Year 5: Bigger numbers, zeros, estimating and checking
Part of the Year 5 short division and remainders chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Bigger numbers, zeros, estimating and checking
Now we divide numbers with up to 4 digits. The method is exactly the same as before. There are just more digits to work through: thousands, then hundreds, then tens, then ones. When the first digit is smaller than the divisor, write 0 above it, exchange it for 10 times as many of the next place, and carry on.
| 0 | 6 | 8 | 4 | |
| 4 | 2 | 27 | 33 | 16 |
Zeros need care. A 0 in the number you are dividing still gets a step. If nothing was carried, 0 ÷ 4 = 0, so write 0 above it. A 0 in the answer is a place holder: it keeps the other digits in the right columns. Without it, 1,014 would look like 114. A zero also appears when a digit plus the carry is smaller than the divisor.
| 1 | 0 | 1 | 4 | |
| 4 | 4 | 0 | 5 | 16 |
| 0 | 6 | 0 | 1 | |
| 5 | 3 | 30 | 0 | 5 |
Estimate first, then check. Before you divide, round the number to something your divisor goes into easily. For 5,736 ÷ 7: 5,736 is about 5,600, and 56 ÷ 7 = 8, so 5,600 ÷ 7 = 800. The exact answer should be close to 800. Afterwards, check by multiplying back: the answer × the divisor (plus any remainder) must give the number you started with.
| Step | Working |
|---|---|
| Estimate | 5,736 ≈ 5,600 and 5,600 ÷ 7 = 800 |
| Divide | 5,736 ÷ 7 = 819 r 3 |
| Check by multiplying | 819 × 7 = 5,733 and 5,733 + 3 = 5,736 |
Key ideas
- Use the same bus stop method. Start with the thousands. If the first digit is smaller than the divisor, write 0 and carry it on.
- A 0 in the number still needs a step. A 0 in the answer is a place holder: never leave it out.
- Estimate first: round to a number the divisor goes into easily, then divide. The exact answer should be close.
- Check by multiplying back: answer × divisor (+ remainder) = the number you started with.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
4 2 7 3 6 - Divide the thousands. Always start on the left, with the biggest place value.2 ÷ 4: 2 is smaller than 4, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 2 thousands for 20 hundreds. Carry 2 to the next digit.0 4 2 27 3 6 - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 7 hundreds there are 20 + 7 = 27 hundreds.
27 ÷ 4: 6 × 4 = 24, and 27 − 24 = 3. Write 6 above the 7.
Exchange: 3 hundreds become 30 tens. Carry 3 to the next digit.0 6 4 2 27 33 6 - Divide the tens. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 tens. With the 3 tens there are 30 + 3 = 33 tens.
33 ÷ 4: 8 × 4 = 32, and 33 − 32 = 1. Write 8 above the 3.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit.0 6 8 4 2 27 33 16 - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 6 ones there are 10 + 6 = 16 ones.
16 ÷ 4: 4 × 4 = 16. Write 4 above the 6.
Nothing is left over, so there is no remainder.0 6 8 4 4 2 27 33 16 - Read the answer. Ignore any 0 at the front of the answer.
0 6 8 4 4 2 27 33 16
2,736 ÷ 4 = 684 - Write the answer. 2,736 ÷ 4 = 684
Check. Multiply back: 684 × 4 = 600 × 4 + 80 × 4 + 4 × 4 = 2,400 + 320 + 16 = 2,736. ✓
Watch out. If the first digit is smaller than 4, write 0 above it (not in the final answer) and carry the digit to the next place.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
6 5 4 1 8 - Divide the thousands. Always start on the left, with the biggest place value.5 ÷ 6: 5 is smaller than 6, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 5 thousands for 50 hundreds. Carry 5 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 hundreds. With the 4 hundreds there are 50 + 4 = 54 hundreds.
54 ÷ 6: 9 × 6 = 54. Write 9 above the 4. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 1 tens.
1 ÷ 6: 1 is smaller than 6, so write 0.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 8 ones there are 10 + 8 = 18 ones.
18 ÷ 6: 3 × 6 = 18. Write 3 above the 8.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 9 0 3 6 5 54 1 18
5,418 ÷ 6 = 903 - Write the answer. 5,418 ÷ 6 = 903
Check. Multiply back: 903 × 6 = 900 × 6 + 3 × 6 = 5,400 + 18 = 5,418. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 903 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
4 4 0 5 6 - Divide the thousands. Always start on the left, with the biggest place value.4 ÷ 4 = 1
Write 1 above the 4.1 4 4 0 5 6 - Divide the hundreds. Move to the next digit on the right.Nothing was carried, so there are just 0 hundreds.
0 ÷ 4 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.1 0 4 4 0 5 6 - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 5 tens.
5 ÷ 4: 1 × 4 = 4, and 5 − 4 = 1. Write 1 above the 5.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit.1 0 1 4 4 0 5 16 - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 6 ones there are 10 + 6 = 16 ones.
16 ÷ 4: 4 × 4 = 16. Write 4 above the 6.
Nothing is left over, so there is no remainder.1 0 1 4 4 4 0 5 16 - Read the answer. Read the digits above the line from left to right.
1 0 1 4 4 4 0 5 16
4,056 ÷ 4 = 1,014 - Write the answer. 4,056 ÷ 4 = 1,014
Check. Multiply back: 1,014 × 4 = 1,000 × 4 + 10 × 4 + 4 × 4 = 4,000 + 40 + 16 = 4,056. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 1,014 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
5 3 0 0 5 - Divide the thousands. Always start on the left, with the biggest place value.3 ÷ 5: 3 is smaller than 5, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 3 thousands for 30 hundreds. Carry 3 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 hundreds. With the 0 hundreds there are 30 + 0 = 30 hundreds.
30 ÷ 5: 6 × 5 = 30. Write 6 above the 0. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 5 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 5 ones.
