Step-by-step Maths Level 5: Three-digit by one-digit numbers
Part of the Step-by-step Maths Level 5 long multiplication of two-digit by one-digit numbers chapter. Chapter overview · whole chapter on one page
Three-digit by one-digit numbers
The same method works for three columns. Start at the ones, then the tens, then the hundreds.
Carry from each column to the next, and write any carried number that is left over at the front.
Key ideas
- Work from the right, one column at a time.
- Carry from each column into the next one on the left.
- Write a carried number left over at the end in front of the answer.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 3. Write 8 in the ones column and carry 1 to the tens column.6 × 3 = 18
- Multiply the tens digit by 3. Write 3 in the tens column and carry 1 to the hundreds column.4 × 3 = 12, plus 1 carried = 13
- Multiply the hundreds digit by 3. Write 7 in the hundreds column.2 × 3 = 6, plus 1 carried = 7
- Write the answer. Read the digits from the bottom of each column, from the left.738
Check. Check: 738 ÷ 3 = 246.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 6. Write 2 in the ones column and carry 4 to the tens column.7 × 6 = 42
- Multiply the tens digit by 6. Write 2 in the tens column and carry 2 to the hundreds column.3 × 6 = 18, plus 4 carried = 22
- Multiply the hundreds digit by 6. Write 2 in the hundreds column and carry 3 to the thousands column.5 × 6 = 30, plus 2 carried = 32
- Write the carried number in front. The carried number is the next digit on the left.3 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.3,222
Check. Check: 3,222 ÷ 6 = 537.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 4. Write 8 in the ones column and carry 2 to the tens column.7 × 4 = 28
- Multiply the tens digit by 4. Write 2 in the tens column and carry 2 to the hundreds column.5 × 4 = 20, plus 2 carried = 22
- Write the carried number in front. The carried number is the next digit on the left.2 in the hundreds column
- Write the answer. Read the digits from the bottom of each column, from the left.228
Check. Check: 228 ÷ 4 = 57.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Watch out
Watch out. Keep the zero column. In 204 × 3, the tens give 0 × 3 = 0, so write 0 in the tens column.
Exam tip
Grown-up tip. Ask the child to count the columns before they start, so that no column is missed.
Exercise 4C Practice: three-digit by one-digit numbers
Non-calculatorMethod. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 4. Write 6 in the ones column and carry 3 to the tens column.9 × 4 = 36
- Multiply the tens digit by 4. Write 1 in the tens column and carry 1 to the hundreds column.2 × 4 = 8, plus 3 carried = 11
- Multiply the hundreds digit by 4. Write 7 in the hundreds column and carry 1 to the thousands column.4 × 4 = 16, plus 1 carried = 17
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,716
Check. Check: 1,716 ÷ 4 = 429.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 2. Write 2 in the ones column and carry 1 to the tens column.6 × 2 = 12
- Multiply the tens digit by 2. Write 9 in the tens column and carry 1 to the hundreds column.9 × 2 = 18, plus 1 carried = 19
- Multiply the hundreds digit by 2. Write 5 in the hundreds column and carry 1 to the thousands column.7 × 2 = 14, plus 1 carried = 15
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,592
Check. Check: 1,592 ÷ 2 = 796.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 3. Write 1 in the ones column and carry 2 to the tens column.7 × 3 = 21
- Multiply the tens digit by 3. Write 8 in the tens column.2 × 3 = 6, plus 2 carried = 8
- Multiply the hundreds digit by 3. Write 4 in the hundreds column and carry 2 to the thousands column.8 × 3 = 24
- Write the carried number in front. The carried number is the next digit on the left.2 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.2,481
Check. Check: 2,481 ÷ 3 = 827.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 2. Write 0 in the ones column and carry 1 to the tens column.5 × 2 = 10
- Multiply the tens digit by 2. Write 3 in the tens column and carry 1 to the hundreds column.6 × 2 = 12, plus 1 carried = 13
- Multiply the hundreds digit by 2. Write 5 in the hundreds column and carry 1 to the thousands column.7 × 2 = 14, plus 1 carried = 15
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,530
Check. Check: 1,530 ÷ 2 = 765.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 4. Write 4 in the ones column and carry 2 to the tens column.6 × 4 = 24
- Multiply the tens digit by 4. Write 4 in the tens column and carry 3 to the hundreds column.8 × 4 = 32, plus 2 carried = 34
- Multiply the hundreds digit by 4. Write 7 in the hundreds column.1 × 4 = 4, plus 3 carried = 7
- Write the answer. Read the digits from the bottom of each column, from the left.744
Check. Check: 744 ÷ 4 = 186.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 9. Write 0 in the ones column.0 × 9 = 0
- Multiply the tens digit by 9. Write 0 in the tens column.0 × 9 = 0
- Multiply the hundreds digit by 9. Write 4 in the hundreds column and carry 5 to the thousands column.6 × 9 = 54
- Write the carried number in front. The carried number is the next digit on the left.5 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.5,400
