Step-by-step Maths Level 5 Long multiplication of two-digit by one-digit numbers: check-up and practice test questions

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

1. Multiply the ones digit by 2. Write 2 in the ones column and carry 1 to the tens column.
   6 × 2 = 12
2. Multiply the tens digit by 2. Write 5 in the tens column and carry 1 to the hundreds column.
   7 × 2 = 14, plus 1 carried = 15
3. Multiply the hundreds digit by 2. Write 1 in the hundreds column and carry 1 to the thousands column.
   5 × 2 = 10, plus 1 carried = 11
4. Write the carried number in front. The carried number is the next digit on the left.
   1 in the thousands column
5. Write the answer. Read the digits from the bottom of each column, from the left.
   1,152

Check. Check: 1,152 ÷ 2 = 576.

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.

1. Multiply the ones digit by 8. Write 6 in the ones column and carry 5 to the tens column.
   7 × 8 = 56
2. Multiply the tens digit by 8. Write 3 in the tens column and carry 1 to the hundreds column.
   1 × 8 = 8, plus 5 carried = 13
3. Write the carried number in front. The carried number is the next digit on the left.
   1 in the hundreds column
4. Write the answer. Read the digits from the bottom of each column, from the left.
   136

Check. Check: 136 ÷ 8 = 17.

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.

1. Multiply the ones digit by 6. Write 6 in the ones column.
   1 × 6 = 6
2. Multiply the tens digit by 6. Write 8 in the tens column and carry 1 to the hundreds column.
   3 × 6 = 18
3. Multiply the hundreds digit by 6. Write 5 in the hundreds column and carry 5 to the thousands column.
   9 × 6 = 54, plus 1 carried = 55
4. Write the carried number in front. The carried number is the next digit on the left.
   5 in the thousands column
5. Write the answer. Read the digits from the bottom of each column, from the left.
   5,586

Check. Check: 5,586 ÷ 6 = 931.

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 the number in each group by the number of groups, or the amount by the number of times.

1. Find the cost of one pen and the number of pens. Each pen costs the same amount.
   63p for each of 4 pens
2. Multiply the cost of one pen by the number of pens. The total cost is the cost of each times the number.
   63p × 4 = 252p
3. Write the answer. Give the cost in pence, as the question asks.
   252p

Check. Check: 252p is more than the first number, because we multiplied by 4.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Method. Multiply the number in each group by the number of groups, or the amount by the number of times.

1. Find the scaling number. Lee has the number of times as many as Sam.
   4 times 28
2. Multiply. Scaling is multiplying by the number of times.
   28 × 4 = 112
3. Write the answer. This is the number of stamps Lee has.
   112 stamps

Check. Check: 112 is more than the first number, because we multiplied by 4.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

1. Multiply the ones digit by 9. Write 3 in the ones column and carry 6 to the tens column.
   7 × 9 = 63
2. Multiply the tens digit by 9. Write 2 in the tens column and carry 4 to the hundreds column.
   4 × 9 = 36, plus 6 carried = 42
3. Write the carried number in front. The carried number is the next digit on the left.
   4 in the hundreds column
4. Write the answer. Read the digits from the bottom of each column, from the left.
   423

Check. Check: 423 ÷ 9 = 47.

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 the number in each group by the number of groups, or the amount by the number of times.

1. Find the scaling number. Lee has the number of times as many as Sam.
   8 times 36
2. Multiply. Scaling is multiplying by the number of times.
   36 × 8 = 288
3. Write the answer. This is the number of stamps Lee has.
   288 stamps

Check. Check: 288 is more than the first number, because we multiplied by 8.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

1. Multiply the ones digit by 6. Write 2 in the ones column and carry 1 to the tens column.
   2 × 6 = 12
2. Multiply the tens digit by 6. Write 3 in the tens column and carry 1 to the hundreds column.
   2 × 6 = 12, plus 1 carried = 13
3. Multiply the hundreds digit by 6. Write 3 in the hundreds column and carry 4 to the thousands column.
   7 × 6 = 42, plus 1 carried = 43
4. Write the carried number in front. The carried number is the next digit on the left.
   4 in the thousands column
5. Write the answer. Read the digits from the bottom of each column, from the left.
   4,332

Check. Check: 4,332 ÷ 6 = 722.

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. Check a multiplication by division: the answer divided by one factor gives the other factor.

1. Divide the answer by 8. If the multiplication is right, dividing by the same number gives back the first number.
   776 ÷ 8 = 97
2. Compare with 97. Is the answer 97?
   Same
3. Write Yes or No. Yes if the check works; No if it does not.
   Yes

Check. The correct answer is 776.