5 ÷ 5: 1 × 5 = 5. Write 1 above the 5.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 6 0 1 5 3 30 0 5
3,005 ÷ 5 = 601 - Write the answer. 3,005 ÷ 5 = 601
Check. Multiply back: 601 × 5 = 600 × 5 + 1 × 5 = 3,000 + 5 = 3,005. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 601 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
7 5 7 4 3 - Divide the thousands. Always start on the left, with the biggest place value.5 ÷ 7: 5 is smaller than 7, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 5 thousands for 50 hundreds. Carry 5 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 hundreds. With the 7 hundreds there are 50 + 7 = 57 hundreds.
57 ÷ 7: 8 × 7 = 56, and 57 − 56 = 1. Write 8 above the 7.
Exchange: 1 hundred becomes 10 tens. Carry 1 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 tens. With the 4 tens there are 10 + 4 = 14 tens.
14 ÷ 7: 2 × 7 = 14. Write 2 above the 4. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 3 ones.
3 ÷ 7: 3 is smaller than 7, so write 0.
The remainder is 3. - Read the answer. Ignore any 0 at the front of the answer.
0 8 2 0 r 3 7 5 57 14 3
5,743 ÷ 7 = 820 r 3 - Write the answer. 5,743 ÷ 7 = 820 r 3
Check. Multiply back: 820 × 7 = 800 × 7 + 20 × 7 = 5,600 + 140 = 5,740
5,740 + 3 (the remainder) = 5,743. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 820 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
9 8 7 6 5 - Divide the thousands. Always start on the left, with the biggest place value.8 ÷ 9: 8 is smaller than 9, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 8 thousands for 80 hundreds. Carry 8 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 8 that was carried.The carried 8 makes 80 hundreds. With the 7 hundreds there are 80 + 7 = 87 hundreds.
87 ÷ 9: 9 × 9 = 81, and 87 − 81 = 6. Write 9 above the 7.
Exchange: 6 hundreds become 60 tens. Carry 6 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 6 that was carried.The carried 6 makes 60 tens. With the 6 tens there are 60 + 6 = 66 tens.
66 ÷ 9: 7 × 9 = 63, and 66 − 63 = 3. Write 7 above the 6.
Exchange: 3 tens become 30 ones. Carry 3 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 ones. With the 5 ones there are 30 + 5 = 35 ones.
35 ÷ 9: 3 × 9 = 27, and 35 − 27 = 8. Write 3 above the 5.
The remainder is 8. - Read the answer. Ignore any 0 at the front of the answer.
0 9 7 3 r 8 9 8 87 66 35
8,765 ÷ 9 = 973 r 8 - Write the answer. 8,765 ÷ 9 = 973 r 8
Check. Multiply back: 973 × 9 = 900 × 9 + 70 × 9 + 3 × 9 = 8,100 + 630 + 27 = 8,757
8,757 + 8 (the remainder) = 8,765. ✓
Watch out. The first digit is smaller than 9: write 0 and carry it. The remainder is always smaller than 9.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Estimate first by rounding. Then use short division, and compare the answer with your estimate.
- Estimate first. Round 5,736 to a number that 7 divides into easily. This tells us roughly what the answer should be.5,736 ≈ 5,600, so 5,600 ÷ 7 = 800
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
7 5 7 3 6 - Divide the thousands. Always start on the left, with the biggest place value.5 ÷ 7: 5 is smaller than 7, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 5 thousands for 50 hundreds. Carry 5 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 hundreds. With the 7 hundreds there are 50 + 7 = 57 hundreds.
57 ÷ 7: 8 × 7 = 56, and 57 − 56 = 1. Write 8 above the 7.
Exchange: 1 hundred becomes 10 tens. Carry 1 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 tens. With the 3 tens there are 10 + 3 = 13 tens.
13 ÷ 7: 1 × 7 = 7, and 13 − 7 = 6. Write 1 above the 3.
Exchange: 6 tens become 60 ones. Carry 6 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 6 that was carried.The carried 6 makes 60 ones. With the 6 ones there are 60 + 6 = 66 ones.
66 ÷ 7: 9 × 7 = 63, and 66 − 63 = 3. Write 9 above the 6.
The remainder is 3. - Read the answer. Ignore any 0 at the front of the answer.
0 8 1 9 r 3 7 5 57 13 66
5,736 ÷ 7 = 819 r 3 - Compare the answer with the estimate. They should be close.819 r 3 is close to 800. ✓
- Write the answer. 819 r 3
Check. Estimate: 5,736 ≈ 5,600, and 5,600 ÷ 7 = 800. The answer 819 is close to 800. ✓
Watch out. If your answer is nowhere near the estimate, check your carries and your zeros.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Use the inverse operation. Multiply your answer by the divisor (and add any remainder). You should get back the number you started with.
- Multiply the answer by the number you divided by. Multiplying is the inverse (opposite) of dividing, so it should take us back to the start.365 × 6 = 300 × 6 + 60 × 6 + 5 × 6 = 1,800 + 360 + 30 = 2,190
- Compare with 2,184. If 365 is right, we get back to exactly 2,184.2,190 ≠ 2,184
- Decide. We did not get back to 2,184, so Priya’s answer is not right.No. The correct answer is 364.
- Find the correct answer. Use short division.
0 3 6 4 6 2 21 38 24
2,184 ÷ 6 = 364
Check. The check itself: 365 groups of 6 is 2,190.
Watch out. Do not forget to add the remainder when you multiply back.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. There are 7 equal shares. Each share is the same size.
- Choose the operation. 2,450 is shared equally between 7, so divide by 7.2,450 ÷ 7
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
7 2 4 5 0 - Divide the thousands. Always start on the left, with the biggest place value.2 ÷ 7: 2 is smaller than 7, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 2 thousands for 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 4 hundreds there are 20 + 4 = 24 hundreds.
24 ÷ 7: 3 × 7 = 21, and 24 − 21 = 3. Write 3 above the 4.
