Year 5: Multiplying by a one-digit number
Part of the Year 5 long multiplication chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Multiplying by a one-digit number
In Year 4 you multiplied 2- and 3-digit numbers by one digit. Now we use bigger numbers, up to 4 digits. There are two methods. Both give the same answer.
The grid method. Split (partition) the big number into thousands, hundreds, tens and ones. Multiply each part by the one-digit number, then add the answers. The picture shows 2,315 × 3: the pieces are 6,000, 900, 30 and 15, and they add up to 6,945.
Short multiplication. This is a quicker way to write the same thing. Write the numbers in columns. Multiply one column at a time, starting with the ones on the right. If a column gives 10 or more, write the ones digit and carry the tens digit to the next column. The carried digit is added after you multiply the next column.
| TTh | Th | H | T | O | |
| 2 | 4 | 8 | 3 | ||
| × | 6 | ||||
| 1 | 4 | 8 | 9 | 8 | |
| 1 | 2 | 4 | 1 |
Always estimate first. Round the big number to one digit followed by zeros: 2,483 is about 2,000, and 2,000 × 6 = 12,000. The real answer, 14,898, is a bit more, which makes sense because 2,483 is more than 2,000. When you work with money, change pounds to pence first so that there is no decimal point, then change back at the end.
Key ideas
- Grid method: partition the number, multiply each part, add the partial products.
- Short multiplication: start with the ones. Multiply each digit, add the carried digit, write the ones digit, carry the tens digit.
- A zero digit still needs a step: 0 × 6 = 0, but you may still need to add a carried digit.
- If there is a carry left at the end, write it as the next digit of the answer.
- Always estimate first by rounding, and check your answer is close.
Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 346 into place-value parts (partition it). Multiply each part by 4, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.346 = 300 + 40 + 6
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
- Multiply each part. Use a times table fact, then put the zeros back.300 × 4: 3 × 4 = 12, then 2 zeros. 1,200
40 × 4: 4 × 4 = 16, then 1 zero. 160
6 × 4 = 24 - Write each answer in the grid. These are the partial products.
- Add the partial products. Add them one at a time. Keep a running total.1,200 + 160 = 1,360
1,360 + 24 = 1,384 - Write the answer. 346 × 4 = 1,384
Check. Estimate: 346 is about 300. 300 × 4 = 1,200. Our answer, 1,384, is close to 1,200. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 2,315 into place-value parts (partition it). Multiply each part by 3, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.2,315 = 2,000 + 300 + 10 + 5
- Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.
- Multiply each part. Use a times table fact, then put the zeros back.2,000 × 3: 2 × 3 = 6, then 3 zeros. 6,000
300 × 3: 3 × 3 = 9, then 2 zeros. 900
10 × 3: 1 × 3 = 3, then 1 zero. 30
5 × 3 = 15 - Write each answer in the grid. These are the partial products.
- Add the partial products. Add them one at a time. Keep a running total.6,000 + 900 = 6,900
6,900 + 30 = 6,930
6,930 + 15 = 6,945 - Write the answer. 2,315 × 3 = 6,945
Check. Estimate: 2,315 is about 2,000. 2,000 × 3 = 6,000. Our answer, 6,945, is close to 6,000. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 2 7 6 × 4 - Multiply the ones. Always start with the ones, on the right.6 × 4 = 24
24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2.Th H T O 2 7 6 × 4 4 2 - Multiply the tens. Multiply, then add the 2 we carried.7 × 4 = 28, and 28 + 2 = 30
30 is 3 hundreds and 0 tens. Write 0 in the tens column and carry 3.Th H T O 2 7 6 × 4 0 4 3 2 - Multiply the hundreds. Multiply, then add the 3 we carried.2 × 4 = 8, and 8 + 3 = 11
11 is 1 thousand and 1 hundred. Write 1 in the hundreds column and carry 1.Th H T O 2 7 6 × 4 1 0 4 1 3 2 - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 1 into it.Write 1 in the thousands column.
