirts at $12 each and uses a $10 coupon. How much does she pay?
Step 1: 4 × 12 = $48 for the shirts. Step 2: 48 − 10 = $38.

2. Equal groups (grade 3-4). A class of 28 students makes teams of 4, and each team gets 3 markers. How many markers are needed?
Step 1: 28 ÷ 4 = 7 teams. Step 2: 7 × 3 = 21 markers.

3. Total cost (grade 4). Sarah buys 2 books and 4 pens. Each pen costs $5 and each book costs twice as much as a pen. How much does she spend?
Step 1: one book = 2 × $5 = $10. Step 2: books = 2 × $10 = $20. Step 3: pens = 4 × $5 = $20. Step 4: 20 + 20 = $40.

4. Distance (grade 5). A bus travels 45 miles per hour for 2 hours, then 60 miles per hour for 1.5 hours. How far does it go?
45 × 2 = 90 miles; 60 × 1.5 = 90 miles; 90 + 90 = 180 miles.

5. Remainders (grade 4-5). 130 students are going on a trip, and each van holds 12 students. How many vans are needed?
130 ÷ 12 = 10 R 10. Ten vans carry 120 students and 10 are left, so 11 vans are needed. The remainder changes the answer.

6. Fractions (grade 5-6). A recipe uses 3/4 cup of sugar per batch. Ana makes 3 batches and has 2 cups of sugar. How much sugar is left?
3 × 3/4 = 9/4 = 2 1/4 cups needed. That is more than 2 cups, so she is 1/4 cup short, not left over. Always check whether the answer is possible.

7. Percent (grade 6-7). A $60 jacket is 25% off, and sales tax is 8%. What is the final price?
Discount: 0.25 × 60 = $15, so the sale price is $45. Tax: 0.08 × 45 = $3.60. Final price: 45 + 3.60 = $48.60.

Using a bar model

Drawing a bar (tape) diagram helps when the steps are not obvious. For “Tom has 3 times as many stickers as Lee. Together they have 48. How many does Tom have?”, draw 1 bar for Lee and 3 equal bars for Tom: 4 equal parts make 48, so one part is 12 and Tom has 3 × 12 = 36.

Common traps

• Answering the hidden question. Finding the total cost when the question asks for the change.
• Trusting key words blindly. “Left” often means subtract, but “How many are left to buy?” can mean add. Picture the story.
• Ignoring the remainder in sharing and grouping problems.
• Using extra numbers. Some problems include information you don’t need.
• Dropping units. Write $, miles or cups with every step.

Practice problems

1. Leo earns $9 an hour. He works 6 hours on Saturday and 4 hours on Sunday, then spends $35. How much does he have left?
2. A box holds 24 crayons. A teacher has 5 boxes and gives 6 crayons to each of 18 students. How many crayons are left?
3. A train travels 240 miles in 4 hours, then 150 more miles at the same speed. How long does the whole trip take?
4. A $40 game is 30% off. How much do you pay?

Answers

1. 9 × (6 + 4) = $90; 90 − 35 = $55.
2. 5 × 24 = 120; 18 × 6 = 108; 120 − 108 = 12 crayons.
3. Speed = 240 ÷ 4 = 60 mph; 150 ÷ 60 = 2.5 hours; total 4 + 2.5 = 6.5 hours.
4. 0.30 × 40 = $12 off; 40 − 12 = $28.

Frequently Asked Questions

What is a multi-step word problem?

A word problem that needs two or more operations to answer, such as multiplying to find a cost and then subtracting to find change. The answer to one step becomes a number you use in the next.

How do you solve multi-step word problems?

Read the question twice and underline what it asks, list the facts you are given, plan the steps in order, solve one step at a time while labeling each result, and check that the final answer answers the actual question and has the right units.

How can you check the answer to a multi-step problem?

Estimate first and compare, work backward from your answer to the starting numbers, and make sure the units and size of the answer make sense in the story.

What grade are multi-step word problems?

Students start two-step problems in grade 2 and grade 3, and multi-step problems with all four operations appear in grade 4 and beyond, including fractions, decimals and percents in grades 5 to 7.

Related: Distance, rate and time problems · Multi-step word problems with remainders · Percent problems