Multiply 4-Digit by 1-Digit

Grade 4 · mathematics · 71 practice problems · read aloud

🔊 Listen to this explanation

Multiplying 4-Digit Numbers by 1-Digit Numbers

🧠 What is it and Why Learn It?

This operation is a way of adding a large number to itself multiple times, very quickly! It's super useful in real life. For example, if one box holds 2,345 crayons, how many crayons are in 4 boxes? Multiplying is much faster than adding 2,345 + 2,345 + 2,345 + 2,345!

📝 Step-by-Step Guide

We solve this using the standard algorithm, which means we multiply from right to left (ones place to thousands place).

  1. Set it up: Write the 4-digit number on top and the 1-digit number underneath, aligning them to the right.
  2. Multiply the Ones: Multiply the bottom digit by the ones digit of the top number. Write the answer below the line. If the answer is 10 or more, regroup (carry over) the tens digit.
  3. Multiply the Tens: Multiply the bottom digit by the tens digit. Add any number you carried over. Write the ones digit of this answer below the line and carry the tens digit.
  4. Multiply the Hundreds: Repeat the process for the hundreds digit.
  5. Multiply the Thousands: Finally, multiply by the thousands digit, remembering to add any carryover.

🔍 Worked Examples

Example 1: 1,234 × 2

1,234
× 2
  2,468

Steps: 2 × 4 = 8, 2 × 3 = 6, 2 × 2 = 4, 2 × 1 = 2. No carrying needed!

Example 2: 3,576 × 4

232  (Carry-over numbers)
3,576
× 4
14,304

Steps:
Ones: 4 × 6 = 24 (write 4, carry 2)
Tens: 4 × 7 = 28, + 2 = 30 (write 0, carry 3)
Hundreds: 4 × 5 = 20, + 3 = 23 (write 3, carry 2)
Thousands: 4 × 3 = 12, + 2 = 14 (write 14)

⚠️ Common Mistakes to Avoid

  • Forgetting to add the carry-over: This is the #1 mistake! Always add the number you carried before you write the answer down.
  • Misaligning the numbers: Make sure all digits are lined up to the right. A messy setup leads to wrong answers.
  • Multiplying from left to right: Always start with the ones place on the right and work your way left.

💡 Tips & Tricks

  • Use Estimation: Before you start, round the 4-digit number. For 4,189 × 3, think "about 4,000 × 3 = 12,000." If your final answer is close, it's probably right!
  • Whisper the Steps: Say the steps quietly as you work: "4 times 6 is 24, write 4, carry 2..." This helps you remember the carry-over.
  • Check Your Work: After you finish, multiply in a different order or use repeated addition to check one of the place values.

🎯 How to Practice

The best way to get better is to practice!

  • Start with problems that don't require carrying (like 1,234 × 2).
  • Then, move to problems with carrying in one place, then two places.
  • Create your own problems using numbers from your life, like the number of students in your school or pages in a book.
  • Ask a friend or family member to give you five problems a day. Consistency is key!

Practice problems

6 of the 71, worked through step by step — try them before opening the answer.

1 234 × 56 = ?

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

Show the answer

Answer: 13104

  1. Break 56 into 50 + 6. So, 234 × 56 = 234 × (50 + 6) = (234 × 50) + (234 × 6).
  2. Calculate 234 × 6. 234 × 6: 4 × 6 = 24 → write 4, carry over 2. 3 × 6 = 18, plus carried 2 = 20 → write 0, carry over 2. 2 × 6 = 12, plus carried 2 = 14 → write 14. So, 234 × 6 = 1404.
  3. Calculate 234 × 50. 234 × 50 = 234 × 5 × 10. First, 234 × 5: 4 × 5 = 20 → write 0, carry over 2. 3 × 5 = 15, plus carried 2 = 17 → write 7, carry over 1. 2 × 5 = 10, plus carried 1 = 11 → write 11. So, 234 × 5 = 1170. Now multiply by 10: 1170 × 10 = 11700. So, 234 × 50 = 11700.
  4. Add the two results. 1404 + 11700: Write them aligned: 1404 + 11700 -------- 4 + 0 = 4. 0 + 0 = 0. 4 + 7 = 11 → write 1, carry over 1. 1 + 1 = 2, plus carried 1 = 3. 1 + 0 = 1 (from 11700's ten-thousands place). So result is 13104. Final answer: 13104.

Let's multiply 234 × 56 step by step.

2 345 × 67 = ?

Hint: Break this into smaller multiplication problems and add the results

Show the answer

Answer: 23115

  1. Multiply 345 by 7 (ones place): 345 × 7 = 2415
  2. Multiply 345 by 60 (tens place): 345 × 60 = 20700
  3. Add the partial products: 2415 + 20700 = 23115

The answer is 23115.

3 245 × 38 = ?

Hint: Break this into smaller multiplication problems and add the results together

Show the answer

Answer: 9310

  1. Multiply 245 by 30: 245 × 30 = 7,350
  2. Multiply 245 by 8: 245 × 8 = 1,960
  3. Add the two results: 7,350 + 1,960 = 9,310

The answer is 9,310.

4 1,234 × 56 = ?

Hint: Break the multiplication into smaller parts by multiplying each digit of the larger number separately, then add the results together.

Show the answer

Answer: 69104

  1. Multiply 1,234 by 6 (the ones digit of 56): 1,234 × 6 = 7,404
  2. Multiply 1,234 by 50 (the tens digit of 56): 1,234 × 50 = 61,700
  3. Add the two partial products: 7,404 + 61,700 = 69,104
  4. The final answer is 69,104.

5 1,248 × 36 = ?

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

Show the answer

Answer: 44928

  1. Multiply 1,248 by 6 (the ones digit of 36) 1,248 × 6 = 7,488
  2. Multiply 1,248 by 30 (the tens digit of 36) 1,248 × 30 = 37,440
  3. Add the two partial products together 7,488 + 37,440 = 44,928
  4. The final answer is 44,928

6 1,248 × 63 = ?

Hint: Break this into smaller multiplication problems and add the results together

Show the answer

Answer: 78624

  1. Multiply 1,248 by 60 1,248 × 60 = (1,248 × 6) × 10 1,248 × 6 = 7,488 7,488 × 10 = 74,880
  2. Multiply 1,248 by 3 1,248 × 3 = 3,744
  3. Add the two results together 74,880 + 3,744 = 78,624

The answer is 78,624.

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