Year 5 Short Division and Remainders: check-up and SATs-style questions
Part of the Year 5 short division and remainders chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Exercise 5Z Check-up (non-calculator)
Non-calculatorKey words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.
Method. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.
- Say what dividing by 10 does. Each digit becomes 10 times smaller, so it moves 1 place to the right. The digits move. The decimal point does not.6 ones become 6 tenths
3 tenths become 3 hundredths - Move every digit 1 place to the right. Use a place-value chart and follow the arrows.
- Fill the empty places with zeros. The ones column is empty. A zero in it is a place holder: it keeps every digit in its right column.6.3 ÷ 10 = 0.63
- Write the answer. 6.3 ÷ 10 = 0.63
Check. Go back: 0.63 × 10 = 6.3 (the digits move 1 place to the left). ✓
Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.63, not .63.
Key words. A mental strategy is a way to work something out in your head by using facts you already know. A factor is a number that divides exactly into another number. To halve is to divide by 2. To double is to multiply by 2.
Method. Use a times table fact. Work out the fact with the zeros hidden, then put the right number of zeros back.
- Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.4,500 ÷ 90: the digits are 45 ÷ 9
45 ÷ 9 = 5 because 9 × 5 = 45 - Take 1 zero off both numbers. Dividing both numbers by 10 does not change the answer, and it makes the divisor a small number.4,500 ÷ 90 = 450 ÷ 9
- Use the fact on the leading digits. 450 is 45 tens. Share 45 tens into 9 equal groups.45 tens ÷ 9 = 5 tens
5 tens = 50 - Write the answer. 4,500 ÷ 90 = 50
Check. Multiply back: 50 × 90 = 4,500. ✓
Watch out. Count the zeros carefully: 4,500 has 2 zeros and 90 has 1 zero. Take the same number off both, then put back what is left.
Key words. A mental strategy is a way to work something out in your head by using facts you already know. A factor is a number that divides exactly into another number. To halve is to divide by 2. To double is to multiply by 2.
Method. To divide by 25, multiply the number by 4 (double, double) and then divide by 100. (There are four 25s in 100.)
- Double the number. We multiply by 4 by doubling twice. (4 × 25 = 100.)1,350 = 1,000 + 300 + 50
double each part: 2,000 + 600 + 100 = 2,700 - Double again. Two doubles make × 4.2,700 = 2,000 + 700
double each part: 4,000 + 1,400 = 5,400 - Divide by 100. Multiplying both numbers by 4 does not change the answer: n ÷ 25 is the same as 4n ÷ 100. Move the digits two places to the right.5,400 ÷ 100 = 54
- Write the answer. 1,350 ÷ 25 = 54
Check. Multiply back: 54 × 25 = 1,350. ✓
Watch out. Remember there are two doubles (× 4), then divide by 100, not 10.
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 2 4 3 6 - Divide the thousands. Always start on the left, with the biggest place value.2 ÷ 6: 2 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 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 ÷ 6: 4 × 6 = 24. Write 4 above the 4. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 3 tens.
3 ÷ 6: 3 is smaller than 6, so write 0.
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 6 ones there are 30 + 6 = 36 ones.
36 ÷ 6: 6 × 6 = 36. Write 6 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 4 0 6 6 2 24 3 36
2,436 ÷ 6 = 406 - Write the answer. 2,436 ÷ 6 = 406
Check. Multiply back: 406 × 6 = 400 × 6 + 6 × 6 = 2,400 + 36 = 2,436. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 406 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 7 2 6 3 - 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 2 hundreds there are 70 + 2 = 72 hundreds.
72 ÷ 9: 8 × 9 = 72. Write 8 above the 2. - Divide the tens. Move to the next digit on the right.Nothing was carried, so there are just 6 tens.
6 ÷ 9: 6 is smaller than 9, so write 0.
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 3 ones there are 60 + 3 = 63 ones.
63 ÷ 9: 7 × 9 = 63. Write 7 above the 3.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 8 0 7 9 7 72 6 63
7,263 ÷ 9 = 807 - Write the answer. 7,263 ÷ 9 = 807
Check. Multiply back: 807 × 9 = 800 × 9 + 7 × 9 = 7,200 + 63 = 7,263. ✓
Watch out. A 0 in the answer is a place holder. Leave it out and 807 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 9 4 7 - 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 9 hundreds there are 50 + 9 = 59 hundreds.
59 ÷ 6: 9 × 6 = 54, and 59 − 54 = 5. Write 9 above the 9.
