Year 5 Short Division and Remainders: worked examples and questions with answers

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   7 tens become 7 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   70 ÷ 10 = 7
3. Write the answer.
   70 ÷ 10 = 7

Check. Go back: 7 × 10 = 70 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 70 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   2 hundreds become 2 tens
   5 tens become 5 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   250 ÷ 10 = 25
3. Write the answer.
   250 ÷ 10 = 25

Check. Go back: 25 × 10 = 250 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 250 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   1 thousand becomes 1 hundred
   3 hundreds become 3 tens
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   1,300 ÷ 10 = 130
3. Write the answer.
   1,300 ÷ 10 = 130

Check. Go back: 130 × 10 = 1,300 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 1,300 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   8 thousands become 8 hundreds
   6 tens become 6 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   8,060 ÷ 10 = 806
3. Write the answer.
   8,060 ÷ 10 = 806

Check. Go back: 806 × 10 = 8,060 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 8,060 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   8 hundreds become 8 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   800 ÷ 100 = 8
3. Write the answer.
   800 ÷ 100 = 8

Check. Go back: 8 × 100 = 800 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 800 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   4 thousands become 4 tens
   5 hundreds become 5 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   4,500 ÷ 100 = 45
3. Write the answer.
   4,500 ÷ 100 = 45

Check. Go back: 45 × 100 = 4,500 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 4,500 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   3 ten thousands become 3 hundreds
   6 thousands become 6 tens
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   36,000 ÷ 100 = 360
3. Write the answer.
   36,000 ÷ 100 = 360

Check. Go back: 360 × 100 = 36,000 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 36,000 ends in 3 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   7 thousands become 7 tens
   3 hundreds become 3 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   7,300 ÷ 100 = 73
3. Write the answer.
   7,300 ÷ 100 = 73

Check. Go back: 73 × 100 = 7,300 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 7,300 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   9 thousands become 9 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   9,000 ÷ 1,000 = 9
3. Write the answer.
   9,000 ÷ 1,000 = 9

Check. Go back: 9 × 1,000 = 9,000 (the digits move 3 places to the left). ✓

Watch out. Taking off zeros works here because 9,000 ends in 3 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   4 ten thousands become 4 tens
   2 thousands become 2 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   42,000 ÷ 1,000 = 42
3. Write the answer.
   42,000 ÷ 1,000 = 42

Check. Go back: 42 × 1,000 = 42,000 (the digits move 3 places to the left). ✓

Watch out. Taking off zeros works here because 42,000 ends in 3 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   6 thousands become 6 ones
   5 hundreds become 5 tenths
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   6,500 ÷ 1,000 = 6.5
3. Write the answer.
   6,500 ÷ 1,000 = 6.5

Check. Go back: 6.5 × 1,000 = 6,500 (the digits move 3 places to the left). ✓

Watch out. The answer has a decimal point because 6,500 does not end in enough zeros. The point goes between the ones and the tenths.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   7 hundreds become 7 tenths
   8 tens become 8 hundredths
2. 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.
   780 ÷ 1,000 = 0.78
3. Write the answer.
   780 ÷ 1,000 = 0.78

Check. Go back: 0.78 × 1,000 = 780 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.78, not .78.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   5 hundreds become 5 tens
   4 tens become 4 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   540 ÷ 10 = 54
3. Write the answer.
   540 ÷ 10 = 54

Check. Go back: 54 × 10 = 540 (the digits move 1 place to the left). ✓

Watch out. Taking off zeros works here because 540 ends in 1 zero. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   5 hundreds become 5 ones
   4 tens become 4 tenths
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   540 ÷ 100 = 5.4
3. Write the answer.
   540 ÷ 100 = 5.4

Check. Go back: 5.4 × 100 = 540 (the digits move 2 places to the left). ✓

Watch out. The answer has a decimal point because 540 does not end in enough zeros. The point goes between the ones and the tenths.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   5 hundreds become 5 tenths
   4 tens become 4 hundredths
2. 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.
   540 ÷ 1,000 = 0.54
3. Write the answer.
   540 ÷ 1,000 = 0.54

Check. Go back: 0.54 × 1,000 = 540 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.54, not .54.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   7 ones become 7 tenths
2. 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.
   7 ÷ 10 = 0.7
3. Write the answer.
   7 ÷ 10 = 0.7

Check. Go back: 0.7 × 10 = 7 (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 0.7, not .7.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   2 thousands become 2 tens
   3 hundreds become 3 ones
2. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   2,300 ÷ 100 = 23
3. Write the answer.
   2,300 ÷ 100 = 23

Check. Go back: 23 × 100 = 2,300 (the digits move 2 places to the left). ✓

Watch out. Taking off zeros works here because 2,300 ends in 2 zeros. It does not work for every number: 47 ÷ 10 is 4.7, not 4.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   9 tens become 9 tenths
   1 one becomes 1 hundredth
2. 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.
   91 ÷ 100 = 0.91
3. Write the answer.
   91 ÷ 100 = 0.91

Check. Go back: 0.91 × 100 = 91 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.91, not .91.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   3 ones become 3 tenths
   6 tenths become 6 hundredths
2. Move every digit 1 place to the right. Use a place-value chart and follow the arrows.
3. 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.
   3.6 ÷ 10 = 0.36
4. Write the answer.
   3.6 ÷ 10 = 0.36

Check. Go back: 0.36 × 10 = 3.6 (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 0.36, not .36.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   7 tenths become 7 hundredths
2. Move every digit 1 place to the right. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.7 ÷ 10 = 0.07
4. Write the answer.
   0.7 ÷ 10 = 0.07

Check. Go back: 0.07 × 10 = 0.7 (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 0.07, not .07.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   1 ten becomes 1 one
   2 ones become 2 tenths
   4 tenths become 4 hundredths
2. Keep the decimal point between the ones and the tenths. The point stays still, so the digits that moved across it are now in the decimal columns.
   12.4 ÷ 10 = 1.24
3. Write the answer.
   12.4 ÷ 10 = 1.24

Check. Go back: 1.24 × 10 = 12.4 (the digits move 1 place to the left). ✓

Watch out. Dividing makes the number smaller. If your answer is bigger than 12.4, the digits moved the wrong way.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   5 hundredths become 5 thousandths
2. Fill the empty places with zeros. The ones and tenths and hundredths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.05 ÷ 10 = 0.005
3. Write the answer.
   0.05 ÷ 10 = 0.005

Check. Go back: 0.005 × 10 = 0.05 (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 0.005, not .005.