Th H T O 2 7 6 × 4 1 1 0 4 1 3 2 - Write the answer. 276 × 4 = 1,104
Check. Estimate: 276 is about 300. 300 × 4 = 1,200. Our answer, 1,104, is close to 1,200. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 3 5 8 × 7 - Multiply the ones. Always start with the ones, on the right.8 × 7 = 56
56 is 5 tens and 6 ones. Write 6 in the ones column and carry 5. - Multiply the tens. Multiply, then add the 5 we carried.5 × 7 = 35, and 35 + 5 = 40
40 is 4 hundreds and 0 tens. Write 0 in the tens column and carry 4. - Multiply the hundreds. Multiply, then add the 4 we carried.3 × 7 = 21, and 21 + 4 = 25
25 is 2 thousands and 5 hundreds. Write 5 in the hundreds column and carry 2. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 2 into it.Write 2 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 3 5 8 × 7 2 5 0 6 2 4 5 - Write the answer. 358 × 7 = 2,506
Check. Estimate: 358 is about 400. 400 × 7 = 2,800. Our answer, 2,506, is close to 2,800. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 2 4 8 3 × 6 - Multiply the ones. Always start with the ones, on the right.3 × 6 = 18
18 is 1 ten and 8 ones. Write 8 in the ones column and carry 1. - Multiply the tens. Multiply, then add the 1 we carried.8 × 6 = 48, and 48 + 1 = 49
49 is 4 hundreds and 9 tens. Write 9 in the tens column and carry 4. - Multiply the hundreds. Multiply, then add the 4 we carried.4 × 6 = 24, and 24 + 4 = 28
28 is 2 thousands and 8 hundreds. Write 8 in the hundreds column and carry 2. - Multiply the thousands. Multiply, then add the 2 we carried.2 × 6 = 12, and 12 + 2 = 14
14 is 1 ten thousand and 4 thousands. Write 4 in the thousands column and carry 1. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 1 into it.Write 1 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 2 4 8 3 × 6 1 4 8 9 8 1 2 4 1 - Write the answer. 2,483 × 6 = 14,898
Check. Estimate: 2,483 is about 2,000. 2,000 × 6 = 12,000. Our answer, 14,898, is a bit more than 12,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 4 0 5 6 × 7 - Multiply the ones. Always start with the ones, on the right.6 × 7 = 42
42 is 4 tens and 2 ones. Write 2 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.5 × 7 = 35, and 35 + 4 = 39
39 is 3 hundreds and 9 tens. Write 9 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.0 × 7 = 0, and 0 + 3 = 3
3 is less than 10, so write 3. Nothing to carry. - Multiply the thousands. Now the next column to the left.4 × 7 = 28
28 is 2 ten thousands and 8 thousands. Write 8 in the thousands column and carry 2. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 2 into it.Write 2 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 4 0 5 6 × 7 2 8 3 9 2 2 3 4 - Write the answer. 4,056 × 7 = 28,392
Check. Estimate: 4,056 is about 4,000. 4,000 × 7 = 28,000. Our answer, 28,392, is close to 28,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 6 7 8 9 × 8 - Multiply the ones. Always start with the ones, on the right.9 × 8 = 72
72 is 7 tens and 2 ones. Write 2 in the ones column and carry 7. - Multiply the tens. Multiply, then add the 7 we carried.8 × 8 = 64, and 64 + 7 = 71
71 is 7 hundreds and 1 ten. Write 1 in the tens column and carry 7. - Multiply the hundreds. Multiply, then add the 7 we carried.7 × 8 = 56, and 56 + 7 = 63
63 is 6 thousands and 3 hundreds. Write 3 in the hundreds column and carry 6. - Multiply the thousands. Multiply, then add the 6 we carried.6 × 8 = 48, and 48 + 6 = 54
54 is 5 ten thousands and 4 thousands. Write 4 in the thousands column and carry 5. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 5 into it.Write 5 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 6 7 8 9 × 8 5 4 3 1 2 5 6 7 7 - Write the answer. 6,789 × 8 = 54,312
Check. Estimate: 6,789 is about 7,000. 7,000 × 8 = 56,000. Our answer, 54,312, is close to 56,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. A bar model shows what we know and what we need to find out.
- Choose the operation. There are 6 equal stands, so multiply the number of seats in one stand by 6.1,375 × 6
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 1 3 7 5 × 6 - Multiply the ones. Always start with the ones, on the right.5 × 6 = 30
30 is 3 tens and 0 ones. Write 0 in the ones column and carry 3. - Multiply the tens. Multiply, then add the 3 we carried.7 × 6 = 42, and 42 + 3 = 45
45 is 4 hundreds and 5 tens. Write 5 in the tens column and carry 4. - Multiply the hundreds. Multiply, then add the 4 we carried.3 × 6 = 18, and 18 + 4 = 22
22 is 2 thousands and 2 hundreds. Write 2 in the hundreds column and carry 2. - Multiply the thousands. Multiply, then add the 2 we carried.1 × 6 = 6, and 6 + 2 = 8
8 is less than 10, so write 8. Nothing to carry. - Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 1 3 7 5 × 6 8 2 5 0 2 4 3 - Write the answer. Include the unit.8,250 seats
Check. Estimate: 1,375 is about 1,000. 1,000 × 6 = 6,000. Our answer, 8,250, is a bit more than 6,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Change the price to pence, multiply, then change the answer back to pounds.
- Change the price to pence. Working in pence means no decimal point. £1 = 100p, so multiply by 100.£12.50 = 1,250p
- Choose the operation. 6 items at 1,250p each: multiply the price by 6.1,250p × 6
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 1 2 5 0 × 6 - Multiply the ones. Always start with the ones, on the right.0 × 6 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the tens. Now the next column to the left.5 × 6 = 30
30 is 3 hundreds and 0 tens. Write 0 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.2 × 6 = 12, and 12 + 3 = 15
15 is 1 thousand and 5 hundreds. Write 5 in the hundreds column and carry 1. - Multiply the thousands. Multiply, then add the 1 we carried.1 × 6 = 6, and 6 + 1 = 7
7 is less than 10, so write 7. Nothing to carry. - Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 1 2 5 0 × 6 7 5 0 0 1 3 - Change back to pounds. Divide by 100: the digits move 2 places to the right.7,500p = £75.00
- Write the answer. Include the unit.£75.00
Check. Estimate: 1,250 is about 1,000. 1,000 × 6 = 6,000. Our answer, 7,500, is a bit more than 6,000. ✓
Watch out. Always change back to pounds at the end. 7,500p is not £7,500.
Watch out
Add the carried digit after you multiply, not before. For 8 × 6 = 48 plus 1 carried is 49: do not do (8 + 1) × 6. Also remember that a 0 digit still needs a step, because a carry may land on it: in 4,056 × 7 the 0 becomes 3.Exercise 4C Multiplying by a one-digit number
Non-calculatorKey words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 253 into place-value parts (partition it). Multiply each part by 3, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.253 = 200 + 50 + 3
- Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.
× 200 50 3 3 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.200 × 3: 2 × 3 = 6, then 2 zeros. 600
50 × 3: 5 × 3 = 15, then 1 zero. 150
3 × 3 = 9 - Write each answer in the grid. These are the partial products.