Exchange: 3 hundreds become 30 tens. Carry 3 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 tens. With the 5 tens there are 30 + 5 = 35 tens.
35 ÷ 7: 5 × 7 = 35. Write 5 above the 5. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 7 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 3 5 0 7 2 24 35 0
2,450 ÷ 7 = 350 - Write the answer. Include the unit.350 books
Check. Multiply back: 350 × 7 = 300 × 7 + 50 × 7 = 2,100 + 350 = 2,450. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 350 would look like a much smaller number. Write a 0 every time a digit does not divide.
Watch out
Do not leave out a zero. In 4,056 ÷ 4 the answer is 1,014. If you write 114 the answer is far too small (the estimate 4,000 ÷ 4 = 1,000 shows this). Also remember to add the carry after the 0 hundreds: 0 hundreds and a carry of 0 gives 0, but a carry of 1 would give 10.Exercise 5D Four-digit numbers and zeros
Non-calculatorKey words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
3 4 3 6 8 - Divide the thousands. Always start on the left, with the biggest place value.4 ÷ 3 = 1, remainder 1
Write 1 above the 4.
Exchange the remainder: 1 thousand becomes 10 hundreds. Carry 1 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 hundreds. With the 3 hundreds there are 10 + 3 = 13 hundreds.
13 ÷ 3: 4 × 3 = 12, and 13 − 12 = 1. Write 4 above the 3.
Exchange: 1 hundred becomes 10 tens. Carry 1 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 tens. With the 6 tens there are 10 + 6 = 16 tens.
16 ÷ 3: 5 × 3 = 15, and 16 − 15 = 1. Write 5 above the 6.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 8 ones there are 10 + 8 = 18 ones.
18 ÷ 3: 6 × 3 = 18. Write 6 above the 8.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 4 5 6 3 4 13 16 18
4,368 ÷ 3 = 1,456 - Write the answer. 4,368 ÷ 3 = 1,456
Check. Multiply back: 1,456 × 3 = 1,000 × 3 + 400 × 3 + 50 × 3 + 6 × 3 = 3,000 + 1,200 + 150 + 18 = 4,368. ✓
Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
5 7 2 4 5 - Divide the thousands. Always start on the left, with the biggest place value.7 ÷ 5 = 1, remainder 2
Write 1 above the 7.
Exchange the remainder: 2 thousands become 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 2 hundreds there are 20 + 2 = 22 hundreds.
22 ÷ 5: 4 × 5 = 20, and 22 − 20 = 2. Write 4 above the 2.
Exchange: 2 hundreds become 20 tens. Carry 2 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 tens. With the 4 tens there are 20 + 4 = 24 tens.
24 ÷ 5: 4 × 5 = 20, and 24 − 20 = 4. Write 4 above the 4.
Exchange: 4 tens become 40 ones. Carry 4 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 ones. With the 5 ones there are 40 + 5 = 45 ones.
45 ÷ 5: 9 × 5 = 45. Write 9 above the 5.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 4 4 9 5 7 22 24 45
7,245 ÷ 5 = 1,449 - Write the answer. 7,245 ÷ 5 = 1,449
Check. Multiply back: 1,449 × 5 = 1,000 × 5 + 400 × 5 + 40 × 5 + 9 × 5 = 5,000 + 2,000 + 200 + 45 = 7,245. ✓
Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
6 8 2 7 4 - Divide the thousands. Always start on the left, with the biggest place value.8 ÷ 6 = 1, remainder 2
Write 1 above the 8.
Exchange the remainder: 2 thousands become 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 2 hundreds there are 20 + 2 = 22 hundreds.
22 ÷ 6: 3 × 6 = 18, and 22 − 18 = 4. Write 3 above the 2.
Exchange: 4 hundreds become 40 tens. Carry 4 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 tens. With the 7 tens there are 40 + 7 = 47 tens.
47 ÷ 6: 7 × 6 = 42, and 47 − 42 = 5. Write 7 above the 7.
Exchange: 5 tens become 50 ones. Carry 5 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 ones. With the 4 ones there are 50 + 4 = 54 ones.
54 ÷ 6: 9 × 6 = 54. Write 9 above the 4.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 3 7 9 6 8 22 47 54
8,274 ÷ 6 = 1,379 - Write the answer. 8,274 ÷ 6 = 1,379
Check. Multiply back: 1,379 × 6 = 1,000 × 6 + 300 × 6 + 70 × 6 + 9 × 6 = 6,000 + 1,800 + 420 + 54 = 8,274. ✓
Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
4 2 0 1 6 - Divide the thousands. Always start on the left, with the biggest place value.2 ÷ 4: 2 is smaller than 4, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 2 thousands for 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 0 hundreds there are 20 + 0 = 20 hundreds.
20 ÷ 4: 5 × 4 = 20. Write 5 above the 0. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 1 tens.
1 ÷ 4: 1 is smaller than 4, so write 0.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 6 ones there are 10 + 6 = 16 ones.
16 ÷ 4: 4 × 4 = 16. Write 4 above the 6.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 5 0 4 4 2 20 1 16
2,016 ÷ 4 = 504 - Write the answer. 2,016 ÷ 4 = 504
Check. Multiply back: 504 × 4 = 500 × 4 + 4 × 4 = 2,000 + 16 = 2,016. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 504 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
5 3 0 6 0 - Divide the thousands. Always start on the left, with the biggest place value.3 ÷ 5: 3 is smaller than 5, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 3 thousands for 30 hundreds. Carry 3 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 hundreds. With the 0 hundreds there are 30 + 0 = 30 hundreds.
30 ÷ 5: 6 × 5 = 30. Write 6 above the 0. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 6 tens.
6 ÷ 5: 1 × 5 = 5, and 6 − 5 = 1. Write 1 above the 6.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 0 ones there are 10 + 0 = 10 ones.