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. To divide by 10, move every digit 1 place to the right. The decimal point does not move. Fill empty places with zeros.

1. 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.
   8 ones become 8 tenths
   2 tenths become 2 hundredths
   5 hundredths become 5 thousandths
2. 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.
   8.25 ÷ 10 = 0.825
3. Write the answer.
   8.25 ÷ 10 = 0.825

Check. Go back: 0.825 × 10 = 8.25 (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 0.825, not .825.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   2 ones become 2 hundredths
   4 tenths become 4 thousandths
2. Move every digit 2 places to the right. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   2.4 ÷ 100 = 0.024
4. Write the answer.
   2.4 ÷ 100 = 0.024

Check. Go back: 0.024 × 100 = 2.4 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.024, not .024.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   3 tens become 3 tenths
   8 ones become 8 hundredths
2. 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.
   38 ÷ 100 = 0.38
3. Write the answer.
   38 ÷ 100 = 0.38

Check. Go back: 0.38 × 100 = 38 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.38, not .38.

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. To divide by 100, move every digit 2 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   7 ones become 7 hundredths
   5 hundredths become 5 ten-thousandths
2. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   7.05 ÷ 100 = 0.0705
3. Write the answer.
   7.05 ÷ 100 = 0.0705

Check. Go back: 0.0705 × 100 = 7.05 (the digits move 2 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.0705, not .0705.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   9 ones become 9 thousandths
2. Fill the empty places with zeros. The ones and tenths and hundredths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   9 ÷ 1,000 = 0.009
3. Write the answer.
   9 ÷ 1,000 = 0.009

Check. Go back: 0.009 × 1,000 = 9 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.009, not .009.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   3 hundreds become 3 tenths
   4 tens become 4 hundredths
   7 ones become 7 thousandths
   2 tenths become 2 ten-thousandths
2. 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.
   347.2 ÷ 1,000 = 0.3472
3. Write the answer.
   347.2 ÷ 1,000 = 0.3472

Check. Go back: 0.3472 × 1,000 = 347.2 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.3472, not .3472.

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. To divide by 1,000, move every digit 3 places to the right. The decimal point does not move. Fill empty places with zeros.

1. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   6 tens become 6 hundredths
   2 ones become 2 thousandths
2. Fill the empty places with zeros. The ones and tenths columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   62 ÷ 1,000 = 0.062
3. Write the answer.
   62 ÷ 1,000 = 0.062

Check. Go back: 0.062 × 1,000 = 62 (the digits move 3 places to the left). ✓

Watch out. Dividing makes a number smaller. Do not forget the zero in the ones column: write 0.062, not .062.

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.

1. Compare the two numbers. Look at how the digits have moved from the start number to the answer.
   4.5 → 0.045
2. Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
3. Say what the number is. Digits that move 2 places to the right mean ÷ 100.
   4.5 ÷ 100 = 0.045

Check. 4.5 ÷ 100 = 0.045. ✓

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

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. Multiplying and dividing undo each other. Multiply the answer by 10 (move the digits 1 place to the left) to find the missing number.

1. Use the opposite (inverse) operation. Multiplying undoes dividing. The missing number is 3.6 × 10.
   3.6 × 10
2. Move the digits 1 place to the left. Multiplying by 10 makes each digit 10 times bigger.
3. Write the missing number. Read the whole sentence back to check it.
   36 ÷ 10 = 3.6

Check. 36 ÷ 10 = 3.6. ✓

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

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.

1. Compare the two numbers. Look at how the digits have moved from the start number to the answer.
   70 → 0.07
2. Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
3. Say what the number is. Digits that move 3 places to the right mean ÷ 1,000.
   70 ÷ 1,000 = 0.07

Check. 70 ÷ 1,000 = 0.07. ✓

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

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. Multiplying and dividing undo each other. Multiply the answer by 100 (move the digits 2 places to the left) to find the missing number.

1. Use the opposite (inverse) operation. Multiplying undoes dividing. The missing number is 0.029 × 100.
   0.029 × 100
2. Move the digits 2 places to the left. Multiplying by 100 makes each digit 100 times bigger.
3. Write the missing number. Read the whole sentence back to check it.
   2.9 ÷ 100 = 0.029

Check. 2.9 ÷ 100 = 0.029. ✓

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

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.

1. Compare the two numbers. Look at how the digits have moved from the start number to the answer.
   63 → 6.3
2. Count how many places the digits moved. Each digit moved to the right, so the number got smaller.
3. Say what the number is. Digits that move 1 place to the right mean ÷ 10.
   63 ÷ 10 = 6.3

Check. 63 ÷ 10 = 6.3. ✓

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

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. Multiplying and dividing undo each other. Multiply the answer by 1,000 (move the digits 3 places to the left) to find the missing number.