× 200 50 3 3 600 150 9 - Add the partial products. Add them one at a time. Keep a running total.600 + 150 = 750
750 + 9 = 759 - Write the answer. 253 × 3 = 759
Check. Estimate: 253 is about 300. 300 × 3 = 900. Our answer, 759, is close to 900. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 417 into place-value parts (partition it). Multiply each part by 5, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.417 = 400 + 10 + 7
- Draw the grid and write the parts across the top. The number on the side is 5. Every part gets multiplied by 5.
× 400 10 7 5 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.400 × 5: 4 × 5 = 20, then 2 zeros. 2,000
10 × 5: 1 × 5 = 5, then 1 zero. 50
7 × 5 = 35 - Write each answer in the grid. These are the partial products.
× 400 10 7 5 2,000 50 35 - Add the partial products. Add them one at a time. Keep a running total.2,000 + 50 = 2,050
2,050 + 35 = 2,085 - Write the answer. 417 × 5 = 2,085
Check. Estimate: 417 is about 400. 400 × 5 = 2,000. Our answer, 2,085, is close to 2,000. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 1,324 into place-value parts (partition it). Multiply each part by 4, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.1,324 = 1,000 + 300 + 20 + 4
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
× 1,000 300 20 4 4 ? ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.1,000 × 4: 1 × 4 = 4, then 3 zeros. 4,000
300 × 4: 3 × 4 = 12, then 2 zeros. 1,200
20 × 4: 2 × 4 = 8, then 1 zero. 80
4 × 4 = 16 - Write each answer in the grid. These are the partial products.
× 1,000 300 20 4 4 4,000 1,200 80 16 - Add the partial products. Add them one at a time. Keep a running total.4,000 + 1,200 = 5,200
5,200 + 80 = 5,280
5,280 + 16 = 5,296 - Write the answer. 1,324 × 4 = 5,296
Check. Estimate: 1,324 is about 1,000. 1,000 × 4 = 4,000. Our answer, 5,296, is a bit more than 4,000. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 2,038 into place-value parts (partition it). Multiply each part by 3, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply. A zero digit means there are none of that place, so it has no box.2,038 = 2,000 + 30 + 8
- Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.
× 2,000 30 8 3 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.2,000 × 3: 2 × 3 = 6, then 3 zeros. 6,000
30 × 3: 3 × 3 = 9, then 1 zero. 90
8 × 3 = 24 - Write each answer in the grid. These are the partial products.
× 2,000 30 8 3 6,000 90 24 - Add the partial products. Add them one at a time. Keep a running total.6,000 + 90 = 6,090
6,090 + 24 = 6,114 - Write the answer. 2,038 × 3 = 6,114
Check. Estimate: 2,038 is about 2,000. 2,000 × 3 = 6,000. Our answer, 6,114, is close to 6,000. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 3 2 5 × 4 - Multiply the ones. Always start with the ones, on the right.5 × 4 = 20
20 is 2 tens and 0 ones. Write 0 in the ones column and carry 2. - Multiply the tens. Multiply, then add the 2 we carried.2 × 4 = 8, and 8 + 2 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1. - Multiply the hundreds. Multiply, then add the 1 we carried.3 × 4 = 12, and 12 + 1 = 13
13 is 1 thousand and 3 hundreds. Write 3 in the hundreds column and carry 1. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 1 into it.Write 1 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 3 2 5 × 4 1 3 0 0 1 1 2 - Write the answer. 325 × 4 = 1,300
Check. Estimate: 325 is about 300. 300 × 4 = 1,200. Our answer, 1,300, is close to 1,200. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 2 4 7 × 6 - Multiply the ones. Always start with the ones, on the right.7 × 6 = 42
42 is 4 tens and 2 ones. Write 2 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.4 × 6 = 24, and 24 + 4 = 28
28 is 2 hundreds and 8 tens. Write 8 in the tens column and carry 2. - Multiply the hundreds. Multiply, then add the 2 we carried.2 × 6 = 12, and 12 + 2 = 14
14 is 1 thousand and 4 hundreds. Write 4 in the hundreds column and carry 1. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 1 into it.Write 1 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 2 4 7 × 6 1 4 8 2 1 2 4 - Write the answer. 247 × 6 = 1,482
Check. Estimate: 247 is about 200. 200 × 6 = 1,200. Our answer, 1,482, is a bit more than 1,200. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 5 1 8 × 3 - Multiply the ones. Always start with the ones, on the right.8 × 3 = 24
24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2. - Multiply the tens. Multiply, then add the 2 we carried.1 × 3 = 3, and 3 + 2 = 5
5 is less than 10, so write 5. Nothing to carry. - Multiply the hundreds. Now the next column to the left.5 × 3 = 15
15 is 1 thousand and 5 hundreds. Write 5 in the hundreds column and carry 1. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 1 into it.Write 1 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 5 1 8 × 3 1 5 5 4 1 2 - Write the answer. 518 × 3 = 1,554
Check. Estimate: 518 is about 500. 500 × 3 = 1,500. Our answer, 1,554, is close to 1,500. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 7 6 9 × 8 - Multiply the ones. Always start with the ones, on the right.9 × 8 = 72
72 is 7 tens and 2 ones. Write 2 in the ones column and carry 7. - Multiply the tens. Multiply, then add the 7 we carried.6 × 8 = 48, and 48 + 7 = 55
55 is 5 hundreds and 5 tens. Write 5 in the tens column and carry 5. - Multiply the hundreds. Multiply, then add the 5 we carried.7 × 8 = 56, and 56 + 5 = 61
