Year 5 Long Multiplication: 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   7 ones become 7 tens
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 = 70
3. Write the answer.
   7 × 10 = 70

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

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   4 tens become 4 hundreds
   6 ones become 6 tens
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.
   46 × 10 = 460
3. Write the answer.
   46 × 10 = 460

Check. Go back: 460 ÷ 10 = 46 (the digits move 1 place to the right). ✓

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 46.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   1 hundred becomes 1 thousand
   3 tens become 3 hundreds
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.
   130 × 10 = 1,300
3. Write the answer.
   130 × 10 = 1,300

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

Watch out. Count the zeros: 130 already ends in 1 zero, so the answer ends in 2 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   9 hundreds become 9 thousands
   5 ones become 5 tens
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.
   905 × 10 = 9,050
3. Write the answer.
   905 × 10 = 9,050

Check. Go back: 9,050 ÷ 10 = 905 (the digits move 1 place to the right). ✓

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 905.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   8 ones become 8 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   8 × 100 = 800
3. Write the answer.
   8 × 100 = 800

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

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 8.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   5 tens become 5 thousands
   3 ones become 3 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   53 × 100 = 5,300
3. Write the answer.
   53 × 100 = 5,300

Check. Go back: 5,300 ÷ 100 = 53 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 53.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   4 hundreds become 4 ten thousands
   2 tens become 2 thousands
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   420 × 100 = 42,000
3. Write the answer.
   420 × 100 = 42,000

Check. Go back: 42,000 ÷ 100 = 420 (the digits move 2 places to the right). ✓

Watch out. Count the zeros: 420 already ends in 1 zero, so the answer ends in 3 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   3 hundreds become 3 ten thousands
   6 ones become 6 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   306 × 100 = 30,600
3. Write the answer.
   306 × 100 = 30,600

Check. Go back: 30,600 ÷ 100 = 306 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 306.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   9 ones become 9 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   9 × 1,000 = 9,000
3. Write the answer.
   9 × 1,000 = 9,000

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

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 9.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 tens become 6 ten thousands
   4 ones become 4 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   64 × 1,000 = 64,000
3. Write the answer.
   64 × 1,000 = 64,000

Check. Go back: 64,000 ÷ 1,000 = 64 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 64.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   3 hundreds become 3 hundred thousands
   8 tens become 8 ten thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   380 × 1,000 = 380,000
3. Write the answer.
   380 × 1,000 = 380,000

Check. Go back: 380,000 ÷ 1,000 = 380 (the digits move 3 places to the right). ✓

Watch out. Count the zeros: 380 already ends in 1 zero, so the answer ends in 4 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   7 hundreds become 7 hundred thousands
   4 tens become 4 ten thousands
   1 one becomes 1 thousand
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   741 × 1,000 = 741,000
3. Write the answer.
   741 × 1,000 = 741,000

Check. Go back: 741,000 ÷ 1,000 = 741 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 741.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   6 tens become 6 hundreds
   2 ones become 2 tens
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.
   62 × 10 = 620
3. Write the answer.
   62 × 10 = 620

Check. Go back: 620 ÷ 10 = 62 (the digits move 1 place to the right). ✓

Watch out. The zeros are place holders. Check the answer is 10 times bigger: it has 1 more digit than 62.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   6 tens become 6 thousands
   2 ones become 2 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   62 × 100 = 6,200
3. Write the answer.
   62 × 100 = 6,200

Check. Go back: 6,200 ÷ 100 = 62 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 62.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 tens become 6 ten thousands
   2 ones become 2 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   62 × 1,000 = 62,000
3. Write the answer.
   62 × 1,000 = 62,000

Check. Go back: 62,000 ÷ 1,000 = 62 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 62.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   3 hundreds become 3 thousands
   1 ten becomes 1 hundred
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.
   310 × 10 = 3,100
3. Write the answer.
   310 × 10 = 3,100

Check. Go back: 3,100 ÷ 10 = 310 (the digits move 1 place to the right). ✓

Watch out. Count the zeros: 310 already ends in 1 zero, so the answer ends in 2 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   2 hundreds become 2 ten thousands
   5 ones become 5 hundreds
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   205 × 100 = 20,500
3. Write the answer.
   205 × 100 = 20,500

