Year 4 Short Multiplication and Short Division: check-up and SATs-style questions

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To multiply by 10, move every digit 1 place to the left and put a zero in the empty place on the right. Do not just “add a zero”: it is the digits that move.

1. Say what each digit is worth. The digits have different values because of their columns.
   4 tens
   7 ones
2. Make every digit 10 times bigger. Multiplying by 10 makes each digit 10 times bigger. That moves it 1 place to the left.
   4 tens become 4 hundreds
   7 ones become 7 tens
3. Show it in a place-value table. The 1 gap on the right is empty, so we put a zero there.

   	Th	H	T	O
   47			4	7
   × 10	← 1 place left
   470		4	7	0

4. Write the answer. The zero place holders keep every digit in the right column.
   47 × 10 = 470

Check. Divide back: 470 ÷ 10 = 47. ✓

Watch out. Move the digits, then fill the empty place with a zero. Check the answer is 10 times bigger.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. To divide by 100, move every digit 2 places to the right. A number that ends in 2 zeros will divide exactly.

1. Look at the end of the number. Are there at least 2 zeros? Every digit moves 2 places to the right, so the ones column must be able to hold the moved digits. A number that ends in 2 zeros divides exactly.
   3,200 ends in 2 zeros. ✓
2. Make every digit 100 times smaller. Dividing by 100 makes each digit 100 times smaller. That moves it 2 places to the right.
   3 thousands become 3 tens
   2 hundreds become 2 ones
3. Show it in a place-value table. The last 2 zeros fall off the end.

   	Th	H	T	O
   3,200	3	2	0	0
   ÷ 100	→ 2 places right
   32			3	2

4. Write the answer.
   3,200 ÷ 100 = 32

Check. Multiply back: 32 × 100 = 3,200. ✓

Watch out. Move the digits 2 places to the right. Check the answer is 100 times smaller.

Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.

Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.

1. Partition the number into tens and ones. Tens and ones are easy to multiply.
   38 = 30 + 8
2. Write it as two multiplications. This is the distributive law: multiplying a sum by 6 is the same as multiplying each part by 6 and adding.
   38 × 6 = (30 + 8) × 6 = (30 × 6) + (8 × 6)
3. Multiply the tens part. 3 × 6 = 18, so 3 tens × 6 = 18 tens.
   30 × 6 = 180
4. Multiply the ones part. Use a times table fact.
   8 × 6 = 48
5. Add the two answers.
   180 + 48 = 228

Check. Estimate: 38 is about 40 (to the nearest 10). 40 × 6 = 240. Our answer, 228, is a bit less than 240, which is right because we rounded up. ✓

Watch out. Both parts must be multiplied by 6. A common mistake is to multiply only the tens, or only the ones.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		4	3	6
   ×				5

2. Multiply the ones. Always start with the ones, on the right.
   6 × 5 = 30
   30 is 3 tens and 0 ones. Write 0 in the ones column and carry 3 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 3 we carried.
   3 × 5 = 15, and 15 + 3 (carried) = 18
   18 is 1 hundred and 8 tens. Write 8 in the tens column and carry 1 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   4 × 5 = 20, and 20 + 1 (carried) = 21
   21 is 2 thousands and 1 hundred. Write 1 in the hundreds column and carry 2 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		4	3	6
   ×				5
   	2	1	8	0
   	2	1	3

   
   436 × 5 = 2,180

Check. Estimate: 436 is about 400 (to the nearest 100). 400 × 5 = 2,000. Our answer, 2,180, is a bit more than 2,000, which is right because we rounded down. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short division (the bus stop method) is a written way to divide. The number you divide goes inside the bus stop and the number you divide by goes outside. A remainder is what is left over when a number does not divide exactly.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, carry it to the next digit as extra ones, tens or hundreds.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   6	1	5	6

2. Divide the hundreds. Always start on the left, with the biggest place value.
   1 ÷ 6: 1 is smaller than 6, so we cannot make a whole hundred for each share. Write 0 (this leading 0 is not part of the answer).
   Exchange the 1 hundred for 10 tens and carry them to the next digit.
3. 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 5 tens there are 10 + 5 = 15 tens.
   15 ÷ 6: 2 × 6 = 12, and 15 − 12 = 3. Write 2 above the 5.
   Carry the remainder 3 to the next digit.
4. 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.
5. Read the answer. Ignore any 0 at the front of the answer.