1. Use the opposite (inverse) operation. Multiplying undoes dividing. The missing number is 0.804 × 1,000.
   0.804 × 1,000
2. Move the digits 3 places to the left. Multiplying by 1,000 makes each digit 1,000 times bigger.
3. Write the missing number. Read the whole sentence back to check it.
   804 ÷ 1,000 = 0.804

Check. 804 ÷ 1,000 = 0.804. ✓

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

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. Look at where each digit starts and where it ends. The number of places it moves tells you what you divided by.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 235.   Bottom: 2.35.
2. Look at the arrows. Every digit moves 2 places to the right. One place is ÷ 10, two places is ÷ 100, three places is ÷ 1,000.
   2 places to the right means ÷ 100.
3. Write the calculation.
   235 ÷ 100 = 2.35

Check. Move the digits of 235 2 places to the right: 2.35. ✓

Watch out. Arrows pointing right mean the number gets smaller, so it is a division.

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. Look at where each digit starts and where it ends. The number of places it moves tells you what you divided by.

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 18.   Bottom: 1.8.
2. Look at the arrows. Every digit moves 1 place to the right. One place is ÷ 10, two places is ÷ 100, three places is ÷ 1,000.
   1 place to the right means ÷ 10.
3. Write the calculation.
   18 ÷ 10 = 1.8

Check. Move the digits of 18 1 place to the right: 1.8. ✓

Watch out. Arrows pointing right mean the number gets smaller, so it is a division.

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. Changing m into km makes the number smaller (the new unit is bigger), so divide by 1,000.

1. Decide what to do. 1 km = 1,000 m, so there are 1,000 times as many m as km. Dividing makes the number smaller.
   3,500 m ÷ 1,000
2. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   3 thousands become 3 ones
   5 hundreds become 5 tenths
3. Move every digit 3 places to the right. Use a place-value chart and follow the arrows.
4. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   3,500 ÷ 1,000 = 3.5
5. Write the answer with its unit.
   3.5 km

Check. Go back: 3.5 × 1,000 = 3,500 (the digits move 3 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The km are the bigger unit.

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. Changing cm into m makes the number smaller (the new unit is bigger), so divide by 100.

1. Decide what to do. 1 m = 100 cm, so there are 100 times as many cm as m. Dividing makes the number smaller.
   450 cm ÷ 100
2. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   4 hundreds become 4 ones
   5 tens become 5 tenths
3. Move every digit 2 places to the right. Use a place-value chart and follow the arrows.
4. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   450 ÷ 100 = 4.5
5. Write the answer with its unit.
   4.5 m

Check. Go back: 4.5 × 100 = 450 (the digits move 2 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The m are the bigger unit.

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. Changing g into kg makes the number smaller (the new unit is bigger), so divide by 1,000.

1. Decide what to do. 1 kg = 1,000 g, so there are 1,000 times as many g as kg. Dividing makes the number smaller.
   2,750 g ÷ 1,000
2. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   2 thousands become 2 ones
   7 hundreds become 7 tenths
   5 tens become 5 hundredths
3. Move every digit 3 places to the right. Use a place-value chart and follow the arrows.
4. Look at the zeros at the end. Zeros at the very end of a decimal do not change its value, so we do not write them.
   2,750 ÷ 1,000 = 2.75
5. Write the answer with its unit.
   2.75 kg

Check. Go back: 2.75 × 1,000 = 2,750 (the digits move 3 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The kg are the bigger unit.

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. Changing ml into litres makes the number smaller (the new unit is bigger), so divide by 1,000.

1. Decide what to do. 1 litres = 1,000 ml, so there are 1,000 times as many ml as litres. Dividing makes the number smaller.
   825 ml ÷ 1,000
2. Say what dividing by 1,000 does. Each digit becomes 1,000 times smaller, so it moves 3 places to the right. The digits move. The decimal point does not.
   8 hundreds become 8 tenths
   2 tens become 2 hundredths
   5 ones become 5 thousandths
3. Move every digit 3 places to the right. Use a place-value chart and follow the arrows.
4. 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.
   825 ÷ 1,000 = 0.825
5. Write the answer with its unit.
   0.825 litres

Check. Go back: 0.825 × 1,000 = 825 (the digits move 3 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The litres are the bigger unit.

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. Changing pence into pounds makes the number smaller (the new unit is bigger), so divide by 100.

1. Decide what to do. £1 = 100p, so there are 100 times as many pence as pounds. Dividing makes the number smaller.
   365p ÷ 100
2. Say what dividing by 100 does. Each digit becomes 100 times smaller, so it moves 2 places to the right. The digits move. The decimal point does not.
   3 hundreds become 3 ones
   6 tens become 6 tenths
   5 ones become 5 hundredths
3. Move every digit 2 places to the right. Use a place-value chart and follow the arrows.
4. Keep the decimal point between the ones and the tenths. The point stays still, so the digits that moved across it are now in the decimal columns.
   365 ÷ 100 = 3.65
5. Write the answer with its unit.
   £3.65

Check. Go back: 3.65 × 100 = 365 (the digits move 2 places to the left). ✓

Watch out. Check the units: a bigger unit means a smaller number. The pounds are the bigger unit.

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”.

1. Try some numbers. Test the statement with some examples.
   300 ÷ 100 = 3 (the 3 moves 2 places to the right)
   45 ÷ 100 = 0.45 (the 4 and 5 both move 2 places)
   7.5 ÷ 100 = 0.075
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Dividing by 100 makes every digit 100 times smaller. A digit that is 100 times smaller is two places to the right. This is true for whole numbers and for decimals.
3. Decide.
   Always

Check. In every example the digits moved two places to the right. ✓

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”.