10 ÷ 5: 2 × 5 = 10. Write 2 above the 0.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 6 1 2 5 3 30 6 10
3,060 ÷ 5 = 612 - Write the answer. 3,060 ÷ 5 = 612
Check. Multiply back: 612 × 5 = 600 × 5 + 10 × 5 + 2 × 5 = 3,000 + 50 + 10 = 3,060. ✓
Watch out. If the first digit is smaller than 5, write 0 above it (not in the final answer) and carry the digit to the next place.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
9 9 0 4 5 - Divide the thousands. Always start on the left, with the biggest place value.9 ÷ 9 = 1
Write 1 above the 9. - Divide the hundreds. Move to the next digit on the right.Nothing was carried, so there are just 0 hundreds.
0 ÷ 9 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 4 tens.
4 ÷ 9: 4 is smaller than 9, so write 0.
Exchange: 4 tens become 40 ones. Carry 4 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 ones. With the 5 ones there are 40 + 5 = 45 ones.
45 ÷ 9: 5 × 9 = 45. Write 5 above the 5.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 0 0 5 9 9 0 4 45
9,045 ÷ 9 = 1,005 - Write the answer. 9,045 ÷ 9 = 1,005
Check. Multiply back: 1,005 × 9 = 1,000 × 9 + 5 × 9 = 9,000 + 45 = 9,045. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 1,005 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
7 6 3 1 4 - Divide the thousands. Always start on the left, with the biggest place value.6 ÷ 7: 6 is smaller than 7, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 6 thousands for 60 hundreds. Carry 6 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 6 that was carried.The carried 6 makes 60 hundreds. With the 3 hundreds there are 60 + 3 = 63 hundreds.
63 ÷ 7: 9 × 7 = 63. Write 9 above the 3. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 1 tens.
1 ÷ 7: 1 is smaller than 7, so write 0.
Exchange: 1 ten becomes 10 ones. Carry 1 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 ones. With the 4 ones there are 10 + 4 = 14 ones.
14 ÷ 7: 2 × 7 = 14. Write 2 above the 4.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 9 0 2 7 6 63 1 14
6,314 ÷ 7 = 902 - Write the answer. 6,314 ÷ 7 = 902
Check. Multiply back: 902 × 7 = 900 × 7 + 2 × 7 = 6,300 + 14 = 6,314. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 902 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
4 8 2 4 0 - Divide the thousands. Always start on the left, with the biggest place value.8 ÷ 4 = 2
Write 2 above the 8. - Divide the hundreds. Move to the next digit on the right.Nothing was carried, so there are just 2 hundreds.
2 ÷ 4: 2 is smaller than 4, so write 0.
Exchange: 2 hundreds become 20 tens. Carry 2 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 tens. With the 4 tens there are 20 + 4 = 24 tens.
24 ÷ 4: 6 × 4 = 24. Write 6 above the 4. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 4 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
2 0 6 0 4 8 2 24 0
8,240 ÷ 4 = 2,060 - Write the answer. 8,240 ÷ 4 = 2,060
Check. Multiply back: 2,060 × 4 = 2,000 × 4 + 60 × 4 = 8,000 + 240 = 8,240. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 2,060 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
6 5 4 0 6 - Divide the thousands. Always start on the left, with the biggest place value.5 ÷ 6: 5 is smaller than 6, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 5 thousands for 50 hundreds. Carry 5 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 hundreds. With the 4 hundreds there are 50 + 4 = 54 hundreds.
54 ÷ 6: 9 × 6 = 54. Write 9 above the 4. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 6 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 6 ones.
6 ÷ 6: 1 × 6 = 6. Write 1 above the 6.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 9 0 1 6 5 54 0 6
5,406 ÷ 6 = 901 - Write the answer. 5,406 ÷ 6 = 901
Check. Multiply back: 901 × 6 = 900 × 6 + 1 × 6 = 5,400 + 6 = 5,406. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 901 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
5 4 0 0 0 - Divide the thousands. Always start on the left, with the biggest place value.4 ÷ 5: 4 is smaller than 5, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 4 thousands for 40 hundreds. Carry 4 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 hundreds. With the 0 hundreds there are 40 + 0 = 40 hundreds.
40 ÷ 5: 8 × 5 = 40. Write 8 above the 0. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 5 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 5 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 8 0 0 5 4 40 0 0
4,000 ÷ 5 = 800 - Write the answer. 4,000 ÷ 5 = 800
Check. Multiply back: 800 × 5 = 4,000. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 800 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
9 6 3 0 0 - Divide the thousands. Always start on the left, with the biggest place value.6 ÷ 9: 6 is smaller than 9, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 6 thousands for 60 hundreds. Carry 6 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 6 that was carried.The carried 6 makes 60 hundreds. With the 3 hundreds there are 60 + 3 = 63 hundreds.
63 ÷ 9: 7 × 9 = 63. Write 7 above the 3. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 9 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 9 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 7 0 0 9 6 63 0 0
6,300 ÷ 9 = 700 - Write the answer. 6,300 ÷ 9 = 700
Check. Multiply back: 700 × 9 = 6,300. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 700 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
3 9 0 0 0 - Divide the thousands. Always start on the left, with the biggest place value.9 ÷ 3 = 3
Write 3 above the 9. - Divide the hundreds. Move to the next digit on the right.Nothing was carried, so there are just 0 hundreds.
0 ÷ 3 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 3 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 3 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
3 0 0 0 3 9 0 0 0
9,000 ÷ 3 = 3,000 - Write the answer. 9,000 ÷ 3 = 3,000
Check. Multiply back: 3,000 × 3 = 9,000. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 3,000 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
8 8 0 0 8 - Divide the thousands. Always start on the left, with the biggest place value.8 ÷ 8 = 1
Write 1 above the 8. - Divide the hundreds. Move to the next digit on the right.Nothing was carried, so there are just 0 hundreds.
0 ÷ 8 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 8 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 8 ones.