   	0	2	6
   6	1	15	36

   
   156 ÷ 6 = 26

Check. Multiply back: 26 × 6 = 20 × 6 + 6 × 6 = 120 + 36 = 156. ✓

Watch out. If the first digit is smaller than 6, 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) is a written way to divide. The number you divide goes inside the bus stop and the number you divide by goes outside. A remainder is what is left over when a number does not divide exactly.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, carry it to the next digit as extra ones, tens or hundreds.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   4	8	7

2. Divide the tens. Always start on the left, with the biggest place value.
   8 ÷ 4 = 2
   Write 2 above the 8.
3. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 7 ones.
   7 ÷ 4: 1 × 4 = 4, and 7 − 4 = 3. Write 1 above the 7.
   The remainder is 3.
4. Read the answer. Read the digits above the line from left to right.

   	2	1	r 3
   4	8	7

   
   87 ÷ 4 = 21 remainder 3

Check. Multiply back: 21 × 4 = 20 × 4 + 1 × 4 = 80 + 4 = 84
84 + 3 (the remainder) = 87. ✓

Watch out. The remainder must always be smaller than the number you divide by (4). If it is not, you can divide again.

Key words. A remainder is what is left over after you divide. What you do with it depends on the story: ignore it, round up, or say how many are left over.

Method. Divide to find how many groups of the number fit. Then think about what the remainder means in the story.

1. Choose the operation. We are putting 75 into equal groups of 8, so we divide.
   75 ÷ 8
2. Work it out with the bus stop. Divide one digit at a time and keep the remainder.
   75 ÷ 8 = 9 remainder 3
   

   	0	9	r 3
   8	7	75

3. Decide what the remainder means. Every one must be in a group. The remainder still needs a group of its own, so we need one more group. We round UP.
   9 boxes are full. The last 3 eggs need another one: 9 + 1 = 10
4. Write the answer. Answer the question that was asked.
   10 boxes.

Check. Multiply back: 9 × 8 = 72, and 72 + 3 = 75. ✓

Watch out. Do not forget the leftovers. They still need somewhere to go, so we round up, not down.

Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.

Method. 7 times as many means 7 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 7.

1. Draw a bar model. Jo has one box. Kim has 7 boxes the same size.
2. Choose the operation. 7 equal boxes: multiply the size of one box by 7.
   12 × 7
3. Work it out. Use a written method if you need to.
   12 × 7 = 84
4. Write the answer. Include the unit.
   84 stickers

Check. Divide back: 84 ÷ 7 = 12. ✓

Watch out. “7 times as many” is multiplying by 7. It is not adding 7.

Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.

Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.

1. Take just one shirt. Pick the first shirt. It can go with any of the 6 pairs of trousers, so that makes 6 outfits.
   1 shirt → 6 outfits
2. Do the same for every shirt. All the shirts have the same choices. There are 4 shirts, so there are 4 groups of 6 outfits.
   6 + 6 + 6 + 6 = 24
3. Show every choice in a table. Each box is one outfit: one shirt with one pair of trousers. Count the boxes: it is an array.

   shirt \ pair of trousers	pair of trousers 1	pair of trousers 2	pair of trousers 3	pair of trousers 4	pair of trousers 5	pair of trousers 6
   shirt 1	1	2	3	4	5	6
   shirt 2	7	8	9	10	11	12
   shirt 3	13	14	15	16	17	18
   shirt 4	19	20	21	22	23	24

4. Multiply. 4 rows of 6 is a multiplication.
   4 × 6 = 24
5. Write the answer. Say what the number means.
   24 different outfits

Check. Swap the numbers: 6 × 4 = 24. ✓

Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every shirt goes with every pair of trousers, so multiply.

Key words. You can multiply three numbers in any order and the answer is the same.

Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.

1. Look for a pair that is easy to multiply. 5 × 2 = 10, and multiplying by 10 is easy.
   5 × 2 = 10
2. Multiply by the last number, 14. Multiplying by 10 moves every digit 1 place to the left.
   10 × 14: move the digits of 14 1 place to the left.
   10 × 14 = 140
3. Write the answer.
   5 × 14 × 2 = 140

Check. Try a different order: 28 × 5 = 140. ✓

Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.

Key words. A digit is one of the symbols 0 to 9. A place holder is a zero that keeps the other digits in the right columns. Place value tells you what each digit is worth.

Method. Find out how far the digits move. One place to the right is ÷ 10. Two places to the right is ÷ 100.

1. Compare the two numbers. 4,500 is divided by the missing number to make 45.
   4,500 → 45
2. Count how many places the digits moved. Each digit of 4,500 moved to the right.