61 is 6 thousands and 1 hundred. Write 1 in the hundreds column and carry 6. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 6 into it.Write 6 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 7 6 9 × 8 6 1 5 2 6 5 7 - Write the answer. 769 × 8 = 6,152
Check. Estimate: 769 is about 800. 800 × 8 = 6,400. Our answer, 6,152, is close to 6,400. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 1 2 3 4 × 5 - Multiply the ones. Always start with the ones, on the right.4 × 5 = 20
20 is 2 tens and 0 ones. Write 0 in the ones column and carry 2. - Multiply the tens. Multiply, then add the 2 we carried.3 × 5 = 15, and 15 + 2 = 17
17 is 1 hundred and 7 tens. Write 7 in the tens column and carry 1. - Multiply the hundreds. Multiply, then add the 1 we carried.2 × 5 = 10, and 10 + 1 = 11
11 is 1 thousand and 1 hundred. Write 1 in the hundreds column and carry 1. - Multiply the thousands. Multiply, then add the 1 we carried.1 × 5 = 5, and 5 + 1 = 6
6 is less than 10, so write 6. Nothing to carry. - Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 1 2 3 4 × 5 6 1 7 0 1 1 2 - Write the answer. 1,234 × 5 = 6,170
Check. Estimate: 1,234 is about 1,000. 1,000 × 5 = 5,000. Our answer, 6,170, is a bit more than 5,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 3 7 2 6 × 4 - Multiply the ones. Always start with the ones, on the right.6 × 4 = 24
24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2. - Multiply the tens. Multiply, then add the 2 we carried.2 × 4 = 8, and 8 + 2 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1. - Multiply the hundreds. Multiply, then add the 1 we carried.7 × 4 = 28, and 28 + 1 = 29
29 is 2 thousands and 9 hundreds. Write 9 in the hundreds column and carry 2. - Multiply the thousands. Multiply, then add the 2 we carried.3 × 4 = 12, and 12 + 2 = 14
14 is 1 ten thousand and 4 thousands. Write 4 in the thousands column and carry 1. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 1 into it.Write 1 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 3 7 2 6 × 4 1 4 9 0 4 1 2 1 2 - Write the answer. 3,726 × 4 = 14,904
Check. Estimate: 3,726 is about 4,000. 4,000 × 4 = 16,000. Our answer, 14,904, is close to 16,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 5 4 0 8 × 6 - Multiply the ones. Always start with the ones, on the right.8 × 6 = 48
48 is 4 tens and 8 ones. Write 8 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.0 × 6 = 0, and 0 + 4 = 4
4 is less than 10, so write 4. Nothing to carry. - Multiply the hundreds. Now the next column to the left.4 × 6 = 24
24 is 2 thousands and 4 hundreds. Write 4 in the hundreds column and carry 2. - Multiply the thousands. Multiply, then add the 2 we carried.5 × 6 = 30, and 30 + 2 = 32
32 is 3 ten thousands and 2 thousands. Write 2 in the thousands column and carry 3. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 3 into it.Write 3 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 5 4 0 8 × 6 3 2 4 4 8 3 2 4 - Write the answer. 5,408 × 6 = 32,448
Check. Estimate: 5,408 is about 5,000. 5,000 × 6 = 30,000. Our answer, 32,448, is close to 30,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 6 8 4 5 × 7 - Multiply the ones. Always start with the ones, on the right.5 × 7 = 35
35 is 3 tens and 5 ones. Write 5 in the ones column and carry 3. - Multiply the tens. Multiply, then add the 3 we carried.4 × 7 = 28, and 28 + 3 = 31
31 is 3 hundreds and 1 ten. Write 1 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.8 × 7 = 56, and 56 + 3 = 59
59 is 5 thousands and 9 hundreds. Write 9 in the hundreds column and carry 5. - Multiply the thousands. Multiply, then add the 5 we carried.6 × 7 = 42, and 42 + 5 = 47
47 is 4 ten thousands and 7 thousands. Write 7 in the thousands column and carry 4. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 4 into it.Write 4 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 6 8 4 5 × 7 4 7 9 1 5 4 5 3 3 - Write the answer. 6,845 × 7 = 47,915
Check. Estimate: 6,845 is about 7,000. 7,000 × 7 = 49,000. Our answer, 47,915, is close to 49,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 2 5 0 0 × 4 - Multiply the ones. Always start with the ones, on the right.0 × 4 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the tens. Now the next column to the left.0 × 4 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the hundreds. Now the next column to the left.5 × 4 = 20
20 is 2 thousands and 0 hundreds. Write 0 in the hundreds column and carry 2. - Multiply the thousands. Multiply, then add the 2 we carried.2 × 4 = 8, and 8 + 2 = 10
10 is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 1 into it.Write 1 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 2 5 0 0 × 4 1 0 0 0 0 1 2 - Write the answer. 2,500 × 4 = 10,000
Check. Estimate: 2,500 is about 3,000. 3,000 × 4 = 12,000. Our answer, 10,000, is close to 12,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 3 0 7 0 × 9 - Multiply the ones. Always start with the ones, on the right.0 × 9 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the tens. Now the next column to the left.7 × 9 = 63
63 is 6 hundreds and 3 tens. Write 3 in the tens column and carry 6. - Multiply the hundreds. Multiply, then add the 6 we carried.0 × 9 = 0, and 0 + 6 = 6
6 is less than 10, so write 6. Nothing to carry. - Multiply the thousands. Now the next column to the left.3 × 9 = 27