1. Try some numbers. Test the statement with some examples.
   70 ÷ 10 = 7 (a whole number)
   75 ÷ 10 = 7.5 (not a whole number)
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   75 ÷ 10 = 7.5 is not a whole number.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   If the number ends in 0, the digits move and the answer is a whole number. If it does not, a digit moves across the decimal point and the answer is a decimal.
4. 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. 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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 9 by to get 36?
   9 × ? = 36
2. Count up in 9s. Say the 9 times table until you reach 36.
   9, 18, 27, 36
3. Write the division. You said 4 numbers, so 9 × 4 = 36.
   36 ÷ 9 = 4

Check. 4 × 9 = 36. ✓

Watch out. Check your answer by multiplying: it should give 36.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 8 by to get 72?
   8 × ? = 72
2. Count up in 8s. Say the 8 times table until you reach 72.
   8, 16, 24, 32, 40, 48, 56, 64, 72
3. Write the division. You said 9 numbers, so 8 × 9 = 72.
   72 ÷ 8 = 9

Check. 9 × 8 = 72. ✓

Watch out. Check your answer by multiplying: it should give 72.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 7 by to get 63?
   7 × ? = 63
2. Count up in 7s. Say the 7 times table until you reach 63.
   7, 14, 21, 28, 35, 42, 49, 56, 63
3. Write the division. You said 9 numbers, so 7 × 9 = 63.
   63 ÷ 7 = 9

Check. 9 × 7 = 63. ✓

Watch out. Check your answer by multiplying: it should give 63.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 12 by to get 48?
   12 × ? = 48
2. Count up in 12s. Say the 12 times table until you reach 48.
   12, 24, 36, 48
3. Write the division. You said 4 numbers, so 12 × 4 = 48.
   48 ÷ 12 = 4

Check. 4 × 12 = 48. ✓

Watch out. Check your answer by multiplying: it should give 48.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 11 by to get 121?
   11 × ? = 121
2. Count up in 11s. Say the 11 times table until you reach 121.
   11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121
3. Write the division. You said 11 numbers, so 11 × 11 = 121.
   121 ÷ 11 = 11

Check. 11 × 11 = 121. ✓

Watch out. Check your answer by multiplying: it should give 121.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 12 by to get 132?
   12 × ? = 132
2. Count up in 12s. Say the 12 times table until you reach 132.
   12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132
3. Write the division. You said 11 numbers, so 12 × 11 = 132.
   132 ÷ 12 = 11

Check. 11 × 12 = 132. ✓

Watch out. Check your answer by multiplying: it should give 132.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 6 by to get 54?
   6 × ? = 54
2. Count up in 6s. Say the 6 times table until you reach 54.
   6, 12, 18, 24, 30, 36, 42, 48, 54
3. Write the division. You said 9 numbers, so 6 × 9 = 54.
   54 ÷ 6 = 9

Check. 9 × 6 = 54. ✓

Watch out. Check your answer by multiplying: it should give 54.

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. Use the times table. Division is the opposite of multiplication.

1. Think of the times table. Division is the opposite of multiplication. Ask: what do I multiply 9 by to get 81?
   9 × ? = 81
2. Count up in 9s. Say the 9 times table until you reach 81.
   9, 18, 27, 36, 45, 54, 63, 72, 81
3. Write the division. You said 9 numbers, so 9 × 9 = 81.
   81 ÷ 9 = 9

Check. 9 × 9 = 81. ✓

Watch out. Check your answer by multiplying: it should give 81.

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.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   3,600 ÷ 9: the digits are 36 ÷ 9
   36 ÷ 9 = 4 because 9 × 4 = 36
2. Use the fact on the leading digits. 3,600 is 36 hundreds. Share 36 hundreds into 9 equal groups.
   36 hundreds ÷ 9 = 4 hundreds
   4 hundreds = 400
3. Write the answer.
   3,600 ÷ 9 = 400

Check. Multiply back: 400 × 9 = 3,600. ✓

Watch out. Count the zeros: 3,600 has 2 zeros, so the answer has 2 zeros after the 4.

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.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   280 ÷ 7: the digits are 28 ÷ 7
   28 ÷ 7 = 4 because 7 × 4 = 28
2. Use the fact on the leading digits. 280 is 28 tens. Share 28 tens into 7 equal groups.
   28 tens ÷ 7 = 4 tens
   4 tens = 40
3. Write the answer.
   280 ÷ 7 = 40

Check. Multiply back: 40 × 7 = 280. ✓

Watch out. Count the zeros: 280 has 1 zero, so the answer has 1 zero after the 4.

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.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   4,500 ÷ 5: the digits are 45 ÷ 5
   45 ÷ 5 = 9 because 5 × 9 = 45
2. Use the fact on the leading digits. 4,500 is 45 hundreds. Share 45 hundreds into 5 equal groups.
   45 hundreds ÷ 5 = 9 hundreds
   9 hundreds = 900
3. Write the answer.
   4,500 ÷ 5 = 900

Check. Multiply back: 900 × 5 = 4,500. ✓

Watch out. Count the zeros: 4,500 has 2 zeros, so the answer has 2 zeros after the 9.

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.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   810 ÷ 9: the digits are 81 ÷ 9
   81 ÷ 9 = 9 because 9 × 9 = 81
2. Use the fact on the leading digits. 810 is 81 tens. Share 81 tens into 9 equal groups.
   81 tens ÷ 9 = 9 tens
   9 tens = 90
3. Write the answer.
   810 ÷ 9 = 90

Check. Multiply back: 90 × 9 = 810. ✓

Watch out. Count the zeros: 810 has 1 zero, so the answer has 1 zero after the 9.