Check. Go back: 20,500 ÷ 100 = 205 (the digits move 2 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 100 times bigger: it has 2 more digits than 205.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   4 tens become 4 ten thousands
   8 ones become 8 thousands
2. Fill the empty places with zeros. The ones and tens and hundreds columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   48 × 1,000 = 48,000
3. Write the answer.
   48 × 1,000 = 48,000

Check. Go back: 48,000 ÷ 1,000 = 48 (the digits move 3 places to the right). ✓

Watch out. The zeros are place holders. Check the answer is 1,000 times bigger: it has 3 more digits than 48.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   7 hundreds become 7 thousands
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.
   700 × 10 = 7,000
3. Write the answer.
   700 × 10 = 7,000

Check. Go back: 7,000 ÷ 10 = 700 (the digits move 1 place to the right). ✓

Watch out. Count the zeros: 700 already ends in 2 zeros, so the answer ends in 3 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   1 thousand becomes 1 hundred thousand
   5 hundreds become 5 ten thousands
2. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   1,500 × 100 = 150,000
3. Write the answer.
   1,500 × 100 = 150,000

Check. Go back: 150,000 ÷ 100 = 1,500 (the digits move 2 places to the right). ✓

Watch out. Count the zeros: 1,500 already ends in 2 zeros, so the answer ends in 4 zeros.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   3 ones become 3 tens
   6 tenths become 6 ones
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   3.6 × 10 = 36, not 36.0
4. Write the answer.
   3.6 × 10 = 36

Check. Go back: 36 ÷ 10 = 3.6 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (3.6 and 3.60 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   7 tenths become 7 ones
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   0.7 × 10 = 7, not 7.0
4. Write the answer.
   0.7 × 10 = 7

Check. Go back: 7 ÷ 10 = 0.7 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (0.7 and 0.70 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   1 ten becomes 1 hundred
   2 ones become 2 tens
   4 tenths become 4 ones
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   12.4 × 10 = 124, not 124.0
4. Write the answer.
   12.4 × 10 = 124

Check. Go back: 124 ÷ 10 = 12.4 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (12.4 and 12.40 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   5 hundredths become 5 tenths
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. 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 whole-number columns.
   0.05 × 10 = 0.5
4. Write the answer.
   0.05 × 10 = 0.5

Check. Go back: 0.5 ÷ 10 = 0.05 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (0.05 and 0.050 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 10, move every digit 1 place to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 10 does. Each digit becomes 10 times bigger, so it moves 1 place to the left. The digits move. The decimal point does not.
   8 ones become 8 tens
   2 tenths become 2 ones
   5 hundredths become 5 tenths
2. Move every digit 1 place to the left. Use a place-value chart and follow the arrows.
3. 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 whole-number columns.
   8.25 × 10 = 82.5
4. Write the answer.
   8.25 × 10 = 82.5

Check. Go back: 82.5 ÷ 10 = 8.25 (the digits move 1 place to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (8.25 and 8.250 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   2 ones become 2 hundreds
   4 tenths become 4 tens
2. Move every digit 2 places to the left. 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.
   2.4 × 100 = 240
4. Write the answer.
   2.4 × 100 = 240

Check. Go back: 240 ÷ 100 = 2.4 (the digits move 2 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (2.4 and 2.40 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   3 tenths become 3 tens
   8 hundredths become 8 ones
2. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   0.38 × 100 = 38, not 38.0
4. Write the answer.
   0.38 × 100 = 38

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

Watch out. Do not just add zeros to a decimal. That does not change its value (0.38 and 0.380 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 100, move every digit 2 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   7 ones become 7 hundreds
   5 hundredths become 5 ones
2. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   7.05 × 100 = 705, not 705.0
4. Write the answer.
   7.05 × 100 = 705

Check. Go back: 705 ÷ 100 = 7.05 (the digits move 2 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (7.05 and 7.050 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   9 tenths become 9 hundreds
2. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
3. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.9 × 1,000 = 900
4. Write the answer.
   0.9 × 1,000 = 900

Check. Go back: 900 ÷ 1,000 = 0.9 (the digits move 3 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (0.9 and 0.90 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   3 ones become 3 thousands
   4 tenths become 4 hundreds
   7 hundredths become 7 tens
   2 thousandths become 2 ones
2. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   3.472 × 1,000 = 3,472, not 3,472.0
4. Write the answer.
   3.472 × 1,000 = 3,472

Check. Go back: 3,472 ÷ 1,000 = 3.472 (the digits move 3 places to the right). ✓

Watch out. Do not just add zeros to a decimal. That does not change its value (3.472 and 3.4720 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. To multiply by 1,000, move every digit 3 places to the left, and fill any empty places on the right with zeros. The decimal point does not move.

1. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 hundredths become 6 tens
   2 thousandths become 2 ones
2. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
3. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   0.062 × 1,000 = 62, not 62.0
4. Write the answer.
   0.062 × 1,000 = 62

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

Watch out. Do not just add zeros to a decimal. That does not change its value (0.062 and 0.0620 are the same number). Move the digits to the left instead.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Find out how far the digits move. One place to the left 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 → 450
2. Count how many places the digits moved. Each digit moved to the left, so the number got bigger.
3. Say what the number is. Digits that move 2 places to the left mean × 100.
   4.5 × 100 = 450

Check. 4.5 × 100 = 450. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

1. Use the opposite (inverse) operation. Dividing undoes multiplying. The missing number is 360 ÷ 10.
   360 ÷ 10
2. Move the digits 1 place to the right. Dividing by 10 makes each digit 10 times smaller.
3. Write the missing number. Read the whole sentence back to check it.
   36 × 10 = 360

Check. 36 × 10 = 360. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Find out how far the digits move. One place to the left 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.
   0.07 → 70
2. Count how many places the digits moved. Each digit moved to the left, so the number got bigger.
3. Say what the number is. Digits that move 3 places to the left mean × 1,000.
   0.07 × 1,000 = 70

Check. 0.07 × 1,000 = 70. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

1. Use the opposite (inverse) operation. Dividing undoes multiplying. The missing number is 290 ÷ 100.
   290 ÷ 100
2. Move the digits 2 places to the right. Dividing by 100 makes each digit 100 times smaller.
3. Write the missing number. Read the whole sentence back to check it.
   2.9 × 100 = 290

Check. 2.9 × 100 = 290. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Find out how far the digits move. One place to the left 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 → 630
2. Count how many places the digits moved. Each digit moved to the left, so the number got bigger.
3. Say what the number is. Digits that move 1 place to the left mean × 10.
   63 × 10 = 630

Check. 63 × 10 = 630. ✓

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

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

Check. 0.804 × 1,000 = 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

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

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

Watch out. Arrows pointing left mean the number gets bigger, so it is a multiplication.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

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

1. Read the top number and the bottom number. The top row is the starting number. The bottom row is the answer.
   Top: 0.18.   Bottom: 1.8.
2. Look at the arrows. Every digit moves 1 place to the left. One place is × 10, two places is × 100, three places is × 1,000.
   1 place to the left means × 10.
3. Write the calculation.
   0.18 × 10 = 1.8

Check. Move the digits of 0.18 1 place to the left: 1.8. ✓

Watch out. Arrows pointing left mean the number gets bigger, so it is a multiplication.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing km into m makes the number bigger (there are more small units), so multiply by 1,000.

1. Decide what to do. 1 km = 1,000 m, so there are 1,000 times as many m as km. Multiply by 1,000.
   2.5 km × 1,000
2. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   2 ones become 2 thousands
   5 tenths become 5 hundreds
3. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   2.5 × 1,000 = 2,500
5. Write the answer with its unit.
   2,500 m

Check. Go back: 2,500 ÷ 1,000 = 2.5 (the digits move 3 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The m are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing kg into g makes the number bigger (there are more small units), so multiply by 1,000.

1. Decide what to do. 1 kg = 1,000 g, so there are 1,000 times as many g as kg. Multiply by 1,000.
   3.7 kg × 1,000
2. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   3 ones become 3 thousands
   7 tenths become 7 hundreds
3. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   3.7 × 1,000 = 3,700
5. Write the answer with its unit.
   3,700 g

Check. Go back: 3,700 ÷ 1,000 = 3.7 (the digits move 3 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The g are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing pounds into pence makes the number bigger (there are more small units), so multiply by 100.

