Year 6 Arithmetic (SATs) · Multiplication and division · Lesson 2.1
Year 6 Arithmetic (SATs): Multiplying by a one-digit number
Part of the Year 6 Arithmetic (SATs) multiplication and division chapter. Chapter overview · whole chapter on one page
2.1
Multiplying by a one-digit number
Practice material. Non-calculator practice. This book is practice in the style of the Year 6 arithmetic test. It is not the official test, and no official test item is used. Do every question without a calculator. Marks and timings are a practice guide only.
Story. A bakery makes 2,075 scones every day. Each scone sits on a tray, and the baker needs to know how many scones it makes in four days. She writes the multiplication in a column.
Rule
In short multiplication, multiply the digits one column at a time, starting from the ones. Write the ones digit of each answer and carry the tens digit to the next column.
Check with an estimate: 4,836 × 7 is about 5,000 × 7 = 35,000, so an answer near 33,852 is sensible.
The full written method for longer numbers is in Year 5 maths, chapter 2.
Key ideas
- Multiply from the ones column first, and carry where needed.
- Estimate first to check that the answer is the right size.
- Every column of the bigger number is multiplied by the one-digit number.
Worked example 2.1.1
Work out 4,836 × 7.
Method. Multiply column by column from the right, carrying where needed.
- Multiply the ones digit 6 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.6 × 7 + 0 = 42, write 2, carry 4
- Multiply the tens digit 3 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.3 × 7 + 4 = 25, write 5, carry 2
- Multiply the hundreds digit 8 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.8 × 7 + 2 = 58, write 8, carry 5
- Multiply the thousands digit 4 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 7 + 5 = 33, write 3, carry 3
- Multiply the ten thousands digit 0 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 7 + 3 = 3, write 3
- Write the answer. 33,852
Check. Estimate: 5,000 × 7 = 35,000, close to 33,852. ✓
Watch out. Do not forget to add the carried tens to the next product.
Worked example 2.1.2
Work out 2,075 × 4.
Method. Start with the ones column, which is 5 × 4.
- Multiply the ones digit 5 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.5 × 4 + 0 = 20, write 0, carry 2
- Multiply the tens digit 7 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.7 × 4 + 2 = 30, write 0, carry 3
- Multiply the hundreds digit 0 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 4 + 3 = 3, write 3
- Multiply the thousands digit 2 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 4 + 0 = 8, write 8
- Write the answer. 8,300
Check. 8,300 ÷ 4 = 2,075. ✓
Watch out. The zero in the tens column still gives a zero in the answer.
Worked example 2.1.3
Work out 3,249 × 6.
Method. Multiply each column, then add the carries.
- Multiply the ones digit 9 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.9 × 6 + 0 = 54, write 4, carry 5
- Multiply the tens digit 4 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 6 + 5 = 29, write 9, carry 2
- Multiply the hundreds digit 2 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 6 + 2 = 14, write 4, carry 1
- Multiply the thousands digit 3 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.3 × 6 + 1 = 19, write 9, carry 1
- Multiply the ten thousands digit 0 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 6 + 1 = 1, write 1
- Write the answer. 19,494
Check. 19,494 ÷ 6 = 3,249. ✓
Exercise 2A Practice: multiplying by one digit
Non-calculator1
FWork out 2,145 × 3.
6,435
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 5 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.5 × 3 + 0 = 15, write 5, carry 1
- Multiply the tens digit 4 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 3 + 1 = 13, write 3, carry 1
- Multiply the hundreds digit 1 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.1 × 3 + 1 = 4, write 4
- Multiply the thousands digit 2 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 3 + 0 = 6, write 6
- Write the answer. 6,435
Check. 6,435 ÷ 3 = 2,145. ✓
2
FWork out 4,672 × 5.
23,360
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 2 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 5 + 0 = 10, write 0, carry 1
- Multiply the tens digit 7 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.7 × 5 + 1 = 36, write 6, carry 3
- Multiply the hundreds digit 6 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.6 × 5 + 3 = 33, write 3, carry 3
- Multiply the thousands digit 4 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 5 + 3 = 23, write 3, carry 2
- Multiply the ten thousands digit 0 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 5 + 2 = 2, write 2
- Write the answer. 23,360
Check. 23,360 ÷ 5 = 4,672. ✓
3
FWork out 1,893 × 8.
15,144
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 3 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.3 × 8 + 0 = 24, write 4, carry 2
- Multiply the tens digit 9 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.9 × 8 + 2 = 74, write 4, carry 7
- Multiply the hundreds digit 8 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.8 × 8 + 7 = 71, write 1, carry 7
- Multiply the thousands digit 1 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.1 × 8 + 7 = 15, write 5, carry 1
- Multiply the ten thousands digit 0 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 8 + 1 = 1, write 1
- Write the answer. 15,144
Check. 15,144 ÷ 8 = 1,893. ✓
4
FWork out 6,024 × 7.
42,168
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 4 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 7 + 0 = 28, write 8, carry 2
- Multiply the tens digit 2 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 7 + 2 = 16, write 6, carry 1
- Multiply the hundreds digit 0 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 7 + 1 = 1, write 1
- Multiply the thousands digit 6 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.6 × 7 + 0 = 42, write 2, carry 4
- Multiply the ten thousands digit 0 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 7 + 4 = 4, write 4
- Write the answer. 42,168
Check. 42,168 ÷ 7 = 6,024. ✓
5
FWork out 3,508 × 4.