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.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   4,200 ÷ 60: the digits are 42 ÷ 6
   42 ÷ 6 = 7 because 6 × 7 = 42
2. Take 1 zero off both numbers. Dividing both numbers by 10 does not change the answer, and it makes the divisor a small number.
   4,200 ÷ 60 = 420 ÷ 6
3. Use the fact on the leading digits. 420 is 42 tens. Share 42 tens into 6 equal groups.
   42 tens ÷ 6 = 7 tens
   7 tens = 70
4. Write the answer.
   4,200 ÷ 60 = 70

Check. Multiply back: 70 × 60 = 4,200. ✓

Watch out. Count the zeros carefully: 4,200 has 2 zeros and 60 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. Use a times table fact. Work out the fact with the zeros hidden, then put the right number of zeros back.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   3,600 ÷ 90: the digits are 36 ÷ 9
   36 ÷ 9 = 4 because 9 × 4 = 36
2. Take 1 zero off both numbers. Dividing both numbers by 10 does not change the answer, and it makes the divisor a small number.
   3,600 ÷ 90 = 360 ÷ 9
3. Use the fact on the leading digits. 360 is 36 tens. Share 36 tens into 9 equal groups.
   36 tens ÷ 9 = 4 tens
   4 tens = 40
4. Write the answer.
   3,600 ÷ 90 = 40

Check. Multiply back: 40 × 90 = 3,600. ✓

Watch out. Count the zeros carefully: 3,600 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. Use a times table fact. Work out the fact with the zeros hidden, then put the right number of zeros back.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   560 ÷ 70: the digits are 56 ÷ 7
   56 ÷ 7 = 8 because 7 × 8 = 56
2. Take 1 zero off both numbers. Dividing both numbers by 10 does not change the answer, and it makes the divisor a small number.
   560 ÷ 70 = 56 ÷ 7
3. Use the fact. After taking the zeros away there is nothing else to put back.
   56 ÷ 7 = 8
4. Write the answer.
   560 ÷ 70 = 8

Check. Multiply back: 8 × 70 = 560. ✓

Watch out. Count the zeros carefully: 560 has 1 zero and 70 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. Use a times table fact. Work out the fact with the zeros hidden, then put the right number of zeros back.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   8,100 ÷ 900: the digits are 81 ÷ 9
   81 ÷ 9 = 9 because 9 × 9 = 81
2. Take 2 zeros off both numbers. Dividing both numbers by 100 does not change the answer, and it makes the divisor a small number.
   8,100 ÷ 900 = 81 ÷ 9
3. Use the fact. After taking the zeros away there is nothing else to put back.
   81 ÷ 9 = 9
4. Write the answer.
   8,100 ÷ 900 = 9

Check. Multiply back: 9 × 900 = 8,100. ✓

Watch out. Count the zeros carefully: 8,100 has 2 zeros and 900 has 2 zeros. Take the same number off both, then put back what is left.

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. Multiplying and dividing are inverse (opposite) operations. Use the multiplication fact to write the division fact.

1. Look at the fact you are given. The three numbers in it are linked: two are factors and one is the product.
   6 × 40 = 240
   
2. Write the division fact. Dividing undoes multiplying. 240 divided by one factor gives the other factor.
   240 ÷ 6 = 40
3. Write the answer. The question asks for 240 ÷ 6.
   240 ÷ 6 = 40

Check. Multiply back: 40 × 6 = 240. ✓

Watch out. The product (240) is always the number you divide, never the number you divide by.

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. Multiplying and dividing are inverse (opposite) operations. Use the multiplication fact to write the division fact.

1. Look at the fact you are given. The three numbers in it are linked: two are factors and one is the product.
   6 × 40 = 240
   
2. Write the division fact. Dividing undoes multiplying. 240 divided by one factor gives the other factor.
   240 ÷ 40 = 6
3. Write the answer. The question asks for 240 ÷ 40.
   240 ÷ 40 = 6

Check. Multiply back: 6 × 40 = 240. ✓

Watch out. The product (240) is always the number you divide, never the number you divide by.

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.

1. Spot the times table fact. Cover the zeros. The digits that are left make a fact you know.
   2,400 ÷ 6: the digits are 24 ÷ 6
   24 ÷ 6 = 4 because 6 × 4 = 24
2. Use the fact on the leading digits. 2,400 is 24 hundreds. Share 24 hundreds into 6 equal groups.
   24 hundreds ÷ 6 = 4 hundreds
   4 hundreds = 400
3. Write the answer.
   2,400 ÷ 6 = 400

Check. Multiply back: 400 × 6 = 2,400. ✓

Watch out. Count the zeros: 2,400 has 2 zeros, so the answer has 2 zeros after the 4.

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. A fact family has four facts that use the same three numbers: two multiplications and two divisions.

1. Find the product. The product is the answer to the multiplication. It is the biggest number of the three.
   9 × 6 = 54
2. Swap the factors. Multiplication can be done in either order, so there are two multiplication facts.
   9 × 6 = 54
   6 × 9 = 54
3. Write the two division facts. Start with the product. Divide it by each factor in turn.
   54 ÷ 9 = 6
   54 ÷ 6 = 9

Check. Check one: 6 × 9 = 54. ✓

Watch out. The product starts both division facts. You cannot start with a factor.

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. A fact family has four facts that use the same three numbers: two multiplications and two divisions.

1. Find the product. The product is the answer to the multiplication. It is the biggest number of the three.
   8 × 70 = 560
2. Swap the factors. Multiplication can be done in either order, so there are two multiplication facts.
   8 × 70 = 560
   70 × 8 = 560
3. Write the two division facts. Start with the product. Divide it by each factor in turn.
   560 ÷ 8 = 70
   560 ÷ 70 = 8

Check. Check one: 70 × 8 = 560. ✓

Watch out. The product starts both division facts. You cannot start with a factor.