Check. Check: 5,400 ÷ 9 = 600.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 9. Write 7 in the ones column and carry 2 to the tens column.3 × 9 = 27
- Multiply the tens digit by 9. Write 4 in the tens column and carry 7 to the hundreds column.8 × 9 = 72, plus 2 carried = 74
- Multiply the hundreds digit by 9. Write 6 in the hundreds column and carry 1 to the thousands column.1 × 9 = 9, plus 7 carried = 16
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,647
Check. Check: 1,647 ÷ 9 = 183.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 6. Write 0 in the ones column.0 × 6 = 0
- Multiply the tens digit by 6. Write 6 in the tens column and carry 3 to the hundreds column.6 × 6 = 36
- Multiply the hundreds digit by 6. Write 5 in the hundreds column and carry 1 to the thousands column.2 × 6 = 12, plus 3 carried = 15
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,560
Check. Check: 1,560 ÷ 6 = 260.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 5. Write 0 in the ones column and carry 1 to the tens column.2 × 5 = 10
- Multiply the tens digit by 5. Write 6 in the tens column and carry 4 to the hundreds column.9 × 5 = 45, plus 1 carried = 46
- Multiply the hundreds digit by 5. Write 9 in the hundreds column and carry 3 to the thousands column.7 × 5 = 35, plus 4 carried = 39
- Write the carried number in front. The carried number is the next digit on the left.3 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.3,960
Check. Check: 3,960 ÷ 5 = 792.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 9. Write 9 in the ones column.1 × 9 = 9
- Multiply the tens digit by 9. Write 5 in the tens column and carry 4 to the hundreds column.5 × 9 = 45
- Multiply the hundreds digit by 9. Write 8 in the hundreds column and carry 5 to the thousands column.6 × 9 = 54, plus 4 carried = 58
- Write the carried number in front. The carried number is the next digit on the left.5 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.5,859
Check. Check: 5,859 ÷ 9 = 651.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 8. Write 6 in the ones column and carry 1 to the tens column.2 × 8 = 16
- Multiply the tens digit by 8. Write 5 in the tens column and carry 6 to the hundreds column.8 × 8 = 64, plus 1 carried = 65
- Multiply the hundreds digit by 8. Write 8 in the hundreds column and carry 3 to the thousands column.4 × 8 = 32, plus 6 carried = 38
- Write the carried number in front. The carried number is the next digit on the left.3 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.3,856
Check. Check: 3,856 ÷ 8 = 482.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 6. Write 6 in the ones column.1 × 6 = 6
- Multiply the tens digit by 6. Write 4 in the tens column and carry 5 to the hundreds column.9 × 6 = 54
- Multiply the hundreds digit by 6. Write 7 in the hundreds column and carry 4 to the thousands column.7 × 6 = 42, plus 5 carried = 47
- Write the carried number in front. The carried number is the next digit on the left.4 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.4,746
Check. Check: 4,746 ÷ 6 = 791.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 4. Write 4 in the ones column.1 × 4 = 4
- Multiply the tens digit by 4. Write 4 in the tens column and carry 2 to the hundreds column.6 × 4 = 24
- Multiply the hundreds digit by 4. Write 8 in the hundreds column and carry 1 to the thousands column.4 × 4 = 16, plus 2 carried = 18
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,844
Check. Check: 1,844 ÷ 4 = 461.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 5. Write 5 in the ones column and carry 3 to the tens column.7 × 5 = 35
- Multiply the tens digit by 5. Write 3 in the tens column and carry 2 to the hundreds column.4 × 5 = 20, plus 3 carried = 23
- Multiply the hundreds digit by 5. Write 7 in the hundreds column and carry 4 to the thousands column.9 × 5 = 45, plus 2 carried = 47
- Write the carried number in front. The carried number is the next digit on the left.4 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.4,735
Check. Check: 4,735 ÷ 5 = 947.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 2. Write 2 in the ones column and carry 1 to the tens column.6 × 2 = 12
- Multiply the tens digit by 2. Write 9 in the tens column and carry 1 to the hundreds column.9 × 2 = 18, plus 1 carried = 19
- Multiply the hundreds digit by 2. Write 7 in the hundreds column and carry 1 to the thousands column.8 × 2 = 16, plus 1 carried = 17
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,792
Check. Check: 1,792 ÷ 2 = 896.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 3. Write 8 in the ones column and carry 1 to the tens column.6 × 3 = 18
- Multiply the tens digit by 3. Write 1 in the tens column.0 × 3 = 0, plus 1 carried = 1
- Multiply the hundreds digit by 3. Write 8 in the hundreds column and carry 1 to the thousands column.6 × 3 = 18
- Write the carried number in front. The carried number is the next digit on the left.1 in the thousands column
- Write the answer. Read the digits from the bottom of each column, from the left.1,818
Check. Check: 1,818 ÷ 3 = 606.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.