Exchange: 5 hundreds become 50 tens. Carry 5 to the next digit. - Divide the tens. Move to the next digit on the right. Add the 5 that was carried.The carried 5 makes 50 tens. With the 4 tens there are 50 + 4 = 54 tens.
54 ÷ 6: 9 × 6 = 54. Write 9 above the 4. - Divide the ones. Move to the next digit on the right.Nothing was carried, so there are just 7 ones.
7 ÷ 6: 1 × 6 = 6, and 7 − 6 = 1. Write 1 above the 7.
The remainder is 1. - Read the answer. Ignore any 0 at the front of the answer.
0 9 9 1 r 1 6 5 59 54 7
5,947 ÷ 6 = 991 r 1 - Write the answer. 5,947 ÷ 6 = 991 r 1
Check. Multiply back: 991 × 6 = 900 × 6 + 90 × 6 + 1 × 6 = 5,400 + 540 + 6 = 5,946
5,946 + 1 (the remainder) = 5,947. ✓
Watch out. The first digit is smaller than 6: write 0 and carry it. The remainder is always smaller than 6.
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 5,918. They tell us how many hundreds there are, roughly.5,918 is about 59 hundreds
- Find the nearest number in the 7 times table. We want a number that 7 divides into exactly.7 × 8 = 56, and 56 is the closest to 59
- Round the number. Replace 59 hundreds by 56 hundreds.5,918 ≈ 5,600
- Divide the rounded number. Use the fact 56 ÷ 7 = 8.56 hundreds ÷ 7 = 8 hundreds
5,600 ÷ 7 = 800 - Write the estimate. Use the sign ≈ for “is about”.5,918 ÷ 7 ≈ 800
Check. Multiply back: 800 × 7 = 5,600, which is close to 5,918. ✓
Watch out. An estimate is not the exact answer. Use it to check that your exact answer is about the right size.
Key words. The remainder is what is left over after you divide. The quotient is the answer to a division. Whether you round the answer up, round it down or use the remainder depends on the question.
Method. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.
- Draw a bar model. We split 95 into groups of 4. Some may be left over.
- Choose the operation. We want to know how many groups of 4 fit into 95, so divide.95 ÷ 4
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
4 9 5 - Divide the tens. Always start on the left, with the biggest place value.9 ÷ 4 = 2, remainder 1
Write 2 above the 9.
Exchange the remainder: 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 5 ones there are 10 + 5 = 15 ones.
15 ÷ 4: 3 × 4 = 12, and 15 − 12 = 3. Write 3 above the 5.
The remainder is 3. - Read the answer. Read the digits above the line from left to right.
2 3 r 3 4 9 15
95 ÷ 4 = 23 r 3 - Say what the remainder means. 95 ÷ 4 = 23 remainder 3: that is 23 full boxes and 3 muffins left over.23 full boxes + 3 left over
- Decide what to do with the remainder. Only full boxes count. The 3 left over cannot make another one. We round the answer down (we ignore the remainder).23 full boxes
- Write the answer. Include the unit.23 boxes
Check. 23 × 4 = 92 and 92 + 3 = 95. ✓
Watch out. Do not round up here: the extra box would not be full.
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. To find a rate, divide the total amount by the number of hours.
- Choose the operation. “A coach travels 252 km in 4 hours at a steady speed” asks for the amount for one hour. The word “per” means “for each”, so divide the total by the number of hours.252 km ÷ 4 hours
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
4 2 5 2 - Divide the hundreds. 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 hundred. Write 0 (a 0 at the front is not part of the answer).
Exchange the 2 hundreds for 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 5 tens there are 20 + 5 = 25 tens.
25 ÷ 4: 6 × 4 = 24, and 25 − 24 = 1. Write 6 above the 5.
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 2 ones there are 10 + 2 = 12 ones.
12 ÷ 4: 3 × 4 = 12. Write 3 above the 2.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 6 3 4 2 25 12
252 ÷ 4 = 63 - Write the answer. Include the unit.63 km per hour
Check. 63 × 4 = 252. ✓
Watch out. Check that you divided the total by the number of units, not the other way round.
Key words. The order of operations says which part of a calculation to do first: brackets first, then × and ÷ (left to right), then + and − (left to right).
Method. Use the order of operations: brackets first, then × and ÷, then + and −. Do one step at a time.
- Do the division. × and ÷ come before + and −. If there are several, go from left to right.6 + 48 ÷ 8 × 3 = 6 + 6 × 3
- Do the multiplication. × and ÷ come before + and −. If there are several, go from left to right.6 + 6 × 3 = 6 + 18
- Add. Only + and − are left. Go from left to right.6 + 18 = 24
- Write the answer. 6 + 48 ÷ 8 × 3 = 24
Check. Work through the steps again, and check the order: brackets, then × and ÷, then + and −.