27 is 2 ten thousands and 7 thousands. Write 7 in the thousands column and carry 2. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 2 into it.Write 2 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 3 0 7 0 × 9 2 7 6 3 0 2 6 - Write the answer. 3,070 × 9 = 27,630
Check. Estimate: 3,070 is about 3,000. 3,000 × 9 = 27,000. Our answer, 27,630, is close to 27,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 4 0 0 8 × 6 - Multiply the ones. Always start with the ones, on the right.8 × 6 = 48
48 is 4 tens and 8 ones. Write 8 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.0 × 6 = 0, and 0 + 4 = 4
4 is less than 10, so write 4. Nothing to carry. - Multiply the hundreds. Now the next column to the left.0 × 6 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the thousands. Now the next column to the left.4 × 6 = 24
24 is 2 ten thousands and 4 thousands. Write 4 in the thousands column and carry 2. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 2 into it.Write 2 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 4 0 0 8 × 6 2 4 0 4 8 2 4 - Write the answer. 4,008 × 6 = 24,048
Check. Estimate: 4,008 is about 4,000. 4,000 × 6 = 24,000. Our answer, 24,048, is close to 24,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 9 9 9 9 × 2 - Multiply the ones. Always start with the ones, on the right.9 × 2 = 18
18 is 1 ten and 8 ones. Write 8 in the ones column and carry 1. - Multiply the tens. Multiply, then add the 1 we carried.9 × 2 = 18, and 18 + 1 = 19
19 is 1 hundred and 9 tens. Write 9 in the tens column and carry 1. - Multiply the hundreds. Multiply, then add the 1 we carried.9 × 2 = 18, and 18 + 1 = 19
19 is 1 thousand and 9 hundreds. Write 9 in the hundreds column and carry 1. - Multiply the thousands. Multiply, then add the 1 we carried.9 × 2 = 18, and 18 + 1 = 19
19 is 1 ten thousand and 9 thousands. Write 9 in the thousands column and carry 1. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 1 into it.Write 1 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 9 9 9 9 × 2 1 9 9 9 8 1 1 1 1 - Write the answer. 9,999 × 2 = 19,998
Check. Estimate: 9,999 is about 10,000. 10,000 × 2 = 20,000. Our answer, 19,998, is close to 20,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 7 3 0 5 × 3 - Multiply the ones. Always start with the ones, on the right.5 × 3 = 15
15 is 1 ten and 5 ones. Write 5 in the ones column and carry 1. - Multiply the tens. Multiply, then add the 1 we carried.0 × 3 = 0, and 0 + 1 = 1
1 is less than 10, so write 1. Nothing to carry. - Multiply the hundreds. Now the next column to the left.3 × 3 = 9
9 is less than 10, so write 9. Nothing to carry. - Multiply the thousands. Now the next column to the left.7 × 3 = 21
21 is 2 ten thousands and 1 thousand. Write 1 in the thousands column and carry 2. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 2 into it.Write 2 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 7 3 0 5 × 3 2 1 9 1 5 2 1 - Write the answer. 7,305 × 3 = 21,915
Check. Estimate: 7,305 is about 7,000. 7,000 × 3 = 21,000. Our answer, 21,915, is close to 21,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit.
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 8 8 8 8 × 5 - Multiply the ones. Always start with the ones, on the right.8 × 5 = 40
40 is 4 tens and 0 ones. Write 0 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.8 × 5 = 40, and 40 + 4 = 44
44 is 4 hundreds and 4 tens. Write 4 in the tens column and carry 4. - Multiply the hundreds. Multiply, then add the 4 we carried.8 × 5 = 40, and 40 + 4 = 44
44 is 4 thousands and 4 hundreds. Write 4 in the hundreds column and carry 4. - Multiply the thousands. Multiply, then add the 4 we carried.8 × 5 = 40, and 40 + 4 = 44
44 is 4 ten thousands and 4 thousands. Write 4 in the thousands column and carry 4. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 4 into it.Write 4 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 8 8 8 8 × 5 4 4 4 4 0 4 4 4 4 - Write the answer. 8,888 × 5 = 44,440
Check. Estimate: 8,888 is about 9,000. 9,000 × 5 = 45,000. Our answer, 44,440, is close to 45,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
| TTh | Th | H | T | O | |
| 3 | 2 | 6 | 4 | ||
| × | 7 | ||||
| 4 | 8 | ||||
| 4 | 2 |
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Carry on from the working. Multiply the next column and add the carried digit.
- Check the working so far. The ones and tens columns are done. The carry from the tens column is 4.Ones: 4 × 7 = 28, write 8, carry 2. Tens: 6 × 7 = 42, plus 2 = 44, write 4, carry 4.
- Hundreds column. Multiply, then add the carry.2 × 7 = 14, plus 4 = 18. Write 8 and carry 1.
- Thousands column. Multiply, then add the carry. There is nothing left to the left, so write the whole number.3 × 7 = 21, plus 1 = 22. Write 22.
- Read the answer.
TTh Th H T O 3 2 6 4 × 7 2 2 8 4 8 2 1 4 2
3,264 × 7 = 22,848
Check. Estimate: 3,264 is about 3,000. 3,000 × 7 = 21,000. Our answer, 22,848, is close to 21,000. ✓
Watch out. Add the carry after you multiply that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Carry on from the working. Multiply the next column and add the carried digit.
- Check the working so far. The ones and tens columns are done. The carry from the tens column is 4.Ones: 4 × 7 = 28, write 8, carry 2. Tens: 6 × 7 = 42, plus 2 = 44, write 4, carry 4.
- Hundreds column. Multiply, then add the carry.2 × 7 = 14, plus 4 = 18. Write 8 and carry 1.