8 ÷ 8: 1 × 8 = 8. Write 1 above the 8.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 0 0 1 8 8 0 0 8
8,008 ÷ 8 = 1,001 - Write the answer. 8,008 ÷ 8 = 1,001
Check. Multiply back: 1,001 × 8 = 1,000 × 8 + 1 × 8 = 8,000 + 8 = 8,008. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 1,001 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
3 2 0 1 0 - Divide the thousands. Always start on the left, with the biggest place value.2 ÷ 3: 2 is smaller than 3, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 2 thousands for 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 0 hundreds there are 20 + 0 = 20 hundreds.
20 ÷ 3: 6 × 3 = 18, and 20 − 18 = 2. Write 6 above the 0.
Exchange: 2 hundreds become 20 tens. Carry 2 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 tens. With the 1 tens there are 20 + 1 = 21 tens.
21 ÷ 3: 7 × 3 = 21. Write 7 above the 1. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 3 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 6 7 0 3 2 20 21 0
2,010 ÷ 3 = 670 - Write the answer. 2,010 ÷ 3 = 670
Check. Multiply back: 670 × 3 = 600 × 3 + 70 × 3 = 1,800 + 210 = 2,010. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 670 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
5 3 4 5 6 - Divide the thousands. Always start on the left, with the biggest place value.3 ÷ 5: 3 is smaller than 5, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 3 thousands for 30 hundreds. Carry 3 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 hundreds. With the 4 hundreds there are 30 + 4 = 34 hundreds.
34 ÷ 5: 6 × 5 = 30, and 34 − 30 = 4. Write 6 above the 4.
Exchange: 4 hundreds become 40 tens. Carry 4 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 tens. With the 5 tens there are 40 + 5 = 45 tens.
45 ÷ 5: 9 × 5 = 45. Write 9 above the 5. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 6 ones.
6 ÷ 5: 1 × 5 = 5, and 6 − 5 = 1. Write 1 above the 6.
The remainder is 1. - Read the answer. Ignore any 0 at the front of the answer.
0 6 9 1 r 1 5 3 34 45 6
3,456 ÷ 5 = 691 r 1 - Write the answer. 3,456 ÷ 5 = 691 r 1
Check. Multiply back: 691 × 5 = 600 × 5 + 90 × 5 + 1 × 5 = 3,000 + 450 + 5 = 3,455
3,455 + 1 (the remainder) = 3,456. ✓
Watch out. The first digit is smaller than 5: write 0 and carry it. The remainder is always smaller than 5.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
8 5 9 2 9 - Divide the thousands. Always start on the left, with the biggest place value.5 ÷ 8: 5 is smaller than 8, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 5 thousands for 50 hundreds. Carry 5 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 hundreds. With the 9 hundreds there are 50 + 9 = 59 hundreds.
59 ÷ 8: 7 × 8 = 56, and 59 − 56 = 3. Write 7 above the 9.
Exchange: 3 hundreds become 30 tens. Carry 3 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 tens. With the 2 tens there are 30 + 2 = 32 tens.
32 ÷ 8: 4 × 8 = 32. Write 4 above the 2. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 9 ones.
9 ÷ 8: 1 × 8 = 8, and 9 − 8 = 1. Write 1 above the 9.
The remainder is 1. - Read the answer. Ignore any 0 at the front of the answer.
0 7 4 1 r 1 8 5 59 32 9
5,929 ÷ 8 = 741 r 1 - Write the answer. 5,929 ÷ 8 = 741 r 1
Check. Multiply back: 741 × 8 = 700 × 8 + 40 × 8 + 1 × 8 = 5,600 + 320 + 8 = 5,928
5,928 + 1 (the remainder) = 5,929. ✓
Watch out. The first digit is smaller than 8: write 0 and carry it. The remainder is always smaller than 8.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
7 9 9 9 9 - Divide the thousands. Always start on the left, with the biggest place value.9 ÷ 7 = 1, remainder 2
Write 1 above the 9.
Exchange the remainder: 2 thousands become 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 9 hundreds there are 20 + 9 = 29 hundreds.
29 ÷ 7: 4 × 7 = 28, and 29 − 28 = 1. Write 4 above the 9.
Exchange: 1 hundred becomes 10 tens. Carry 1 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 1 that was carried.The carried 1 makes 10 tens. With the 9 tens there are 10 + 9 = 19 tens.
19 ÷ 7: 2 × 7 = 14, and 19 − 14 = 5. Write 2 above the 9.
Exchange: 5 tens become 50 ones. Carry 5 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 ones. With the 9 ones there are 50 + 9 = 59 ones.
59 ÷ 7: 8 × 7 = 56, and 59 − 56 = 3. Write 8 above the 9.
The remainder is 3. - Read the answer. Read the digits above the line from left to right.
1 4 2 8 r 3 7 9 29 19 59
9,999 ÷ 7 = 1,428 r 3 - Write the answer. 9,999 ÷ 7 = 1,428 r 3
Check. Multiply back: 1,428 × 7 = 1,000 × 7 + 400 × 7 + 20 × 7 + 8 × 7 = 7,000 + 2,800 + 140 + 56 = 9,996
9,996 + 3 (the remainder) = 9,999. ✓
Watch out. The remainder must always be smaller than the number you divide by (7). If it is not, you can divide again.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Round the number being divided to a number that is easy to divide, then divide it.
- Look at the first two digits of 4,823. They tell us how many hundreds there are, roughly.4,823 is about 48 hundreds
- Find the nearest number in the 6 times table. We want a number that 6 divides into exactly.6 × 8 = 48, and 48 is the closest to 48
- Round the number. Replace 48 hundreds by 48 hundreds.4,823 ≈ 4,800
- Divide the rounded number. Use the fact 48 ÷ 6 = 8.48 hundreds ÷ 6 = 8 hundreds
4,800 ÷ 6 = 800 - Write the estimate. Use the sign ≈ for “is about”.4,823 ÷ 6 ≈ 800
Check. Multiply back: 800 × 6 = 4,800, which is close to 4,823. ✓
Watch out. An estimate is not the exact answer. Use it to check that your exact answer is about the right size.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Round the number being divided to a number that is easy to divide, then divide it.