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. Division and multiplication undo each other. Use the opposite operation to find the missing number.

1. Use the opposite operation. The missing number was divided by 7 to make 12. To undo the division, multiply.
   12 × 7
2. Work it out. Use a times table fact or place value.
   12 × 7 = 84

Check. 84 ÷ 7 = 12. ✓

Watch out. Put your answer back in the box and read the whole sentence.

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. Division and multiplication undo each other. Use the opposite operation to find the missing number.

1. Use the opposite operation. The missing number was divided by 9 to make 8. To undo the division, multiply.
   8 × 9
2. Work it out. Use a times table fact or place value.
   8 × 9 = 72

Check. 72 ÷ 9 = 8. ✓

Watch out. Put your answer back in the box and read the whole sentence.

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. Write the matching multiplication, then use the fact family to find the missing number.

1. Think about the fact family. 72 is the product. It is shared into groups of the missing size to make 9 groups.
   9 × ? = 72
2. Divide the product by the number you know. The missing factor is the product divided by the factor we know.
   72 ÷ 9 = 8

Check. 72 ÷ 8 = 9. ✓

Watch out. The missing number can be the divisor: the number you divide by.

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. Write the matching multiplication, then use the fact family to find the missing number.

1. Think about the fact family. 55 is the product. It is shared into groups of the missing size to make 11 groups.
   11 × ? = 55
2. Divide the product by the number you know. The missing factor is the product divided by the factor we know.
   55 ÷ 11 = 5

Check. 55 ÷ 5 = 11. ✓

Watch out. The missing number can be the divisor: the number you divide by.

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. Dividing by 2 is the same as halving.

1. Halve 148. Partition into place-value parts, halve each part, then add.
   148 = 100 + 40 + 8
   half of each part: 50 + 20 + 4 = 74
2. Write the answer.
   148 ÷ 2 = 74

Check. Double back: 74 × 2 = 148. ✓

Watch out. Halve each place-value part and add the halves back together.

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. Dividing by 2 is the same as halving.

1. Halve 356. Partition into place-value parts, halve each part, then add.
   356 = 300 + 50 + 6
   half of each part: 150 + 25 + 3 = 178
2. Write the answer.
   356 ÷ 2 = 178

Check. Double back: 178 × 2 = 356. ✓

Watch out. Halve each place-value part and add the halves back together.

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. Dividing by 2 is the same as halving.

1. Halve 762. Partition into place-value parts, halve each part, then add.
   762 = 700 + 60 + 2
   half of each part: 350 + 30 + 1 = 381
2. Write the answer.
   762 ÷ 2 = 381

Check. Double back: 381 × 2 = 762. ✓

Watch out. Halve each place-value part and add the halves back together.

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. Dividing by 2 is the same as halving.

1. Halve 1,584. Partition into place-value parts, halve each part, then add.
   1,584 = 1,000 + 500 + 80 + 4
   half of each part: 500 + 250 + 40 + 2 = 792
2. Write the answer.
   1,584 ÷ 2 = 792

Check. Double back: 792 × 2 = 1,584. ✓

Watch out. Halve each place-value part and add the halves back together.

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. Dividing by 4 is the same as halving twice, because 4 = 2 × 2.

1. Halve 316. Partition into place-value parts, halve each part, then add.
   316 = 300 + 10 + 6
   half of each part: 150 + 5 + 3 = 158
2. Halve 158 again. Partition into place-value parts, halve each part, then add.
   158 = 100 + 50 + 8
   half of each part: 50 + 25 + 4 = 79
3. Write the answer.
   316 ÷ 4 = 79

Check. Double back: 79 × 4 = 316. ✓

Watch out. Halve twice, not once. Halving once is only ÷ 2.

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. Dividing by 4 is the same as halving twice, because 4 = 2 × 2.

1. Halve 528. Partition into place-value parts, halve each part, then add.
   528 = 500 + 20 + 8
   half of each part: 250 + 10 + 4 = 264
2. Halve 264 again. Partition into place-value parts, halve each part, then add.
   264 = 200 + 60 + 4
   half of each part: 100 + 30 + 2 = 132
3. Write the answer.
   528 ÷ 4 = 132

Check. Double back: 132 × 4 = 528. ✓

Watch out. Halve twice, not once. Halving once is only ÷ 2.

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. Dividing by 8 is the same as halving three times, because 8 = 2 × 2 × 2.

1. Halve 456. Partition into place-value parts, halve each part, then add.
   456 = 400 + 50 + 6
   half of each part: 200 + 25 + 3 = 228
2. Halve 228 again. Partition into place-value parts, halve each part, then add.
   228 = 200 + 20 + 8
   half of each part: 100 + 10 + 4 = 114
3. Halve 114 again. Partition into place-value parts, halve each part, then add.
   114 = 100 + 10 + 4
   half of each part: 50 + 5 + 2 = 57
4. Write the answer.
   456 ÷ 8 = 57

Check. Double back: 57 × 8 = 456. ✓

Watch out. Halve three times, not once. Halving once is only ÷ 2.

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. Dividing by 8 is the same as halving three times, because 8 = 2 × 2 × 2.

1. Halve 1,208. Partition into place-value parts, halve each part, then add.
   1,208 = 1,000 + 200 + 8
   half of each part: 500 + 100 + 4 = 604
2. Halve 604 again. Partition into place-value parts, halve each part, then add.
   604 = 600 + 4
   half of each part: 300 + 2 = 302
3. Halve 302 again. Partition into place-value parts, halve each part, then add.
   302 = 300 + 2
   half of each part: 150 + 1 = 151
4. Write the answer.
   1,208 ÷ 8 = 151

Check. Double back: 151 × 8 = 1,208. ✓

Watch out. Halve three times, not once. Halving once is only ÷ 2.