Watch out. Do not just work from left to right. Brackets first, then × and ÷, then + and −.
Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. A missing number is the number that makes both sides balance.
Method. The equals sign means both sides have the same value. Work out the side you can, then find the number that makes the other side match.
- Work out the side with no missing number. The two sides of an equals sign must have the same value, so first find the value of the side we can work out.72 ÷ 8 = 9
- Look at the other side. It must also be worth 9. Picture a balance.
- Use the opposite operation. 3 times the missing number is 9. Undo the multiplication with a division.9 ÷ 3 = 3
- Write the missing number. Put it back in the box and read the whole sentence.3
Check. 3 × 3 = 9 and 72 ÷ 8 = 9. Both sides are equal. ✓
Watch out. The equals sign does not mean “the answer comes next”. It means both sides balance.
Total 20 marks. Allow about 20 minutes.
Exercise 5X SATs-style questions
Non-calculatorKey words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.
Method. First work out 4.5 ÷ 10. Then find the option with the same value.
- Work out the calculation in the question. We need its value to compare with the options.4.5 ÷ 10 = 0.45
- Work out every option. Do not stop at the first one that looks right. Use place value or a known fact.
Option Calculation Value Equal to 0.45? A 45 ÷ 100 0.45 yes B 4.5 ÷ 100 0.045 no C 450 ÷ 10 45 no D 0.45 ÷ 10 0.045 no - Choose the option that matches. Only one option has the right value.A (45 ÷ 100)
Check. Check the chosen option again: it has the value 0.45. ✓
Watch out. Work out all four options. Two of them might look similar.
Key words. Place value tells you what each digit is worth. A place holder is a zero that keeps the other digits in the right columns. Dividing by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times smaller.
Method. Find out how far the digits move. One place to the right is ÷ 10, two places is ÷ 100 and three places is ÷ 1,000.
- Compare the two numbers. Look at how the digits have moved from the start number to the answer.7.2 → 0.072
- Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
- Say what the number is. Digits that move 2 places to the right mean ÷ 100.7.2 ÷ 100 = 0.072
Check. 7.2 ÷ 100 = 0.072. ✓
Watch out. Put your answer back in the box and read the whole sentence. It must be true.
Key words. A mental strategy is a way to work something out in your head by using facts you already know. A factor is a number that divides exactly into another number. To halve is to divide by 2. To double is to multiply by 2.
Method. Use a times table fact. Work out the fact with the zeros hidden, then put the right number of zeros back.
- Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.5,600 ÷ 70: the digits are 56 ÷ 7
56 ÷ 7 = 8 because 7 × 8 = 56 - Take 1 zero off both numbers. Dividing both numbers by 10 does not change the answer, and it makes the divisor a small number.5,600 ÷ 70 = 560 ÷ 7
- Use the fact on the leading digits. 560 is 56 tens. Share 56 tens into 7 equal groups.56 tens ÷ 7 = 8 tens
8 tens = 80 - Write the answer. 5,600 ÷ 70 = 80
Check. Multiply back: 80 × 70 = 5,600. ✓
Watch out. Count the zeros carefully: 5,600 has 2 zeros and 70 has 1 zero. Take the same number off both, then put back what is left.
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 4 3 5 2 - Divide the thousands. Always start on the left, with the biggest place value.4 ÷ 8: 4 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 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 3 hundreds there are 40 + 3 = 43 hundreds.
43 ÷ 8: 5 × 8 = 40, and 43 − 40 = 3. Write 5 above the 3.
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 ÷ 8: 4 × 8 = 32, and 35 − 32 = 3. Write 4 above the 5.
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 2 ones there are 30 + 2 = 32 ones.
32 ÷ 8: 4 × 8 = 32. Write 4 above the 2.
Nothing is left over, so there is no remainder. - Read the answer. Ignore any 0 at the front of the answer.
0 5 4 4 8 4 43 35 32
4,352 ÷ 8 = 544 - Write the answer. 4,352 ÷ 8 = 544
Check. Multiply back: 544 × 8 = 500 × 8 + 40 × 8 + 4 × 8 = 4,000 + 320 + 32 = 4,352. ✓
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. The remainder is what is left over after you divide. The quotient is the answer to a division. Whether you round the answer up, round it down or use the remainder depends on the question.
Method. Divide, then think about what the remainder means in the story. The answer might be rounded up, rounded down, or be the remainder itself.
