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Multi-Digit Multiplication by a One-Digit Number (Grade 4)
The step-by-step method for multiplying a multi-digit number by a one-digit number, worked examples with carrying, a free online practice with instant checking, and printable cards with answers.
Multi-digit multiplication uses the same one-digit facts you already know, just repeated at every place value. Once you can multiply by a single digit, you can multiply any number by it, no matter how many digits it has.
Start at the ones place and work left, one digit at a time. Multiply the one-digit number by each digit of the other number, write the last digit of the product in that column, and carry the rest to the next place. Add the carry to the next product before you multiply, then carry again if needed.
For 448 × 9: 8 × 9 = 72, write 2 and carry 7. 4 × 9 = 36, plus the carry 7 is 43, write 3 and carry 4. 4 × 9 = 36, plus the carry 4 is 40, write 40. Reading the digits together gives 4,032.
To check your answer, round the multi-digit number and estimate. 2,864 rounds to 2,900, and 2,900 × 6 = 17,400, close to the exact answer 2,864 × 6 = 17,184. If the estimate and the exact answer are far apart, a digit or a carry was probably missed.
Worked examples
7,656 × 7 = 53,592
- ones: 6 × 7 = 42, write 2, carry 4
- tens: 5 × 7 + 4 = 39, write 9, carry 3
- hundreds: 6 × 7 + 3 = 45, write 5, carry 4
- thousands: 7 × 7 + 4 = 53
- Answer: 53,592
3,474 × 7 = 24,318
- ones: 4 × 7 = 28, write 8, carry 2
- tens: 7 × 7 + 2 = 51, write 1, carry 5
- hundreds: 4 × 7 + 5 = 33, write 3, carry 3
- thousands: 3 × 7 + 3 = 24
- Answer: 24,318
7,600 × 6 = 45,600
- ones: 0 × 6 = 0, write 0, carry 0
- tens: 0 × 6 = 0, write 0, carry 0
- hundreds: 6 × 6 = 36, write 6, carry 3
- thousands: 7 × 6 + 3 = 45
- Answer: 45,600
Practice: solve 10 problems
Examples with answers
| Problem | Answer |
|---|---|
| 7,656 × 8 | 61,248 |
| 1,060 × 3 | 3,180 |
| 2,983 × 7 | 20,881 |
| 3,989 × 4 | 15,956 |
| 3,492 × 6 | 20,952 |
| 5,692 × 9 | 51,228 |
| 3,689 × 7 | 25,823 |
| 8,538 × 4 | 34,152 |
| 2,682 × 4 | 10,728 |
| 1,503 × 2 | 3,006 |
| 9,411 × 2 | 18,822 |
| 9,648 × 7 | 67,536 |
Common mistakes
In 448 × 9, 8 × 9 = 72, so you write 2 and carry 7 to the tens column. Drop that 7 and every digit after it comes out wrong.
Each digit of the answer goes under the place you just multiplied: ones under ones, tens under tens, and so on, the same way you line up digits when you add.
In 2,864 × 6, multiplying only 864 × 6 gives 5,184 and misses the thousands digit. Multiply all four digits, including the 2, to get 17,184.
Practice in the game
Each right answer builds a tower that defends the fortress. Free, no sign-up, phone or computer.
For parents: practising at home
Practice 5 to 10 problems a day instead of a long worksheet. Ask your child to say each step out loud: multiply, write, carry, next digit. If the carries keep going wrong, review the multiplication table for that one-digit number first.
Assign multi-digit multiplication to a student in ZnayQuest: they practice at home in the game, and you see every mistake, what they answered and the correct answer, so you know which place value or carry step to review.
FAQ
How do you multiply a multi-digit number by a one-digit number?
Multiply one place at a time, starting from the ones. Write the last digit of each product, carry the rest to the next place, and add the carry before you multiply there.
What if the carry has two digits?
Add the whole carry to the next product, then carry again if the result still has two digits. In 9,986 × 8 the carries go 4, then 6, then 7, before the final answer 79,888.
Is it free?
Yes. The lesson, the practice, and the printable cards are free, with no sign-up.