- Look at the first two digits of 7,184. They tell us how many hundreds there are, roughly.7,184 is about 71 hundreds
- Find the nearest number in the 9 times table. We want a number that 9 divides into exactly.9 × 8 = 72, and 72 is the closest to 71
- Round the number. Replace 71 hundreds by 72 hundreds.7,184 ≈ 7,200
- Divide the rounded number. Use the fact 72 ÷ 9 = 8.72 hundreds ÷ 9 = 8 hundreds
7,200 ÷ 9 = 800 - Write the estimate. Use the sign ≈ for “is about”.7,184 ÷ 9 ≈ 800
Check. Multiply back: 800 × 9 = 7,200, which is close to 7,184. ✓
Watch out. An estimate is not the exact answer. Use it to check that your exact answer is about the right size.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Round the number being divided to a number that is easy to divide, then divide it.
- Look at the first two digits of 2,968. They tell us how many hundreds there are, roughly.2,968 is about 29 hundreds
- Find the nearest number in the 3 times table. We want a number that 3 divides into exactly.3 × 10 = 30, and 30 is the closest to 29
- Round the number. Replace 29 hundreds by 30 hundreds.2,968 ≈ 3,000
- Divide the rounded number. Use the fact 30 ÷ 3 = 10.30 hundreds ÷ 3 = 10 hundreds
3,000 ÷ 3 = 1,000 - Write the estimate. Use the sign ≈ for “is about”.2,968 ÷ 3 ≈ 1,000
Check. Multiply back: 1,000 × 3 = 3,000, which is close to 2,968. ✓
Watch out. An estimate is not the exact answer. Use it to check that your exact answer is about the right size.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Estimate first by rounding. Then use short division, and compare the answer with your estimate.
- Estimate first. Round 7,184 to a number that 9 divides into easily. This tells us roughly what the answer should be.7,184 ≈ 7,200, so 7,200 ÷ 9 = 800
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
9 7 1 8 4 - Divide the thousands. Always start on the left, with the biggest place value.7 ÷ 9: 7 is smaller than 9, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 7 thousands for 70 hundreds. Carry 7 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 7 that was carried.The carried 7 makes 70 hundreds. With the 1 hundreds there are 70 + 1 = 71 hundreds.
71 ÷ 9: 7 × 9 = 63, and 71 − 63 = 8. Write 7 above the 1.
Exchange: 8 hundreds become 80 tens. Carry 8 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 8 that was carried.The carried 8 makes 80 tens. With the 8 tens there are 80 + 8 = 88 tens.
88 ÷ 9: 9 × 9 = 81, and 88 − 81 = 7. Write 9 above the 8.
Exchange: 7 tens become 70 ones. Carry 7 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 7 that was carried.The carried 7 makes 70 ones. With the 4 ones there are 70 + 4 = 74 ones.
74 ÷ 9: 8 × 9 = 72, and 74 − 72 = 2. Write 8 above the 4.
The remainder is 2. - Read the answer. Ignore any 0 at the front of the answer.
0 7 9 8 r 2 9 7 71 88 74
7,184 ÷ 9 = 798 r 2 - Compare the answer with the estimate. They should be close.798 r 2 is close to 800. ✓
- Write the answer. 798 r 2
Check. Estimate: 7,184 ≈ 7,200, and 7,200 ÷ 9 = 800. The answer 798 is close to 800. ✓
Watch out. If your answer is nowhere near the estimate, check your carries and your zeros.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Estimate first by rounding. Then use short division, and compare the answer with your estimate.
- Estimate first. Round 4,823 to a number that 6 divides into easily. This tells us roughly what the answer should be.4,823 ≈ 4,800, so 4,800 ÷ 6 = 800
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
6 4 8 2 3 - Divide the thousands. Always start on the left, with the biggest place value.4 ÷ 6: 4 is smaller than 6, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 4 thousands for 40 hundreds. Carry 4 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 hundreds. With the 8 hundreds there are 40 + 8 = 48 hundreds.
48 ÷ 6: 8 × 6 = 48. Write 8 above the 8. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 2 tens.
2 ÷ 6: 2 is smaller than 6, so write 0.
Exchange: 2 tens become 20 ones. Carry 2 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 ones. With the 3 ones there are 20 + 3 = 23 ones.
23 ÷ 6: 3 × 6 = 18, and 23 − 18 = 5. Write 3 above the 3.
The remainder is 5. - Read the answer. Ignore any 0 at the front of the answer.
0 8 0 3 r 5 6 4 48 2 23
4,823 ÷ 6 = 803 r 5 - Compare the answer with the estimate. They should be close.803 r 5 is close to 800. ✓
- Write the answer. 803 r 5
Check. Estimate: 4,823 ≈ 4,800, and 4,800 ÷ 6 = 800. The answer 803 is close to 800. ✓
Watch out. If your answer is nowhere near the estimate, check your carries and your zeros.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Use the inverse operation. Multiply your answer by the divisor (and add any remainder). You should get back the number you started with.
- Multiply the answer by the number you divided by. Multiplying is the inverse (opposite) of dividing, so it should take us back to the start.453 × 3 = 400 × 3 + 50 × 3 + 3 × 3 = 1,200 + 150 + 9 = 1,359
- Compare with 1,359. If 453 is right, we get back to exactly 1,359.1,359 = 1,359
- Decide. We got back to the number we started with.Yes, Zainab is correct: 1,359 ÷ 3 = 453.
Check. The check itself: 453 groups of 3 is 1,359.
Watch out. This check works for any division. Use it whenever you want to be sure.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Use the inverse operation. Multiply your answer by the divisor (and add any remainder). You should get back the number you started with.