- Thousands column. Multiply, then add the carry. There is nothing left to the left, so write the whole number.3 × 7 = 21, plus 1 = 22. Write 22.
- Read the answer.
TTh Th H T O 3 2 6 4 × 7 2 2 8 4 8 2 1 4 2
3,264 × 7 = 22,848
Check. Estimate: 3,264 is about 3,000. 3,000 × 7 = 21,000. Our answer, 22,848, is close to 21,000. ✓
Watch out. Add the carry after you multiply that column.
Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.
Method. Split 1,426 into place-value parts (partition it). Multiply each part by 5, then add the answers.
- Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.1,426 = 1,000 + 400 + 20 + 6
- Draw the grid and write the parts across the top. The number on the side is 5. Every part gets multiplied by 5.
- Multiply each part. Use a times table fact, then put the zeros back.1,000 × 5: 1 × 5 = 5, then 3 zeros. 5,000
400 × 5: 4 × 5 = 20, then 2 zeros. 2,000
20 × 5: 2 × 5 = 10, then 1 zero. 100
6 × 5 = 30 - Write each answer in the grid. These are the partial products.
- Add the partial products. Add them one at a time. Keep a running total.5,000 + 2,000 = 7,000
7,000 + 100 = 7,100
7,100 + 30 = 7,130 - Write the answer. 1,426 × 5 = 7,130
Check. Estimate: 1,426 is about 1,000. 1,000 × 5 = 5,000. Our answer, 7,130, is a bit more than 5,000. ✓
Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. A bar model shows what we know and what we need to find out.
- Choose the operation. There are 8 equal groups, so multiply by 8.245 × 8
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 2 4 5 × 8 - Multiply the ones. Always start with the ones, on the right.5 × 8 = 40
40 is 4 tens and 0 ones. Write 0 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.4 × 8 = 32, and 32 + 4 = 36
36 is 3 hundreds and 6 tens. Write 6 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.2 × 8 = 16, and 16 + 3 = 19
19 is 1 thousand and 9 hundreds. Write 9 in the hundreds column and carry 1. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 1 into it.Write 1 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 2 4 5 × 8 1 9 6 0 1 3 4 - Write the answer. Include the unit.1,960 seats
Check. Estimate: 245 is about 200. 200 × 8 = 1,600. Our answer, 1,960, is a bit more than 1,600. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. A bar model shows what we know and what we need to find out.
- Choose the operation. There are 5 equal groups, so multiply by 5.2,150 × 5
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 2 1 5 0 × 5 - Multiply the ones. Always start with the ones, on the right.0 × 5 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the tens. Now the next column to the left.5 × 5 = 25
25 is 2 hundreds and 5 tens. Write 5 in the tens column and carry 2. - Multiply the hundreds. Multiply, then add the 2 we carried.1 × 5 = 5, and 5 + 2 = 7
7 is less than 10, so write 7. Nothing to carry. - Multiply the thousands. Now the next column to the left.2 × 5 = 10
10 is 1 ten thousand and 0 thousands. Write 0 in the thousands column and carry 1. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 1 into it.Write 1 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 2 1 5 0 × 5 1 0 7 5 0 1 2 - Write the answer. Include the unit.10,750 sheets
Check. Estimate: 2,150 is about 2,000. 2,000 × 5 = 10,000. Our answer, 10,750, is close to 10,000. ✓
Watch out. A zero digit still needs a step: 0 × the number is 0, but do not forget to add the carried digit.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. A bar model shows what we know and what we need to find out.
- Choose the operation. There are 9 equal groups, so multiply by 9.1,672 × 9
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 1 6 7 2 × 9 - Multiply the ones. Always start with the ones, on the right.2 × 9 = 18
18 is 1 ten and 8 ones. Write 8 in the ones column and carry 1. - Multiply the tens. Multiply, then add the 1 we carried.7 × 9 = 63, and 63 + 1 = 64
64 is 6 hundreds and 4 tens. Write 4 in the tens column and carry 6. - Multiply the hundreds. Multiply, then add the 6 we carried.6 × 9 = 54, and 54 + 6 = 60
60 is 6 thousands and 0 hundreds. Write 0 in the hundreds column and carry 6. - Multiply the thousands. Multiply, then add the 6 we carried.1 × 9 = 9, and 9 + 6 = 15
15 is 1 ten thousand and 5 thousands. Write 5 in the thousands column and carry 1. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 1 into it.Write 1 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 1 6 7 2 × 9 1 5 0 4 8 1 6 6 1 - Write the answer. Include the unit.15,048 steps
Check. Estimate: 1,672 is about 2,000. 2,000 × 9 = 18,000. Our answer, 15,048, is close to 18,000. ✓
Watch out. Write each carry small, then add it in the next column AFTER you have multiplied that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Change the price to pence, multiply, then change the answer back to pounds.
- Change the price to pence. Working in pence means no decimal point. £1 = 100p, so multiply by 100.£12.50 = 1,250p
- Choose the operation. 6 items at 1,250p each: multiply the price by 6.1,250p × 6
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 1 2 5 0 × 6 - Multiply the ones. Always start with the ones, on the right.0 × 6 = 0
0 is less than 10, so write 0. Nothing to carry. - Multiply the tens. Now the next column to the left.5 × 6 = 30
30 is 3 hundreds and 0 tens. Write 0 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.2 × 6 = 12, and 12 + 3 = 15
15 is 1 thousand and 5 hundreds. Write 5 in the hundreds column and carry 1. - Multiply the thousands. Multiply, then add the 1 we carried.1 × 6 = 6, and 6 + 1 = 7
7 is less than 10, so write 7. Nothing to carry. - Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 1 2 5 0 × 6 7 5 0 0 1 3 - Change back to pounds. Divide by 100: the digits move 2 places to the right.7,500p = £75.00
- Write the answer. Include the unit.£75.00
Check. Estimate: 1,250 is about 1,000. 1,000 × 6 = 6,000. Our answer, 7,500, is a bit more than 6,000. ✓
Watch out. Always change back to pounds at the end. 7,500p is not £7,500.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Change the price to pence, multiply, then change the answer back to pounds.
