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D.10 Multiply whole numbers by 2-digit numbers: word problems

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What is multiplication with 2-digit numbers?

Multiplying by 2-digit numbers means finding the product when one factor has two digits (like 24 or 57). This builds on your knowledge of basic multiplication facts and place value.

Examples:
  • 36 × 14
  • 125 × 23
  • 78 × 45
Note

In real life, we often multiply by 2-digit numbers when calculating costs, measurements, or quantities of items.

The standard algorithm for 2-digit multiplication

The standard algorithm is a step-by-step method that uses place value to multiply larger numbers efficiently.

Steps for 47 × 36:
  • Step 1: Multiply 47 × 6 (ones place) = 282
  • Step 2: Write a 0 in the ones place, then multiply 47 × 3 (tens place) = 141
  • Step 3: Add the partial products: 282 + 1,410 = 1,692
Note

Remember to align numbers by place value when writing partial products. The zero in the second line represents the tens place.

Solving word problems with 2-digit multiplication

Word problems require you to identify when multiplication is needed and then apply the standard algorithm to find the solution.

Example problem:
  • "A factory produces 28 toys each hour. How many toys will it produce in 15 hours?"
  • Step 1: Identify the numbers: 28 toys × 15 hours
  • Step 2: Multiply 28 × 15 = 420 toys
Note

Always check if your answer makes sense. If a factory makes 28 toys each hour, in 15 hours it should make more than 280 toys (10 hours) but less than 600 toys (20 hours).

Checking your work

Estimation helps verify that your multiplication answer is reasonable before you finish solving the problem.

Estimation example:
  • For 47 × 36:
  • Round 47 to 50 and 36 to 40
  • Estimate: 50 × 40 = 2,000
  • Actual answer (1,692) is close to our estimate
Note

If your actual answer is very different from your estimate, check your work again. You might have made a calculation error.

Common mistakes to avoid

Being aware of common errors helps you check your work more carefully.

Watch out for:
  • Forgetting to add the zero when multiplying by the tens digit
  • Misaligning partial products when adding
  • Making basic multiplication fact errors
  • Forgetting to add carried numbers
Note

Always double-check your multiplication facts and addition. Working neatly with proper alignment helps prevent errors.