Multi-Digit Multiplication

Grade 5 · mathematics · 84 practice problems · read aloud

🔊 Listen to this explanation

Multi-Digit Multiplication Mastery 🧮

This is how we multiply numbers that have more than one digit, like 34 × 6 or 27 × 43. It's a super useful skill for real-life problems, like figuring out the total cost of multiple items or calculating the area of a large space.

How to Solve: The Standard Algorithm

We solve these by breaking the problem into smaller, easier steps.

  1. Set it up: Write the problem vertically, lining up the digits by their place value (ones under ones, tens under tens).
  2. Multiply the ones: Multiply the bottom ones digit by each digit in the top number, from right to left. Regroup (carry over) if needed.
  3. Multiply the tens: Write a zero in the ones column of a new row as a placeholder. Then, multiply the bottom tens digit by each digit in the top number.
  4. Add the partial products: Add the two rows (the partial products) you just made together to get your final answer.

Visual Examples

Example 1: 36 × 4

  3 6
 ×  4
————
+ 1 4 4  ← (6×4=24, write 4, carry 2; 3×4=12, +2=14)
 1 4 4

Example 2: 27 × 34

  2 7
 × 3 4
————
+ 1 0 8  ← (27 × 4) First Partial Product
+ 8 1 0  ← (27 × 30, remember the zero placeholder!)
 9 1 8   ← Final Answer

Common Mistakes to Avoid 🚫

  • Forgetting the placeholder zero: When you move to multiply by the tens digit, you MUST put a zero in the ones column first. This is the #1 mistake!
  • Misplacing the carried number: Write the number you carry over small and clearly above the next digit so you don't forget to add it.
  • Adding instead of multiplying: Remember the step you're on. After you get your partial products, the final step is always addition.

Tips & Tricks

  • Estimate First: Round the numbers (e.g., 27×34 is about 30×30=900). If your answer isn't close, you know to check your work.
  • Check Your Work: Use the inverse operation! Divide your final answer by one of the original numbers to see if you get the other one.
  • Zero is a Hero: That placeholder zero is your best friend for keeping place values correct.

How to Practice

  • Start with 2-digit by 1-digit problems (e.g., 45 × 7) to build confidence.
  • Move on to 2-digit by 2-digit problems (e.g., 56 × 23).
  • Create your own problems and solve them, or ask a friend to make some for you.
  • Use online math games or flashcards for quick, fun practice sessions.

Practice problems

6 of the 84, worked through step by step — try them before opening the answer.

1 324 × 67 = ?

Hint: Break this into smaller multiplication problems. Multiply each digit of the second number by the entire first number, then add the results together, remembering to shift left for place value.

Show the answer

Answer: 21708

  1. Multiply 324 by 7 (ones place): 324 × 7 = 2268
  2. Multiply 324 by 60 (tens place): 324 × 60 = 19440
  3. Add the partial products: 2268 + 19440 = 21708
  4. Verify: 324 × 67 = 21708

The answer is 21708.

2 648 × 37 = ?

Hint: Break the problem into smaller parts by multiplying each digit separately, then add the partial products together.

Show the answer

Answer: 23976

  1. Multiply 648 by 7 (ones place): 648 × 7 = 4536
  2. Multiply 648 by 30 (tens place): 648 × 30 = 19440
  3. Add the partial products: 4536 + 19440 = 23976

The answer is 23976.

3 784 × 56 = ?

Hint: Break the multiplication into smaller parts by multiplying each digit of the second number with the first number, then add the partial products.

Show the answer

Answer: 43904

  1. Multiply 784 by 6 (units digit of 56) 784 × 6 = 4704
  2. Multiply 784 by 50 (tens digit of 56) 784 × 50 = 39200
  3. Add the partial products 4704 + 39200 = 43904

The answer is 43904.

4 748 × 56 = ?

Hint: Break down the multiplication into smaller, more manageable parts by multiplying each digit of the larger number separately.

Show the answer

Answer: 41888

  1. Multiply 748 by 6 (the ones digit of 56) 748 × 6 = 4488
  2. Multiply 748 by 50 (the tens digit of 56) 748 × 50 = 37400
  3. Add the two partial products together 4488 + 37400 = 41888
  4. The final answer is 41888

5 728 × 45 = ?

Hint: Break down the multiplication into smaller, manageable parts using place value.

Show the answer

Answer: 32760

  1. Multiply 728 by the ones digit of 45, which is 5. 728 × 5 = 3640
  2. Multiply 728 by the tens digit of 45, which is 4. Remember to add a zero at the end since you are multiplying by 40. 728 × 4 = 2912 Then, 2912 × 10 = 29120
  3. Add the two partial products together. 3640 + 29120 = 32760 The final answer is 32760.

6 927 × 48 = ?

Hint: Break the multiplication into two simpler multiplications by considering the place values of the second number, then combine the results.

Show the answer

Answer: 44496

  1. Multiply 927 by the ones digit of 48, which is 8. 927 × 8 = 7416
  2. Multiply 927 by the tens digit of 48, which is 4 (representing 40). 927 × 40 = 37080
  3. Add the two partial products together. 7416 + 37080 = 44496 The final answer is 44496.
Practise this topic — 10 free problems, no signup →