- Change the price to pence. Working in pence means no decimal point. £1 = 100p, so multiply by 100.£3.45 = 345p
- Choose the operation. 8 items at 345p each: multiply the price by 8.345p × 8
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 3 4 5 × 8 - Multiply the ones. Always start with the ones, on the right.5 × 8 = 40
40 is 4 tens and 0 ones. Write 0 in the ones column and carry 4. - Multiply the tens. Multiply, then add the 4 we carried.4 × 8 = 32, and 32 + 4 = 36
36 is 3 hundreds and 6 tens. Write 6 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.3 × 8 = 24, and 24 + 3 = 27
27 is 2 thousands and 7 hundreds. Write 7 in the hundreds column and carry 2. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 2 into it.Write 2 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 3 4 5 × 8 2 7 6 0 2 3 4 - Change back to pounds. Divide by 100: the digits move 2 places to the right.2,760p = £27.60
- Write the answer. Include the unit.£27.60
Check. Estimate: 345 is about 300. 300 × 8 = 2,400. Our answer, 2,760, is close to 2,400. ✓
Watch out. Always change back to pounds at the end. 7,500p is not £7,500.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Change the price to pence, multiply, then change the answer back to pounds.
- Change the price to pence. Working in pence means no decimal point. £1 = 100p, so multiply by 100.£7.99 = 799p
- Choose the operation. 4 items at 799p each: multiply the price by 4.799p × 4
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 7 9 9 × 4 - Multiply the ones. Always start with the ones, on the right.9 × 4 = 36
36 is 3 tens and 6 ones. Write 6 in the ones column and carry 3. - Multiply the tens. Multiply, then add the 3 we carried.9 × 4 = 36, and 36 + 3 = 39
39 is 3 hundreds and 9 tens. Write 9 in the tens column and carry 3. - Multiply the hundreds. Multiply, then add the 3 we carried.7 × 4 = 28, and 28 + 3 = 31
31 is 3 thousands and 1 hundred. Write 1 in the hundreds column and carry 3. - Write the carried digit. There is nothing left to multiply in the thousands column, but we carried 3 into it.Write 3 in the thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 7 9 9 × 4 3 1 9 6 3 3 3 - Change back to pounds. Divide by 100: the digits move 2 places to the right.3,196p = £31.96
- Write the answer. Include the unit.£31.96
Check. Estimate: 799 is about 800. 800 × 4 = 3,200. Our answer, 3,196, is close to 3,200. ✓
Watch out. Always change back to pounds at the end. 7,500p is not £7,500.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Estimate first by rounding. Then use short multiplication, and compare the answer with your estimate.
- Estimate first. Round the big number to one digit followed by zeros. This tells us roughly what the answer should be.2,618 ≈ 3,000, so 3,000 × 3 = 9,000
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
Th H T O 2 6 1 8 × 3 - Multiply the ones. Always start with the ones, on the right.8 × 3 = 24
24 is 2 tens and 4 ones. Write 4 in the ones column and carry 2. - Multiply the tens. Multiply, then add the 2 we carried.1 × 3 = 3, and 3 + 2 = 5
5 is less than 10, so write 5. Nothing to carry. - Multiply the hundreds. Now the next column to the left.6 × 3 = 18
18 is 1 thousand and 8 hundreds. Write 8 in the hundreds column and carry 1. - Multiply the thousands. Multiply, then add the 1 we carried.2 × 3 = 6, and 6 + 1 = 7
7 is less than 10, so write 7. Nothing to carry. - Read the answer from the final layout. Check that it has about the right number of digits.
Th H T O 2 6 1 8 × 3 7 8 5 4 1 2 - Compare the answer with the estimate. They should be close.7,854 is close to 9,000. ✓
- Write the answer. 7,854
Check. Estimate: 3,000 × 3 = 9,000, and 7,854 is close. ✓
Watch out. If your answer is nowhere near the estimate, check your carries.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Estimate first by rounding. Then use short multiplication, and compare the answer with your estimate.
- Estimate first. Round the big number to one digit followed by zeros. This tells us roughly what the answer should be.7,481 ≈ 7,000, so 7,000 × 8 = 56,000
- Write the numbers in columns. Ones go under ones, tens under tens and so on. The one-digit number goes under the ones.
TTh Th H T O 7 4 8 1 × 8 - Multiply the ones. Always start with the ones, on the right.1 × 8 = 8
8 is less than 10, so write 8. Nothing to carry. - Multiply the tens. Now the next column to the left.8 × 8 = 64
64 is 6 hundreds and 4 tens. Write 4 in the tens column and carry 6. - Multiply the hundreds. Multiply, then add the 6 we carried.4 × 8 = 32, and 32 + 6 = 38
38 is 3 thousands and 8 hundreds. Write 8 in the hundreds column and carry 3. - Multiply the thousands. Multiply, then add the 3 we carried.7 × 8 = 56, and 56 + 3 = 59
59 is 5 ten thousands and 9 thousands. Write 9 in the thousands column and carry 5. - Write the carried digit. There is nothing left to multiply in the ten thousands column, but we carried 5 into it.Write 5 in the ten thousands column.
- Read the answer from the final layout. Check that it has about the right number of digits.