- Multiply the answer by the number you divided by. Multiplying is the inverse (opposite) of dividing, so it should take us back to the start.365 × 6 = 300 × 6 + 60 × 6 + 5 × 6 = 1,800 + 360 + 30 = 2,190
- Compare with 2,184. If 365 is right, we get back to exactly 2,184.2,190 ≠ 2,184
- Decide. We did not get back to 2,184, so Leo’s answer is not right.No. The correct answer is 364.
- Find the correct answer. Use short division.
0 3 6 4 6 2 21 38 24
2,184 ÷ 6 = 364
Check. The check itself: 365 groups of 6 is 2,190.
Watch out. Do not forget to add the remainder when you multiply back.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. Use the inverse operation. Multiply your answer by the divisor (and add any remainder). You should get back the number you started with.
- Multiply the answer by the number you divided by. Multiplying is the inverse (opposite) of dividing, so it should take us back to the start.83 × 5 = 80 × 5 + 3 × 5 = 400 + 15 = 415
- Compare with 4,015. If 83 is right, we get back to exactly 4,015.415 ≠ 4,015
- Decide. We did not get back to 4,015, so Mei’s answer is not right.No. The correct answer is 803.
- Find the correct answer. Use short division.
0 8 0 3 5 4 40 1 15
4,015 ÷ 5 = 803
Check. The check itself: 83 groups of 5 is 415.
Watch out. Do not forget to add the remainder when you multiply back.
| 0 | ||||
| 8 | 6 | 60 | 4 | 8 |
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. The 6 thousands were too small to share (grey 0), so they were carried. Use the carried 6 to divide the hundreds.
- Exchange the carried 6. 6 thousands become 60 hundreds. There are 0 hundreds in the number, so we have 60 hundreds.60 + 0 = 60 hundreds
- Divide. Use the 8 times table.60 ÷ 8 = 7 remainder 4, because 7 × 8 = 56 and 60 − 56 = 4
Write 7 above the 0.0 7 8 6 60 44 8
Check. 7 × 8 = 56. ✓
Watch out. The carried digit is added to the digit it is in front of, as tens of that place.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. The remainder from the last step is carried to the next digit.
- Find the remainder. From the last step: 60 ÷ 8 = 7 remainder 4.60 − 56 = 4
- Carry the remainder. 4 hundreds are exchanged for 40 tens, so the 4 is written small in front of the next digit, the 4 in the tens place.
0 7 8 6 60 44 8
Check. The tens column now has 40 + 4 = 44 tens.
Watch out. The carried number is the remainder.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, exchange it for the next smaller place value and carry it to the next digit.
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
8 6 0 4 8 - Divide the thousands. Always start on the left, with the biggest place value.6 ÷ 8: 6 is smaller than 8, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 6 thousands for 60 hundreds. Carry 6 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 6 that was carried.The carried 6 makes 60 hundreds. With the 0 hundreds there are 60 + 0 = 60 hundreds.
60 ÷ 8: 7 × 8 = 56, and 60 − 56 = 4. Write 7 above the 0.
Exchange: 4 hundreds become 40 tens. Carry 4 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 tens. With the 4 tens there are 40 + 4 = 44 tens.
44 ÷ 8: 5 × 8 = 40, and 44 − 40 = 4. Write 5 above the 4.
Exchange: 4 tens become 40 ones. Carry 4 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 ones. With the 8 ones there are 40 + 8 = 48 ones.
48 ÷ 8: 6 × 8 = 48. Write 6 above the 8.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 7 5 6 8 6 60 44 48
6,048 ÷ 8 = 756 - Write the answer. 6,048 ÷ 8 = 756
Check. Multiply back: 756 × 8 = 700 × 8 + 50 × 8 + 6 × 8 = 5,600 + 400 + 48 = 6,048. ✓
Watch out. If the first digit is smaller than 8, write 0 above it (not in the final answer) and carry the digit to the next place.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. There are 8 equal shares. Each share is the same size.
- Choose the operation. 3,648 is shared equally between 8, so divide by 8.3,648 ÷ 8
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
8 3 6 4 8 - Divide the thousands. Always start on the left, with the biggest place value.3 ÷ 8: 3 is smaller than 8, so we cannot give each share a whole thousand. Write 0 (a 0 at the front is not part of the answer).
Exchange the 3 thousands for 30 hundreds. Carry 3 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 3 that was carried.The carried 3 makes 30 hundreds. With the 6 hundreds there are 30 + 6 = 36 hundreds.
36 ÷ 8: 4 × 8 = 32, and 36 − 32 = 4. Write 4 above the 6.
Exchange: 4 hundreds become 40 tens. Carry 4 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 tens. With the 4 tens there are 40 + 4 = 44 tens.
44 ÷ 8: 5 × 8 = 40, and 44 − 40 = 4. Write 5 above the 4.
Exchange: 4 tens become 40 ones. Carry 4 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 4 that was carried.The carried 4 makes 40 ones. With the 8 ones there are 40 + 8 = 48 ones.
48 ÷ 8: 6 × 8 = 48. Write 6 above the 8.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 4 5 6 8 3 36 44 48
3,648 ÷ 8 = 456 - Write the answer. Include the unit.456 books
Check. Multiply back: 456 × 8 = 400 × 8 + 50 × 8 + 6 × 8 = 3,200 + 400 + 48 = 3,648. ✓
Watch out. If the first digit is smaller than 8, write 0 above it (not in the final answer) and carry the digit to the next place.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. Each box is a group of 5. We count how many boxes make 7,500.
- Choose the operation. We find how many groups of 5 fit into 7,500, so divide by 5.7,500 ÷ 5
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
5 7 5 0 0 - Divide the thousands. Always start on the left, with the biggest place value.7 ÷ 5 = 1, remainder 2
Write 1 above the 7.
Exchange the remainder: 2 thousands become 20 hundreds. Carry 2 to the next digit. - Divide the hundreds. Move to the next digit on the right. Add the 2 that was carried.The carried 2 makes 20 hundreds. With the 5 hundreds there are 20 + 5 = 25 hundreds.
25 ÷ 5: 5 × 5 = 25. Write 5 above the 5. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 0 tens.