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 5, double the number and then divide by 10. (5 is half of 10, so there are twice as many 5s as 10s.)

1. Double the number. Doubling both numbers does not change the answer: n ÷ 5 is the same as 2n ÷ 10.
   235 = 200 + 30 + 5
   double each part: 400 + 60 + 10 = 470
2. Divide by 10. Move every digit one place to the right.
   470 ÷ 10 = 47
3. Write the answer.
   235 ÷ 5 = 47

Check. Multiply back: 47 × 5 = 235. ✓

Watch out. Double first, then divide by 10. Do not halve: that is for dividing by 20.

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. Dividing by 20 is the same as dividing by 10 and then halving, because 20 = 10 × 2.

1. Divide by 10. Move every digit one place to the right. (20 = 10 × 2.)
   460 ÷ 10 = 46
2. Halve the answer. Now divide by the other factor, 2.
   46 = 40 + 6
   half of each part: 20 + 3 = 23
3. Write the answer.
   460 ÷ 20 = 23

Check. Multiply back: 23 × 20 = 460. ✓

Watch out. Do both steps. Dividing by 10 on its own gives an answer that is twice too big.

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.)

1. Double the number. We multiply by 4 by doubling twice. (4 × 25 = 100.)
   375 = 300 + 70 + 5
   double each part: 600 + 140 + 10 = 750
2. Double again. Two doubles make × 4.
   750 = 700 + 50
   double each part: 1,400 + 100 = 1,500
3. 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.
   1,500 ÷ 100 = 15
4. Write the answer.
   375 ÷ 25 = 15

Check. Multiply back: 15 × 25 = 375. ✓

Watch out. Remember there are two doubles (× 4), then divide by 100, not 10.

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.)

1. Double the number. We multiply by 4 by doubling twice. (4 × 25 = 100.)
   1,200 = 1,000 + 200
   double each part: 2,000 + 400 = 2,400
2. Double again. Two doubles make × 4.
   2,400 = 2,000 + 400
   double each part: 4,000 + 800 = 4,800
3. 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.
   4,800 ÷ 100 = 48
4. Write the answer.
   1,200 ÷ 25 = 48

Check. Multiply back: 48 × 25 = 1,200. ✓

Watch out. Remember there are two doubles (× 4), then divide by 100, not 10.

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. 6 = 2 × 3, so dividing by 6 is the same as dividing by 2 and then by 3.

1. Divide by 2. 6 = 2 × 3, so divide by 2 first.
   324 = 200 + 120 + 4
   200 ÷ 2 = 100
   120 ÷ 2 = 60
   4 ÷ 2 = 2
   100 + 60 + 2 = 162
2. Divide the answer by 3. Now divide by the other factor.
   162 = 150 + 12
   150 ÷ 3 = 50
   12 ÷ 3 = 4
   50 + 4 = 54
3. Write the answer.
   324 ÷ 6 = 54

Check. Multiply back: 54 × 6 = 324. ✓

Watch out. Divide the answer from step 1, not the original number again.

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. 12 = 3 × 4, so dividing by 12 is the same as dividing by 3 and then by 4.

1. Divide by 3. 12 = 3 × 4, so divide by 3 first.
   252 = 240 + 12
   240 ÷ 3 = 80
   12 ÷ 3 = 4
   80 + 4 = 84
2. Divide the answer by 4. Now divide by the other factor.
   84 = 80 + 4
   80 ÷ 4 = 20
   4 ÷ 4 = 1
   20 + 1 = 21
3. Write the answer.
   252 ÷ 12 = 21

Check. Multiply back: 21 × 12 = 252. ✓

Watch out. Divide the answer from step 1, not the original number again.

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. 15 = 3 × 5, so dividing by 15 is the same as dividing by 3 and then by 5.

1. Divide by 3. 15 = 3 × 5, so divide by 3 first.
   480 = 300 + 180
   300 ÷ 3 = 100
   180 ÷ 3 = 60
   100 + 60 = 160
2. Divide the answer by 5. Now divide by the other factor.
   160 = 150 + 10
   150 ÷ 5 = 30
   10 ÷ 5 = 2
   30 + 2 = 32
3. Write the answer.
   480 ÷ 15 = 32

Check. Multiply back: 32 × 15 = 480. ✓

Watch out. Divide the answer from step 1, not the original number again.

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. Split the number into chunks that are easy to divide (multiples of the divisor), divide each chunk, then add the answers.

1. Split 168 into numbers that 7 divides into easily. Use multiples of 7, 70: the biggest chunk first.
   168 = 140 + 28
2. Divide each chunk. Use a times table fact and place value.
   140 ÷ 7 = 20
   28 ÷ 7 = 4
3. Add the answers. The pieces of the answer add together.
   20 + 4 = 24
4. Write the answer.
   168 ÷ 7 = 24

Check. Multiply back: 24 × 7 = 168. ✓

Watch out. Check that the chunks add back to the original number.

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. Split the number into chunks that are easy to divide (multiples of the divisor), divide each chunk, then add the answers.

1. Split 1,140 into numbers that 6 divides into easily. Use multiples of 6, 60, 600: the biggest chunk first.
   1,140 = 600 + 540
2. Divide each chunk. Use a times table fact and place value.
   600 ÷ 6 = 100
   540 ÷ 6 = 90
3. Add the answers. The pieces of the answer add together.
   100 + 90 = 190
4. Write the answer.
   1,140 ÷ 6 = 190

Check. Multiply back: 190 × 6 = 1,140. ✓

Watch out. Check that the chunks add back to the original number.

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. Split the number into chunks that are easy to divide (multiples of the divisor), divide each chunk, then add the answers.