1. Decide what to do. £1 = 100p, so there are 100 times as many pence as pounds. Multiply by 100.
   £4.85 × 100
2. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   4 ones become 4 hundreds
   8 tenths become 8 tens
   5 hundredths become 5 ones
3. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
4. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   4.85 × 100 = 485, not 485.0
5. Write the answer with its unit.
   485p

Check. Go back: 485 ÷ 100 = 4.85 (the digits move 2 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The pence are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing litres into ml makes the number bigger (there are more small units), so multiply by 1,000.

1. Decide what to do. 1 litres = 1,000 ml, so there are 1,000 times as many ml as litres. Multiply by 1,000.
   0.6 litres × 1,000
2. Say what multiplying by 1,000 does. Each digit becomes 1,000 times bigger, so it moves 3 places to the left. The digits move. The decimal point does not.
   6 tenths become 6 hundreds
3. Move every digit 3 places to the left. Use a place-value chart and follow the arrows.
4. Fill the empty places with zeros. The ones and tens columns are empty. A zero in each is a place holder: it keeps every digit in its right column.
   0.6 × 1,000 = 600
5. Write the answer with its unit.
   600 ml

Check. Go back: 600 ÷ 1,000 = 0.6 (the digits move 3 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The ml are the smaller 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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Changing m into cm makes the number bigger (there are more small units), so multiply by 100.

1. Decide what to do. 1 m = 100 cm, so there are 100 times as many cm as m. Multiply by 100.
   1.25 m × 100
2. Say what multiplying by 100 does. Each digit becomes 100 times bigger, so it moves 2 places to the left. The digits move. The decimal point does not.
   1 one becomes 1 hundred
   2 tenths become 2 tens
   5 hundredths become 5 ones
3. Move every digit 2 places to the left. Use a place-value chart and follow the arrows.
4. Look at what is left after the decimal point. Nothing is left, so we do not write the point or any zeros after it.
   1.25 × 100 = 125, not 125.0
5. Write the answer with its unit.
   125 cm

Check. Go back: 125 ÷ 100 = 1.25 (the digits move 2 places to the right). ✓

Watch out. Check the units: a smaller unit means a bigger number. The cm are the smaller 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.
   Move the digits 2 places left:
   3 × 100 = 300   0.4 × 100 = 40   12.5 × 100 = 1,250
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Multiplying by 100 makes every digit 100 times bigger, which is always a move of 2 places to the left. This is true for whole numbers and for decimals.
3. Decide.
   Always

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

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.
   Whole numbers: 7 × 10 = 70   45 × 10 = 450 (ends in 0)
   Decimals: 0.5 × 10 = 5   3.2 × 10 = 32 (does not end in 0)
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   0.5 × 10 = 5, and 5 does not end in 0.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   A whole number always gets a 0 place holder on the end. But a decimal can have digits move across the decimal point, so there might be no 0.
4. Decide.
   Sometimes

Check. Whole numbers always end in 0, but not every number is a whole number. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Use the fact 6 × 8 = 48. Multiply the numbers without their zeros, then put all the zeros back.

1. Find the multiplication fact you know. Take the zeros off both numbers. What is left is a times table fact.
   60 = 6 × 10  and  8 = 8 × 1
   The fact is 6 × 8 = 48
2. Count the zeros you took off. Each zero means one × 10. Together they make 10.
   1 zero + 0 zeros = 1 zero, so × 10
3. Multiply the fact by that power of ten. Move the digits of the fact to the left, filling the gaps with zeros.
   48 × 10 = 480
4. Write the answer.
   60 × 8 = 480

Check. Check by dividing: 480 ÷ 8 = 60. ✓

Watch out. Count ALL the zeros from BOTH numbers, then put them after 48.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Use the fact 7 × 4 = 28. Multiply the numbers without their zeros, then put all the zeros back.

