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J.2 Multi-step word problems: without remainders

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What are multi-step word problems?

Multi-step word problems are problems that require more than one operation to find the correct answer. You may need to add, subtract, multiply, or divide β€” or use a combination of these operations β€” to solve the problem completely.

Example:
  • Maria bought 3 boxes of pencils. Each box has 12 pencils. She gave 10 pencils to her friends. How many pencils does she have left?
  • Step 1: 3 × 12 = 36 pencils
  • Step 2: 36 − 10 = 26 pencils left
Note

Always read the problem carefully to decide which operations are needed and in what order to perform them.

How to solve multi-step word problems

To solve multi-step word problems, follow a logical plan. Start by understanding what the question is asking, then choose the correct operations to find the answer.

Steps:
  • Step 1: Read the problem carefully and identify key information.
  • Step 2: Decide which operations (addition, subtraction, multiplication, or division) you need.
  • Step 3: Solve each step in order and check your work as you go.
  • Step 4: Write your final answer in a complete sentence that makes sense.
Note

Show all your work clearly. Writing each step helps prevent mistakes and makes it easier to check your answer.

Choosing the correct operations

Each problem gives clues that tell you which operations to use. Look for words and phrases that signal what to do.

Examples:
  • Addition: total, altogether, in all
  • Subtraction: how many more, how many left, difference
  • Multiplication: each, times, groups of
  • Division: share equally, each group gets, how many in each
Note

Some problems use more than one clue word. Always think about what the problem means before deciding on the operations.

Checking your answer

After solving, check that your answer makes sense. You can use the opposite operation to verify your work or estimate to see if the answer is reasonable.

Example:
  • Problem: A farmer packed 4 baskets with 25 apples in each. He sold 60 apples. How many apples remain?
  • Step 1: 4 × 25 = 100 apples
  • Step 2: 100 − 60 = 40 apples remain
  • Check: 40 + 60 = 100 βœ“
Note

If your check does not work or your answer seems too high or too low, go back and review each step carefully.

Using estimation to solve or check

Estimation helps you quickly predict what the answer should be. Round numbers to the nearest ten or hundred to make calculations easier, then solve to see if your estimate matches your final answer.

Example:
  • Problem: A store sells 48 notebooks for $2 each. Estimate the total cost.
  • Estimate: Round 48 to 50 β†’ 50 × 2 = $100
  • Actual: 48 × 2 = $96
  • The estimate and actual answer are close, so the work makes sense.
Note

Estimation helps you check if your exact answer is reasonable before or after solving a problem.