- Draw a bar model. We split 130 into groups of 9. Some may be left over.
- Choose the operation. We want to know how many groups of 9 fit into 130, so divide.130 ÷ 9
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
9 1 3 0 - Divide the hundreds. Always start on the left, with the biggest place value.1 ÷ 9: 1 is smaller than 9, so we cannot give each share a whole hundred. Write 0 (a 0 at the front is not part of the answer).
Exchange the 1 hundred for 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 ÷ 9: 1 × 9 = 9, and 13 − 9 = 4. Write 1 above the 3.
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 0 ones there are 40 + 0 = 40 ones.
40 ÷ 9: 4 × 9 = 36, and 40 − 36 = 4. Write 4 above the 0.
The remainder is 4. - Read the answer. Ignore any 0 at the front of the answer.
0 1 4 r 4 9 1 13 40
130 ÷ 9 = 14 r 4 - Say what the remainder means. 130 ÷ 9 = 14 remainder 4: that is 14 full minibuses and 4 children left over.14 full minibuses + 4 left over
- Decide what to do with the remainder. The 4 left over still need somewhere to go, so one more minibus is needed. We round the answer up.14 + 1 = 15
- Write the answer. Include the unit.15 minibuses
Check. 14 × 9 = 126 and 126 + 4 = 130. ✓
Watch out. Do not round down here. The 4 left over would have no minibus.
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.5,432 ÷ 8 = 679
- Multiply the answer by the divisor. If the division is right, this must give the number we started with.679 × 8 = 600 × 8 + 70 × 8 + 9 × 8 = 4,800 + 560 + 72 = 5,432
- Compare and write a conclusion. Say what the working shows.679 × 8 = 5,432, so 5,432 ÷ 8 = 679. It is shown.
Check. Use short division: 5,432 ÷ 8 = 679. ✓
Watch out. Write a sentence at the end. The working alone is not a conclusion.
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. Use a table. Divide both amounts by the same number and the rate stays the same.
- Put the facts in a table. 12 pens go with £9. We want to know about 4 pens.
÷ 3 → Pens 12 4 Cost £9 ? ÷ 3 → - Find the scale factor. Look at the top row. What do we divide 12 by to get 4?12 ÷ 3 = 4, so divide by 3
- Divide the bottom row by 3 as well. The rate stays the same only if both rows are divided by the same number.£9 ÷ 3
- Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.
3 9 - Divide the ones. Always start on the left, with the biggest place value.9 ÷ 3 = 3
Write 3 above the 9.
Nothing is left over, so there is no remainder. - Read the answer. Read the digits above the line from left to right.
3 3 9
9 ÷ 3 = 3 - Write the answer. £3
Check. £3 × 3 = £9. ✓
Watch out. Divide the top and the bottom by the SAME number.
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. 7 sheets of 54 stickers. Then the total is shared between 9 friends.
- Find the number of stickers. 7 sheets with 54 stickers on each, so multiply.7 × 54 = 378
- Share the stickers. The stickers are shared equally between 9 friends, so divide by 9.378 ÷ 9 = 42
- Write the answer. Include the unit.42 stickers
Check. 42 × 9 = 378. ✓
Watch out. Marks: 1 for 7 × 54 = 378, 1 for 378 ÷ 9, 1 for the correct answer.
Key words. The order of operations says which part of a calculation to do first: brackets first, then × and ÷ (left to right), then + and − (left to right).
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.Divide first: 18 ÷ 3 = 6. Then add: 6 + 6 = 12.
- Compare with the answer in the question. Leo wrote 8. He did 6 + 18 = 24 and then 24 ÷ 3 = 8.
- Find the mistake. Leo worked from left to right, but the division must be done before the addition.
- Write the correct answer. The correct answer is 12, so Leo is not correct.
Check. With brackets, (6 + 18) ÷ 3 = 8. Leo needed brackets for his answer.
Watch out. Without brackets, ÷ comes before +.
Key words. Multiplying and dividing are inverse (opposite) operations: one undoes the other. A fact family is a set of multiplication and division facts that use the same three numbers.
Method. Work backwards. Undo each step in the opposite order, using the opposite (inverse) operation.
- Write the steps in order. List what was done to the secret number.1. divide by 5
2. add 14
The answer was 30. - Work backwards with the opposite operations. Start at the end and undo each step in reverse order.take away 14: 30 − 14 = 16
multiply by 5: 16 × 5 = 80 - Write the number. The number was 80.
Check. 80 ÷ 5 = 16
16 + 14 = 30
We end at 30. ✓
Watch out. Undo the LAST step first.