1. Find the multiplication fact you know. Take the zeros off both numbers. What is left is a times table fact.
   700 = 7 × 100  and  4 = 4 × 1
   The fact is 7 × 4 = 28
2. Count the zeros you took off. Each zero means one × 10. Together they make 100.
   2 zeros + 0 zeros = 2 zeros, so × 100
3. Multiply the fact by that power of ten. Move the digits of the fact to the left, filling the gaps with zeros.
   28 × 100 = 2,800
4. Write the answer.
   700 × 4 = 2,800

Check. Check by dividing: 2,800 ÷ 4 = 700. ✓

Watch out. Count ALL the zeros from BOTH numbers, then put them after 28.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Use the fact 5 × 9 = 45. Multiply the numbers without their zeros, then put all the zeros back.

1. Find the multiplication fact you know. Take the zeros off both numbers. What is left is a times table fact.
   50 = 5 × 10  and  90 = 9 × 10
   The fact is 5 × 9 = 45
2. Count the zeros you took off. Each zero means one × 10. Together they make 100.
   1 zero + 1 zero = 2 zeros, so × 100
3. Multiply the fact by that power of ten. Move the digits of the fact to the left, filling the gaps with zeros.
   45 × 100 = 4,500
4. Write the answer.
   50 × 90 = 4,500

Check. Check by dividing: 4,500 ÷ 90 = 50. ✓

Watch out. Count ALL the zeros from BOTH numbers, then put them after 45.

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. Multiplying by 10, 100 or 1,000 makes a number 10, 100 or 1,000 times bigger.

Method. Use the fact 3 × 7 = 21. Multiply the numbers without their zeros, then put all the zeros back.

1. Find the multiplication fact you know. Take the zeros off both numbers. What is left is a times table fact.
   300 = 3 × 100  and  70 = 7 × 10
   The fact is 3 × 7 = 21
2. Count the zeros you took off. Each zero means one × 10. Together they make 1,000.
   2 zeros + 1 zero = 3 zeros, so × 1,000
3. Multiply the fact by that power of ten. Move the digits of the fact to the left, filling the gaps with zeros.
   21 × 1,000 = 21,000
4. Write the answer.
   300 × 70 = 21,000

Check. Check by dividing: 21,000 ÷ 70 = 300. ✓

Watch out. Count ALL the zeros from BOTH numbers, then put them after 21.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 23 into place-value parts. Multiply each part by 4, then add the answers.

1. Partition the bigger number. Split it into hundreds, tens and ones. Each part is easy to multiply.
   23 = 20 + 3
2. Multiply each part by 4. Use a times table fact, then put the zeros back.
   20 × 4 = 80
   3 × 4 = 12
3. Add the answers. Add them one at a time, starting with the biggest.
   80 + 12 = 92
4. Write the answer.
   23 × 4 = 92

Check. Estimate: 23 is about 20. 20 × 4 = 80. Our answer, 92, is close to 80. ✓

Watch out. Multiply every part. Do not forget a part, and do not lose the zeros: 40 × 6 is 240, not 24.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 38 into place-value parts. Multiply each part by 6, then add the answers.

1. Partition the bigger number. Split it into hundreds, tens and ones. Each part is easy to multiply.
   38 = 30 + 8
2. Multiply each part by 6. Use a times table fact, then put the zeros back.
   30 × 6 = 180
   8 × 6 = 48
3. Add the answers. Add them one at a time, starting with the biggest.
   180 + 48 = 228
4. Write the answer.
   38 × 6 = 228

Check. Estimate: 38 is about 40. 40 × 6 = 240. Our answer, 228, is close to 240. ✓

Watch out. Multiply every part. Do not forget a part, and do not lose the zeros: 40 × 6 is 240, not 24.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 52 into place-value parts. Multiply each part by 7, then add the answers.

1. Partition the bigger number. Split it into hundreds, tens and ones. Each part is easy to multiply.
   52 = 50 + 2
2. Multiply each part by 7. Use a times table fact, then put the zeros back.
   50 × 7 = 350
   2 × 7 = 14
3. Add the answers. Add them one at a time, starting with the biggest.
   350 + 14 = 364
4. Write the answer.
   52 × 7 = 364

Check. Estimate: 52 is about 50. 50 × 7 = 350. Our answer, 364, is close to 350. ✓

Watch out. Multiply every part. Do not forget a part, and do not lose the zeros: 40 × 6 is 240, not 24.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 206 into place-value parts. Multiply each part by 5, then add the answers.

