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E.7 Divide whole numbers by 2-digit numbers: word problems

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Understanding division in real-world problems

Division helps us find how many equal groups can be made or how many items are in each group. When we divide by a 2-digit number, we are often solving a problem about sharing or grouping in real-life situations.

Example:
  • There are 624 apples, and each box holds 24 apples.
  • We divide 624 ÷ 24 = 26.
  • There will be 26 full boxes of apples.
Note

Division connects numbers to real situations. Always think about what the quotient means in the story.

What happens when there is a remainder?

Sometimes division does not come out evenly. The number left over is called the remainder. In word problems, we must decide what to do with it based on the situation.

Example:
  • A farmer has 650 apples. Each box holds 24 apples.
  • Divide 650 ÷ 24 = 27 remainder 2.
  • There are 27 full boxes, and 2 apples are left over.
Note

The remainder tells us what is left when we cannot make another full group. Sometimes the remainder means a partial group or something that cannot be used completely.

Deciding what to do with the remainder

How we use the remainder depends on what the problem is asking. We may ignore it, use it as a part of the answer, or round up to make an extra group.

Examples:
  • Ignore the remainder: 650 ÷ 24 = 27 R2 → 27 full boxes (the 2 apples stay out).
  • Round up: 650 apples need boxes of 24 → 28 boxes are needed, because one more box is required for the leftover apples.
  • Use the remainder as part of the answer: 27 full boxes and 2 extra apples remain.
Note

Always reread the question to know whether the remainder means “extra,” “left over,” or “round up.”

Solving multi-step word problems

Some problems require more than one operation. You may need to multiply or add after dividing to find the final answer.

Example:
  • A store has 1,248 cans. Each box holds 24 cans. How many full boxes can be made, and how many cans are left over?
  • Step 1: 1,248 ÷ 24 = 52 boxes.
  • Step 2: 52 × 24 = 1,248 (no remainder). All cans fit perfectly.
  • If there were 1,250 cans, then 1,250 ÷ 24 = 52 R2. There would be 2 cans left over.
Note

Label each part of your answer clearly. In multi-step problems, show all your math to explain how you found the result.

Checking your division answers

After solving, check your work by multiplying the quotient by the divisor and adding any remainder. The result should equal the dividend.

Example:
  • Check 650 ÷ 24 = 27 R2.
  • Now multiply: 27 × 24 = 648.
  • Add the remainder: 648 + 2 = 650.
  • The answer checks out because it matches the original total.
Note

Always verify your division with multiplication. This helps you avoid simple mistakes and ensures your answer makes sense in the problem’s context.

Thinking about reasonableness

Before finishing, check if your answer is reasonable. Use estimation to see if your result is close to what makes sense.

Example:
  • Estimate 650 ÷ 24. Since 24 is close to 25, use 650 ÷ 25 = 26.
  • The exact quotient of 27 makes sense because it is close to the estimate.
Note

Estimating before and after dividing helps you know if your answer is realistic.