   	Th	H	T	O
   4,500	4	5	0	0
   ÷ 100	→ 2 places right
   45			4	5

3. Say what the number is. Digits that move 2 places to the right mean ÷ 100.
   4,500 ÷ 100 = 45

Check. 45 × 100 = 4,500. ✓

Watch out. Put your answer back in the box and read the whole sentence. It must be true.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	H	T	O
   		3	8
   ×			7

2. Multiply the ones. Always start with the ones, on the right.
   8 × 7 = 56
   56 is 5 tens and 6 ones. Write 6 in the ones column and carry 5 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 5 we carried.
   3 × 7 = 21, and 21 + 5 (carried) = 26
   26 is 2 hundreds and 6 tens. Write 6 in the tens column and carry 2 to the hundreds column.
4. Write the carried digit. There are no digits left to multiply in the hundreds column, but we carried 2 into it.
   Nothing to multiply. Write 2 in the hundreds column.
5. Read the answer. Check that the answer has about the right number of digits, then write it.

   	H	T	O
   		3	8
   ×			7
   	2	6	6
   	2	5

   
   38 × 7 = 266

Check. Estimate: 38 is about 40 (to the nearest 10). 40 × 7 = 280. Our answer, 266, is a bit less than 280, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short multiplication is a written method. You write the number to multiply on top, the one-digit number below it, and multiply one column at a time, starting with the ones. When a column makes 10 or more, you carry the tens digit to the next column and add it there.

Method. Write the numbers in columns. Multiply each digit by the one-digit number, starting with the ones. If an answer is 10 or more, write the ones digit and carry the tens digit to the next column.

1. Write the numbers in columns. Ones go under ones, tens under tens and hundreds under hundreds. The one-digit number goes under the ones.

   	Th	H	T	O
   		3	6	5
   ×				3

2. Multiply the ones. Always start with the ones, on the right.
   5 × 3 = 15
   15 is 1 ten and 5 ones. Write 5 in the ones column and carry 1 to the tens column.
3. Multiply the tens. Now the next column to the left. Multiply, then add the 1 we carried.
   6 × 3 = 18, and 18 + 1 (carried) = 19
   19 is 1 hundred and 9 tens. Write 9 in the tens column and carry 1 to the hundreds column.
4. Multiply the hundreds. Now the next column to the left. Multiply, then add the 1 we carried.
   3 × 3 = 9, and 9 + 1 (carried) = 10
   10 is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column.
5. Write the carried digit. There are no digits left to multiply in the thousands column, but we carried 1 into it.
   Nothing to multiply. Write 1 in the thousands column.
6. Read the answer. Check that the answer has about the right number of digits, then write it.

   	Th	H	T	O
   		3	6	5
   ×				3
   	1	0	9	5
   	1	1	1

   
   365 × 3 = 1,095

Check. Estimate: 365 is about 400 (to the nearest 100). 400 × 3 = 1,200. Our answer, 1,095, is a bit less than 1,200, which is right because we rounded up. ✓

Watch out. Do not forget the carried digits. Write each one small, then add it in the next column AFTER you have multiplied.

Key words. Short division (the bus stop method) is a written way to divide. The number you divide goes inside the bus stop and the number you divide by goes outside. A remainder is what is left over when a number does not divide exactly.

Method. Draw the bus stop. Divide one digit at a time, starting on the left. If there is a remainder, carry it to the next digit as extra ones, tens or hundreds.

1. Draw the bus stop. The number we are dividing goes inside. The number we divide by goes outside, on the left.

   7	9	5	2

2. Divide the hundreds. Always start on the left, with the biggest place value.
   9 ÷ 7 = 1, remainder 2
   Write 1 above the 9.
   Exchange the remainder: 2 hundreds become 20 tens. Carry 2 to the next digit.
3. 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 ÷ 7: 3 × 7 = 21, and 25 − 21 = 4. Write 3 above the 5.
   Carry the remainder 4 to the next digit.
4. 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 2 ones there are 40 + 2 = 42 ones.
   42 ÷ 7: 6 × 7 = 42. Write 6 above the 2.
   Nothing is left over, so there is no remainder.
5. Read the answer. Read the digits above the line from left to right.

   	1	3	6
   7	9	25	42

   
   952 ÷ 7 = 136

Check. Multiply back: 136 × 7 = 100 × 7 + 30 × 7 + 6 × 7 = 700 + 210 + 42 = 952. ✓

Watch out. Start on the left, with the biggest place value. Carry any remainder to the next digit.

Method. Work out each multiplication. Then tick the two that make 240.