1. Partition the bigger number. Split it into hundreds, tens and ones. Each part is easy to multiply.
   206 = 200 + 6
2. Multiply each part by 5. Use a times table fact, then put the zeros back.
   200 × 5 = 1,000
   6 × 5 = 30
3. Add the answers. Add them one at a time, starting with the biggest.
   1,000 + 30 = 1,030
4. Write the answer.
   206 × 5 = 1,030

Check. Estimate: 206 is about 200. 200 × 5 = 1,000. Our answer, 1,030, is close to 1,000. ✓

Watch out. Multiply every part. Do not forget a part, and do not lose the zeros: 40 × 6 is 240, not 24.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 14 into tens and ones. Multiply 12 by each part, then add the answers.

1. Partition 14. Split the second number into tens and ones. Multiplying by tens and by ones is easier.
   14 = 10 + 4
2. Multiply by each part. Multiply by the tens first (move the digits), then by the ones.
   12 × 10 = 120
   12 × 4 = 48
3. Add the answers.
   120 + 48 = 168
4. Write the answer.
   12 × 14 = 168

Check. Estimate: 12 is about 10; 14 is about 10. 10 × 10 = 100. Our answer, 168, is a bit more than 100. ✓

Watch out. You must multiply 12 by BOTH parts, not just by the tens.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 13 into tens and ones. Multiply 15 by each part, then add the answers.

1. Partition 13. Split the second number into tens and ones. Multiplying by tens and by ones is easier.
   13 = 10 + 3
2. Multiply by each part. Multiply by the tens first (move the digits), then by the ones.
   15 × 10 = 150
   15 × 3 = 10 × 3 + 5 × 3 = 30 + 15 = 45
3. Add the answers.
   150 + 45 = 195
4. Write the answer.
   15 × 13 = 195

Check. Estimate: 15 is about 20; 13 is about 10. 20 × 10 = 200. Our answer, 195, is close to 200. ✓

Watch out. You must multiply 15 by BOTH parts, not just by the tens.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 12 into tens and ones. Multiply 22 by each part, then add the answers.

1. Partition 12. Split the second number into tens and ones. Multiplying by tens and by ones is easier.
   12 = 10 + 2
2. Multiply by each part. Multiply by the tens first (move the digits), then by the ones.
   22 × 10 = 220
   22 × 2 = 20 × 2 + 2 × 2 = 40 + 4 = 44
3. Add the answers.
   220 + 44 = 264
4. Write the answer.
   22 × 12 = 264

Check. Estimate: 22 is about 20; 12 is about 10. 20 × 10 = 200. Our answer, 264, is a bit more than 200. ✓

Watch out. You must multiply 22 by BOTH parts, not just by the tens.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Partition 15 into tens and ones. Multiply 17 by each part, then add the answers.

1. Partition 15. Split the second number into tens and ones. Multiplying by tens and by ones is easier.
   15 = 10 + 5
2. Multiply by each part. Multiply by the tens first (move the digits), then by the ones.
   17 × 10 = 170
   17 × 5 = 10 × 5 + 7 × 5 = 50 + 35 = 85
3. Add the answers.
   170 + 85 = 255
4. Write the answer.
   17 × 15 = 255

Check. Estimate: 17 is about 20; 15 is about 20. 20 × 20 = 400. Our answer, 255, is a bit less than 400. ✓

Watch out. You must multiply 17 by BOTH parts, not just by the tens.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Halve one number and double the other. The answer stays the same, but the sum gets easier.

1. Look for an even number to halve. If you halve one number and double the other, the answer stays the same. This is because 2 × (1/2) = 1.
   25 × 16: halve 16, double 25
2. Halve one number and double the other. Do this until the multiplication is easy.
   25 × 16 = (25 × 2) × (16 ÷ 2) = 50 × 8
   50 × 8 = (50 × 2) × (8 ÷ 2) = 100 × 4
3. Work out the easy multiplication. Now use a fact you know or move the digits.
   100 × 4 = 400
4. Write the answer.
   25 × 16 = 400

Check. Check with a different method: 25 × 16 = 10 × 25 + 6 × 25 = 250 + 150 = 400

Watch out. Halve ONE number and double the OTHER. If you halve both, the answer is four times too small.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Halve one number and double the other. The answer stays the same, but the sum gets easier.