TTh Th H T O 7 4 8 1 × 8 5 9 8 4 8 5 3 6 - Compare the answer with the estimate. They should be close.59,848 is close to 56,000. ✓
- Write the answer. 59,848
Check. Estimate: 7,000 × 8 = 56,000, and 59,848 is close. ✓
Watch out. If your answer is nowhere near the estimate, check your carries.
Key words. A bar model is a drawing that shows the amounts in a problem as bars, so you can see which calculation to do.
Method. Break the problem into steps. Work out one thing at a time and write down what each answer means.
- Draw a bar model. A bar model shows what we know and what we need to find out.
- Find the cost of the laptops. 6 laptops at £349 each. Multiply.349 × 6 = 2,094
- Find the cost of the cases. 6 cases at £18 each.18 × 6 = 108
- Add the two costs. The total is the laptops plus the cases.2,094 + 108 = 2,202
- Write the answer. Include the unit.£2,202
Check. Another way: one laptop and one case cost 349 + 18 = £367, and 367 × 6 = 2,202. ✓
Watch out. Check that you answer the question: the TOTAL cost, not just the laptops.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Work out the correct answer yourself first. Then compare it with the answer in the question to find the mistake.
- Work it out carefully. Do the question again, one step at a time.
Th H T O 3 4 8 × 6 2 0 8 8 2 2 4
348 × 6 = 2,088 - Compare with the answer in the question. Jack wrote 1,848, which is not 2,088, so Jack made a mistake.
- Find the mistake. Jack forgot to add the carried digits in the tens and hundreds columns.
- Write the correct answer. The correct answer is 2,088.
Check. Estimate: 348 is about 300. 300 × 6 = 1,800. Our answer, 2,088, is close to 1,800. ✓
Watch out. Write each carry small under the next column, and add it AFTER multiplying that column.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Work out the correct answer yourself first. Then compare it with the answer in the question to find the mistake.
- Work it out carefully. Do the question again, one step at a time.
TTh Th H T O 4 0 5 6 × 7 2 8 3 9 2 2 3 4
4,056 × 7 = 28,392 - Compare with the answer in the question. Priya wrote 28,092, which is not 28,392.
- Find the mistake. Priya got the hundreds column wrong. 0 × 7 = 0, but there was a carry of 3 to add, so the digit is 3, not 0.
- Write the correct answer. The correct answer is 28,392.
Check. Estimate: 4,056 is about 4,000. 4,000 × 7 = 28,000. Our answer, 28,392, is close to 28,000. ✓
Watch out. A zero digit still needs a step: 0 × 7 = 0, then add the carry.
Key words. A counter-example is one example that shows a statement is false.
Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.
- Try some numbers. Test the statement with some examples.Try 3 × 6 = 18, 14 × 6 = 84, 207 × 6 = 1,242. All the answers are even.
- Explain why. A reason shows what is happening for every number, not just the ones we tried.The 6 times table is all even numbers. Any whole number times 6 is 6 lots of something, which can be split into pairs, so it is even.
- Decide. Always
Check. Each answer was even. ✓
Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.
Key words. A counter-example is one example that shows a statement is false.
Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.
- Try some numbers. Test the statement with some examples.1,000 × 5 = 5,000 (4 digits).
2,000 × 5 = 10,000 (5 digits). - Look for one that does not work. One example that breaks the rule is called a counter-example.1,000 × 5 = 5,000 has 4 digits, so the statement is not always true.
- Explain why. A reason shows what is happening for every number, not just the ones we tried.1,000 × 5 = 5,000 has 4 digits, but 2,000 × 5 = 10,000 has 5 digits. It depends on the number.
- Decide. Sometimes
Check. We found one example for each case. ✓
Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.
Key words. A digit is one of the symbols 0 to 9. A number like 326 has three digits.
Method. Try each digit in the box. Only one gives the right answer. (Estimating first can cut down the choices.)
- Think about the size of the answer. The answer is 1,630, so the number is about 326 (that is 1,630 shared into 5 equal parts).1,630 ÷ 5 is about 300
- Try each digit. Work out the multiplication each time.
Digit Calculation Answer = 1,630? 0 306 × 5 1,530 no 1 316 × 5 1,580 no 2 326 × 5 1,630 yes 3 336 × 5 1,680 no 4 346 × 5 1,730 no 5 356 × 5 1,780 no 6 366 × 5 1,830 no 7 376 × 5 1,880 no 8 386 × 5 1,930 no 9 396 × 5 1,980 no - Write the digit. Only one row matches.The digit is 2.
Check. 326 × 5 = 1,630. ✓
Watch out. Put your digit back in the box and read the whole multiplication. It must be true.
Key words. Short multiplication is a written method for multiplying by a one-digit number. Write the numbers in columns and multiply one column at a time, starting with the ones. If a column makes 10 or more, write the ones digit and carry the tens digit to the next column.
Method. Try each card as the one-digit number. For each choice, put the other three cards in decreasing order to make the biggest 3-digit number. Compare the products.
- Choose the one-digit number. There are four cards, so there are four choices. We try them all.2, 4, 7, 9
- Make the best 3-digit number each time. The biggest digit goes in the hundreds place when we want the biggest number.
One-digit number 3-digit number Calculation Product 2 974 974 × 2 1,948 4 972 972 × 4 3,888 7 942 942 × 7 6,594 9 742 742 × 9 6,678 - Pick the biggest product. Compare the four answers.The biggest product is 6,678, from 742 × 9.
Check. 742 × 9 = 6,678. ✓
Watch out. Try every card as the one-digit number. The best answer is not always from the biggest card.