Watch out. Find the mistake in the columns if the check does not work.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

1. Multiply the ones digit by 2. Write 4 in the ones column and carry 1 to the tens column.
   7 × 2 = 14
2. Multiply the tens digit by 2. Write 1 in the tens column and carry 1 to the hundreds column.
   5 × 2 = 10, plus 1 carried = 11
3. Multiply the hundreds digit by 2. Write 5 in the hundreds column.
   2 × 2 = 4, plus 1 carried = 5
4. Write the answer. Read the digits from the bottom of each column, from the left.
   514

Check. Check: 514 ÷ 2 = 257.

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.

1. Multiply the ones digit by 6. Write 4 in the ones column and carry 2 to the tens column.
   4 × 6 = 24
2. Multiply the tens digit by 6. Write 2 in the tens column.
   0 × 6 = 0, plus 2 carried = 2
3. Multiply the hundreds digit by 6. Write 2 in the hundreds column and carry 1 to the thousands column.
   2 × 6 = 12
4. Write the carried number in front. The carried number is the next digit on the left.
   1 in the thousands column
5. Write the answer. Read the digits from the bottom of each column, from the left.
   1,224

Check. Check: 1,224 ÷ 6 = 204.

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.

1. Multiply the ones digit by 3. Write 9 in the ones column.
   3 × 3 = 9
2. Multiply the tens digit by 3. Write 9 in the tens column.
   3 × 3 = 9
3. Write the answer. Read the digits from the bottom of each column, from the left.
   99

Check. Check: 99 ÷ 3 = 33.

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. Round to a number that is easy to multiply, then calculate.

1. Round 67 to the nearest 10. Look at the ones digit: 5 or more rounds up.
   67 is about 70
2. Multiply the rounded number. Use a fact we know from the tables.
   70 × 4 = 280
3. Write the estimate. The exact answer should be close to this.
   280

Check. The exact answer is 268, which is close to 280.

Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.

Method. Round to a number that is easy to multiply, then calculate.

1. Round 58 to the nearest 10. Look at the ones digit: 5 or more rounds up.
   58 is about 60
2. Multiply the rounded number. Use a fact we know from the tables.
   60 × 2 = 120
3. Write the estimate. The exact answer should be close to this.
   120

Check. The exact answer is 116, which is close to 120.

Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

1. Multiply the ones digit by 3. Write 6 in the ones column.
   2 × 3 = 6
2. Multiply the tens digit by 3. Write 3 in the tens column.
   1 × 3 = 3
3. Write the answer. Read the digits from the bottom of each column, from the left.
   36

Check. Check: 36 ÷ 3 = 12.

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.

1. Multiply the ones digit by 7. Write 9 in the ones column and carry 4 to the tens column.
   7 × 7 = 49
2. Multiply the tens digit by 7. Write 3 in the tens column and carry 5 to the hundreds column.
   7 × 7 = 49, plus 4 carried = 53
3. Write the carried number in front. The carried number is the next digit on the left.
   5 in the hundreds column
4. Write the answer. Read the digits from the bottom of each column, from the left.
   539

Check. Check: 539 ÷ 7 = 77.

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.

1. Multiply the ones digit by 9. Write 8 in the ones column and carry 1 to the tens column.
   2 × 9 = 18
2. Multiply the tens digit by 9. Write 9 in the tens column and carry 1 to the hundreds column.
   2 × 9 = 18, plus 1 carried = 19
3. Write the carried number in front. The carried number is the next digit on the left.
   1 in the hundreds column
4. Write the answer. Read the digits from the bottom of each column, from the left.
   198

Check. Check: 198 ÷ 9 = 22.

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.

1. Multiply the ones digit by 4. Write 2 in the ones column and carry 1 to the tens column.
   3 × 4 = 12
2. Multiply the tens digit by 4. Write 7 in the tens column and carry 1 to the hundreds column.
   4 × 4 = 16, plus 1 carried = 17
3. Write the carried number in front. The carried number is the next digit on the left.
   1 in the hundreds column
4. Write the answer. Read the digits from the bottom of each column, from the left.
   172

Check. Check: 172 ÷ 4 = 43.

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 the number in each group by the number of groups, or the amount by the number of times.

1. Find the number in each group and the number of groups. Each box is one group.
   35 pencils in each of 9 boxes
2. Multiply to find the total. Equal groups: multiply the number in each group by the number of groups.
   35 × 9 = 315
3. Write the answer. This is the total number of pencils.
   315 pencils

Check. Check: 315 is more than the first number, because we multiplied by 9.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Method. Check a multiplication by division: the answer divided by one factor gives the other factor.

1. Divide the answer by 5. If the multiplication is right, dividing by the same number gives back the first number.
   85 ÷ 5 = 17
2. Compare with 17. Is the answer 17?
   Same
3. Write Yes or No. Yes if the check works; No if it does not.
   Yes

Check. The correct answer is 85.

Watch out. Find the mistake in the columns if the check does not work.