14,032
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 8 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.8 × 4 + 0 = 32, write 2, carry 3
- Multiply the tens digit 0 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 4 + 3 = 3, write 3
- Multiply the hundreds digit 5 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.5 × 4 + 0 = 20, write 0, carry 2
- Multiply the thousands digit 3 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.3 × 4 + 2 = 14, write 4, carry 1
- Multiply the ten thousands digit 0 by 4. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 4 + 1 = 1, write 1
- Write the answer. 14,032
Check. 14,032 ÷ 4 = 3,508. ✓
6
FWork out 7,316 × 9.
65,844
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 6 by 9. Write the ones digit of the answer in this column and carry the tens digit to the next column.6 × 9 + 0 = 54, write 4, carry 5
- Multiply the tens digit 1 by 9. Write the ones digit of the answer in this column and carry the tens digit to the next column.1 × 9 + 5 = 14, write 4, carry 1
- Multiply the hundreds digit 3 by 9. Write the ones digit of the answer in this column and carry the tens digit to the next column.3 × 9 + 1 = 28, write 8, carry 2
- Multiply the thousands digit 7 by 9. Write the ones digit of the answer in this column and carry the tens digit to the next column.7 × 9 + 2 = 65, write 5, carry 6
- Multiply the ten thousands digit 0 by 9. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 9 + 6 = 6, write 6
- Write the answer. 65,844
Check. 65,844 ÷ 9 = 7,316. ✓
7
FWork out 2,964 × 6.
17,784
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 4 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 6 + 0 = 24, write 4, carry 2
- Multiply the tens digit 6 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.6 × 6 + 2 = 38, write 8, carry 3
- Multiply the hundreds digit 9 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.9 × 6 + 3 = 57, write 7, carry 5
- Multiply the thousands digit 2 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 6 + 5 = 17, write 7, carry 1
- Multiply the ten thousands digit 0 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 6 + 1 = 1, write 1
- Write the answer. 17,784
Check. 17,784 ÷ 6 = 2,964. ✓
8
FWork out 1,459 × 5.
7,295
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 9 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.9 × 5 + 0 = 45, write 5, carry 4
- Multiply the tens digit 5 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.5 × 5 + 4 = 29, write 9, carry 2
- Multiply the hundreds digit 4 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.4 × 5 + 2 = 22, write 2, carry 2
- Multiply the thousands digit 1 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.1 × 5 + 2 = 7, write 7
- Write the answer. 7,295
Check. 7,295 ÷ 5 = 1,459. ✓
9
FWork out 8,207 × 3.
24,621
Method. Multiply each column from the right, carrying where needed.
- Multiply the ones digit 7 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.7 × 3 + 0 = 21, write 1, carry 2
- Multiply the tens digit 0 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 3 + 2 = 2, write 2
- Multiply the hundreds digit 2 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 3 + 0 = 6, write 6
- Multiply the thousands digit 8 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.8 × 3 + 0 = 24, write 4, carry 2
- Multiply the ten thousands digit 0 by 3. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 3 + 2 = 2, write 2
- Write the answer. 24,621
Check. 24,621 ÷ 3 = 8,207. ✓
10
PSA factory makes 2,638 bolts an hour. How many bolts does it make in 6 hours?
15,828
Method. Multiply the bolts in one hour by the number of hours.
- Multiply the ones digit 8 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.8 × 6 + 0 = 48, write 8, carry 4
- Multiply the tens digit 3 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.3 × 6 + 4 = 22, write 2, carry 2
- Multiply the hundreds digit 6 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.6 × 6 + 2 = 38, write 8, carry 3
- Multiply the thousands digit 2 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 6 + 3 = 15, write 5, carry 1
- Multiply the ten thousands digit 0 by 6. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 6 + 1 = 1, write 1
- Write the answer. 15,828
Check. About 2,600 × 6 = 15,600, close to 15,828. ✓
11
PSEach packet holds 1,205 stickers. Sam buys 8 packets. How many stickers does he have?
9,640
Method. Multiply the stickers in one packet by 8.
- Multiply the ones digit 5 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.5 × 8 + 0 = 40, write 0, carry 4
- Multiply the tens digit 0 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.0 × 8 + 4 = 4, write 4
- Multiply the hundreds digit 2 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.2 × 8 + 0 = 16, write 6, carry 1
- Multiply the thousands digit 1 by 8. Write the ones digit of the answer in this column and carry the tens digit to the next column.1 × 8 + 1 = 9, write 9
- Write the answer. 9,640
Check. 9,640 ÷ 8 = 1,205. ✓
12
REstimate 4,932 × 6 by rounding 4,932 to the nearest 1,000, then say whether the exact answer is close.
Accept any answer that rounds 4,932 to 5,000, gives 30,000 as the estimate, and says the exact answer 29,592 is close. For example: Round to 5,000; 5,000 × 6 = 30,000, and 29,592 is close to 30,000.
Method. Round first, multiply the rounded number, then compare with the exact answer.
- Round the number. 4,932 is nearer to 5,000 than to 4,000.4,932 → 5,000
- Estimate the answer. 5,000 × 6 = 30,000.30,000
- Work out the exact answer. Short multiplication gives 4,932 × 6 = 29,592.29,592
- Compare. 29,592 is close to 30,000.29,592 ≈ 30,000
- Write the answer. Round to 5,000; 5,000 × 6 = 30,000, and 29,592 is close to 30,000.
Check. The estimate and the exact answer differ by 408. ✓