1. Split 3,150 into numbers that 5 divides into easily. Use multiples of 5, 50, 500: the biggest chunk first.
   3,150 = 3,000 + 150
2. Divide each chunk. Use a times table fact and place value.
   3,000 ÷ 5 = 600
   150 ÷ 5 = 30
3. Add the answers. The pieces of the answer add together.
   600 + 30 = 630
4. Write the answer.
   3,150 ÷ 5 = 630

Check. Multiply back: 630 × 5 = 3,150. ✓

Watch out. Check that the chunks add back to the original number.

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.

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

   2	6	8

2. Divide the tens. Always start on the left, with the biggest place value.
   6 ÷ 2 = 3
   Write 3 above the 6.
3. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 8 ones.
   8 ÷ 2: 4 × 2 = 8. Write 4 above the 8.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	3	4
   2	6	8

   
   68 ÷ 2 = 34
5. Write the answer.
   68 ÷ 2 = 34

Check. Multiply back: 34 × 2 = 30 × 2 + 4 × 2 = 60 + 8 = 68. ✓

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.

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

   3	9	3

2. Divide the tens. Always start on the left, with the biggest place value.
   9 ÷ 3 = 3
   Write 3 above the 9.
3. Divide the ones. Move to the next digit on the right.
   Nothing was carried, so there are just 3 ones.
   3 ÷ 3: 1 × 3 = 3. Write 1 above the 3.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	3	1
   3	9	3

   
   93 ÷ 3 = 31
5. Write the answer.
   93 ÷ 3 = 31

Check. Multiply back: 31 × 3 = 30 × 3 + 1 × 3 = 90 + 3 = 93. ✓

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.

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

   6	6	6

2. Divide the tens. Always start on the left, with the biggest place value.
   6 ÷ 6 = 1
   Write 1 above the 6.
3. 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.
4. Read the answer. Read the digits above the line from left to right.

   	1	1
   6	6	6

   
   66 ÷ 6 = 11
5. Write the answer.
   66 ÷ 6 = 11

Check. Multiply back: 11 × 6 = 10 × 6 + 1 × 6 = 60 + 6 = 66. ✓

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.

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

   4	6	4

2. Divide the tens. Always start on the left, with the biggest place value.
   6 ÷ 4 = 1, remainder 2
   Write 1 above the 6.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. 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 4 ones there are 20 + 4 = 24 ones.
   24 ÷ 4: 6 × 4 = 24. Write 6 above the 4.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	1	6
   4	6	24

   
   64 ÷ 4 = 16
5. Write the answer.
   64 ÷ 4 = 16

Check. Multiply back: 16 × 4 = 10 × 4 + 6 × 4 = 40 + 24 = 64. ✓

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.

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

   3	8	7

2. Divide the tens. Always start on the left, with the biggest place value.
   8 ÷ 3 = 2, remainder 2
   Write 2 above the 8.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. 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 7 ones there are 20 + 7 = 27 ones.
   27 ÷ 3: 9 × 3 = 27. Write 9 above the 7.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	2	9
   3	8	27

   
   87 ÷ 3 = 29
5. Write the answer.
   87 ÷ 3 = 29

Check. Multiply back: 29 × 3 = 20 × 3 + 9 × 3 = 60 + 27 = 87. ✓

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.

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

   8	9	6

2. Divide the tens. Always start on the left, with the biggest place value.
   9 ÷ 8 = 1, remainder 1
   Write 1 above the 9.
   Exchange the remainder: 1 ten becomes 10 ones. Carry 1 to the next digit.
3. 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 ÷ 8: 2 × 8 = 16. Write 2 above the 6.
   Nothing is left over, so there is no remainder.
4. Read the answer. Read the digits above the line from left to right.

   	1	2
   8	9	16

   
   96 ÷ 8 = 12
5. Write the answer.
   96 ÷ 8 = 12

Check. Multiply back: 12 × 8 = 10 × 8 + 2 × 8 = 80 + 16 = 96. ✓

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.

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

   5	7	5

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

   	1	5
   5	7	25

   
   75 ÷ 5 = 15
5. Write the answer.
   75 ÷ 5 = 15

Check. Multiply back: 15 × 5 = 10 × 5 + 5 × 5 = 50 + 25 = 75. ✓

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.

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

   4	5	8

2. Divide the tens. Always start on the left, with the biggest place value.
   5 ÷ 4 = 1, remainder 1
   Write 1 above the 5.
   Exchange the remainder: 1 ten becomes 10 ones. Carry 1 to the next digit.
3. 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 ÷ 4: 4 × 4 = 16, and 18 − 16 = 2. Write 4 above the 8.
   The remainder is 2.
4. Read the answer. Read the digits above the line from left to right.

   	1	4	r 2
   4	5	18

   
   58 ÷ 4 = 14 r 2
5. Write the answer.
   58 ÷ 4 = 14 r 2

Check. Multiply back: 14 × 4 = 10 × 4 + 4 × 4 = 40 + 16 = 56
56 + 2 (the remainder) = 58. ✓

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. 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.

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

   6	8	3

2. Divide the tens. Always start on the left, with the biggest place value.
   8 ÷ 6 = 1, remainder 2
   Write 1 above the 8.
   Exchange the remainder: 2 tens become 20 ones. Carry 2 to the next digit.
3. 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.
4. Read the answer. Read the digits above the line from left to right.

   	1	3	r 5
   6	8	23

   
   83 ÷ 6 = 13 r 5
5. Write the answer.
   83 ÷ 6 = 13 r 5

Check. Multiply back: 13 × 6 = 10 × 6 + 3 × 6 = 60 + 18 = 78
78 + 5 (the remainder) = 83. ✓