1. Work out each one. Use place value: multiply the digits, then put the zeros back.
   A: 6 × 40 = 240
   B: 8 × 30 = 240
   C: 4 × 50 = 200
   D: 5 × 45 = 225
2. Choose the two that make 240.
   A and B

Check. 240 ÷ 6 = 40 and 240 ÷ 8 = 30. ✓

Watch out. 2 marks: 1 mark for each correct box. If you tick three boxes you lose the marks.

Key words. A remainder is what is left over after you divide. What you do with it depends on the story: ignore it, round up, or say how many are left over.

Method. Divide to find how many groups of the number fit. Then think about what the remainder means in the story.

1. Choose the operation. We are putting 100 into equal groups of 9, so we divide.
   100 ÷ 9
2. Work it out with the bus stop. Divide one digit at a time and keep the remainder.
   100 ÷ 9 = 11 remainder 1
   

   	0	1	1	r 1
   9	1	10	10

3. Decide what the remainder means. Every one must be in a group. The remainder still needs a group of its own, so we need one more group. We round UP.
   11 minibuses are full. The last 1 pupils need another one: 11 + 1 = 12
4. Write the answer. Answer the question that was asked.
   12 minibuses.

Check. Multiply back: 11 × 9 = 99, and 99 + 1 = 100. ✓

Watch out. Do not forget the leftovers. They still need somewhere to go, so we round up, not down.

Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.

Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.

1. Find how many choices there are for the first two. Each of the 5 tops can go with each of the 4 pairs of trousers.
   5 × 4 = 20
2. Now bring in the hats. Each of those 20 choices can go with each of the 2 hats.
   20 × 2 = 40
3. Write the answer. Say what the number means.
   40 different outfits

Check. Multiply in a different order: 4 × 2 = 8, then 8 × 5 = 40. ✓

Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every top goes with every pair of trousers, so multiply.

Method. Read the problem, draw a bar model, then decide which operations to use. Work out one step at a time.

1. Draw a bar model. A bar model shows what we know and what we need to find out.
2. Step 1: Find the height of Ben’s tower. Ben’s tower is 6 times as tall as Tia’s, so multiply.
   18 × 6 = 108
   

   	H	T	O
   		1	8
   ×			6
   	1	0	8
   	1	4

3. Step 2: Find how much taller it is. Subtract Tia’s height.
   108 − 18 = 90
   

   	H	T	O
   	01	100	8
   −		1	8
   		9	0

4. Write the answer. Include the unit and make sure it answers the question.
   90 cm taller

Check. Another way: the difference is 5 more towers the size of Tia’s tower. 5 × 18 = 90. ✓

Watch out. 2 marks: 1 mark for 18 × 6 = 108 and 1 mark for 108 − 18 = 90.

Method. Read the problem, draw a bar model, then decide which operations to use. Work out one step at a time.

1. Draw a bar model. A bar model shows what we know and what we need to find out.
2. Step 1: Find how many pencils there are. 8 packs with 36 pencils in each, so multiply.
   36 × 8 = 288
   

   	H	T	O
   		3	6
   ×			8
   	2	8	8
   	2	4

3. Step 2: Share the pencils between the classes. 288 pencils are shared equally between 6 classes, so divide.
   288 ÷ 6 = 48
   

   	0	4	8
   6	2	28	48

4. Write the answer. Include the unit and make sure it answers the question.
   48 pencils for each class

Check. Multiply back: 48 × 6 = 288, and 36 × 8 = 288. ✓

Watch out. 3 marks: 1 mark for 36 × 8 = 288, 1 mark for dividing 288 by 6, and 1 mark for the answer 48.

Method. Read the problem, draw a bar model, then decide which operations to use. Work out one step at a time.

1. Draw a bar model. Bea has one box. Amir has three boxes the same size.
2. Step 1: Find how many equal boxes there are altogether. Bea has 1 box and Amir has 3 boxes the same size.
   1 + 3 = 4
3. Step 2: Find the size of one box. The 4 boxes make 84 cards, so divide.
   84 ÷ 4 = 21
   

   	2	1
   4	8	4

4. Step 3: Find how many cards Amir has. Amir has 3 boxes.
   21 × 3 = 63
   

   	T	O
   	2	1
   ×		3
   	6	3

5. Write the answer. Include the unit and make sure it answers the question.
   63 cards

Check. 21 + 63 = 84. ✓

Watch out. 3 marks: 1 mark for 1 + 3 = 4 boxes, 1 mark for 84 ÷ 4 = 21, and 1 mark for 21 × 3 = 63.