0 ÷ 5 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 0 ones.
0 ÷ 5 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 5 0 0 5 7 25 0 0
7,500 ÷ 5 = 1,500 - Write the answer. Include the unit.1,500 boxes
Check. Multiply back: 1,500 × 5 = 1,000 × 5 + 500 × 5 = 5,000 + 2,500 = 7,500. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 1,500 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Draw a bar model, choose the operation, then work it out.
- Draw a bar model. There are 9 equal shares. Each share is the same size.
- Choose the operation. 9,072 is shared equally between 9, so divide by 9.9,072 ÷ 9
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
9 9 0 7 2 - Divide the thousands. Always start on the left, with the biggest place value.9 ÷ 9 = 1
Write 1 above the 9. - Divide the hundreds. Move to the next digit on the right.Nothing was carried, so there are just 0 hundreds.
0 ÷ 9 = 0. Write 0 above. This 0 is a place holder, and it must stay in the answer. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 7 tens.
7 ÷ 9: 7 is smaller than 9, so write 0.
Exchange: 7 tens become 70 ones. Carry 7 to the next digit. - Divide the ones. Move to the next digit on the right. Add the 7 that was carried.The carried 7 makes 70 ones. With the 2 ones there are 70 + 2 = 72 ones.
72 ÷ 9: 8 × 9 = 72. Write 8 above the 2.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
1 0 0 8 9 9 0 7 72
9,072 ÷ 9 = 1,008 - Write the answer. Include the unit.1,008 seats
Check. Multiply back: 1,008 × 9 = 1,000 × 9 + 8 × 9 = 9,000 + 72 = 9,072. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 1,008 would look like a much smaller number. Write a 0 every time a digit does not divide.
Key words. A rate compares two amounts, such as £12 for 4 pens or 60 km each hour. A unit rate is the amount for just one (one pen, one hour, one litre). The word “per” means “for each” and tells you to divide.
Method. Break the problem into steps. Work out one thing at a time and write down what each answer means.
- Draw a bar model. Each box is one hour. The 8 boxes make 2,480, and we need the value of 5 boxes.
- Find the buns made in one hour. The same number is made every hour, so divide the total by 8.2,480 ÷ 8 = 310
- Find the buns made in 5 hours. 5 hours of 310 buns, so multiply by 5.310 × 5 = 1,550
- Write the answer. Include the unit.1,550 buns
Check. 310 × 8 = 2,480, so one hour is right. ✓
Watch out. Find one hour first (divide), then scale up to 5 hours (multiply).
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
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.
0 9 0 3 6 5 54 1 18
5,418 ÷ 6 = 903 - Compare with the answer in the question. Mia wrote 93, which is not 903.
- Find the mistake. Mia left out a zero. Some digits do not divide, and the zero is a place holder. Without it, every digit after it is in the wrong column.
- Write the correct answer. The correct answer is 903.
Check. Multiply back: 903 × 6 = 900 × 6 + 3 × 6 = 5,400 + 18 = 5,418. ✓
Watch out. Write a 0 above every digit that has nothing to give.
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 ÷ 4 = 250 (3 digits)
4,000 ÷ 4 = 1,000 (4 digits) - Look for one that does not work. One example that breaks the rule is called a counter-example.4,000 ÷ 4 = 1,000 has 4 digits.
- Explain why. A reason shows what is happening for every number, not just the ones we tried.1,000 to 3,999 divided by 4 give 250 to 999 (3 digits). From 4,000 upwards the answer has 4 digits. It depends on the number.
- Decide. Sometimes
Check. We found one example each way. ✓
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.12 ÷ 4 = 3 and 12 ÷ 2 = 6
36 ÷ 4 = 9 and 36 ÷ 2 = 18
1,000 ÷ 4 = 250 and 1,000 ÷ 2 = 500 - Explain why. A reason shows what is happening for every number, not just the ones we tried.Dividing by 4 means dividing by 2 and then by 2 again. If a number divides by 4 exactly, the first division by 2 is already exact, so it also divides by 2.
- Decide. Always
Check. Every example worked. ✓
Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.
Key words. To estimate is to find an answer that is close, but not exact. To round a number is to change it to a nearby number that is easier to use. The inverse of dividing is multiplying, and we can use it to check an answer.
Method. To show that a division is right, use the opposite operation: multiply the answer by the number you divided by.
- Write what we have to show. We need to check the division is right.3,150 ÷ 6 = 525
- Multiply the answer by the divisor. If the division is right, this must give the number we started with.525 × 6 = 500 × 6 + 20 × 6 + 5 × 6 = 3,000 + 120 + 30 = 3,150
- Compare and write a conclusion. Say what the working shows.525 × 6 = 3,150, so 3,150 ÷ 6 = 525. It is shown.
Check. Use short division: 3,150 ÷ 6 = 525. ✓
Watch out. Write a sentence at the end. The working alone is not a conclusion.
Key words. Short division (the bus stop method): the number you divide goes inside the bus stop and the divisor goes outside. A remainder is what is left over. To exchange is to swap 1 of a place value for 10 of the next smaller one.
Method. Try each card as the divisor. For each choice, make the biggest 3-digit number from the other three cards. Compare the answers.
- Choose the one-digit number. There are four cards, so there are four choices for the divisor. We try them all.2, 4, 6, 9
- Make the biggest 3-digit number each time. To get the biggest answer, put the biggest digit in the hundreds place, then the next biggest in the tens place.
Divisor 3-digit number Division Answer 2 964 964 ÷ 2 482 4 962 962 ÷ 4 240 r 2 6 942 942 ÷ 6 157 9 642 642 ÷ 9 71 r 3 - Pick the biggest answer. Compare the four answers.The biggest answer is 482, from 964 ÷ 2.
Check. 482 × 2 = 964, and 964 − 964 = 0. ✓
Watch out. The biggest answer comes from dividing by the smallest card. Try them all to be sure.