1. Look for an even number to halve. If you halve one number and double the other, the answer stays the same. This is because 2 × (1/2) = 1.
   15 × 14: halve 14, double 15
2. Halve one number and double the other. Do this until the multiplication is easy.
   15 × 14 = (15 × 2) × (14 ÷ 2) = 30 × 7
3. Work out the easy multiplication. Now use a fact you know or move the digits.
   30 × 7 = 210
4. Write the answer.
   15 × 14 = 210

Check. Check with a different method: 15 × 14 = 10 × 15 + 4 × 15 = 150 + 60 = 210

Watch out. Halve ONE number and double the OTHER. If you halve both, the answer is four times too small.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Halve one number and double the other. The answer stays the same, but the sum gets easier.

1. Look for an even number to halve. If you halve one number and double the other, the answer stays the same. This is because 2 × (1/2) = 1.
   45 × 18: halve 18, double 45
2. Halve one number and double the other. Do this until the multiplication is easy.
   45 × 18 = (45 × 2) × (18 ÷ 2) = 90 × 9
3. Work out the easy multiplication. Now use a fact you know or move the digits.
   90 × 9 = 810
4. Write the answer.
   45 × 18 = 810

Check. Check with a different method: 45 × 18 = 10 × 45 + 8 × 45 = 450 + 360 = 810

Watch out. Halve ONE number and double the OTHER. If you halve both, the answer is four times too small.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Halve one number and double the other. The answer stays the same, but the sum gets easier.

1. Look for an even number to halve. If you halve one number and double the other, the answer stays the same. This is because 2 × (1/2) = 1.
   35 × 12: halve 12, double 35
2. Halve one number and double the other. Do this until the multiplication is easy.
   35 × 12 = (35 × 2) × (12 ÷ 2) = 70 × 6
3. Work out the easy multiplication. Now use a fact you know or move the digits.
   70 × 6 = 420
4. Write the answer.
   35 × 12 = 420

Check. Check with a different method: 35 × 12 = 10 × 35 + 2 × 35 = 350 + 70 = 420

Watch out. Halve ONE number and double the OTHER. If you halve both, the answer is four times too small.

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 double is to multiply by 2. To halve is to divide by 2.

Method. 4 is 2 × 2. Multiply 17 by each factor in turn.

1. Split 4 into factors. A factor pair gives two easier multiplications that make the same answer.
   4 = 2 × 2
2. Multiply by 2. Double it.
   17 × 2 = 10 × 2 + 7 × 2 = 20 + 14 = 34
3. Multiply by 2. Double it.
   34 × 2 = 30 × 2 + 4 × 2 = 60 + 8 = 68
4. Write the answer.
   17 × 4 = 68

Check. 17 × 4 = 10 × 4 + 7 × 4 = 40 + 28 = 68

Watch out. Multiply by each factor, one after the other. Do not add the factors: 4 is 2 × 2, not 2 + 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 double is to multiply by 2. To halve is to divide by 2.

Method. 8 is 2 × 2 × 2. Multiply 14 by each factor in turn.

1. Split 8 into factors. A factor pair gives two easier multiplications that make the same answer.
   8 = 2 × 2 × 2
2. Multiply by 2. Double it.
   14 × 2 = 10 × 2 + 4 × 2 = 20 + 8 = 28
3. Multiply by 2. Double it.
   28 × 2 = 20 × 2 + 8 × 2 = 40 + 16 = 56
4. Multiply by 2. Double it.
   56 × 2 = 50 × 2 + 6 × 2 = 100 + 12 = 112
5. Write the answer.
   14 × 8 = 112

Check. 14 × 8 = 10 × 8 + 4 × 8 = 80 + 32 = 112

Watch out. Multiply by each factor, one after the other. Do not add the factors: 8 is 2 × 2 × 2, not 2 + 2 + 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 double is to multiply by 2. To halve is to divide by 2.

Method. 12 is 3 × 4. Multiply 23 by each factor in turn.

1. Split 12 into factors. A factor pair gives two easier multiplications that make the same answer.
   12 = 3 × 4
2. Multiply by 3. Use the 3 times table and partition if you need to.
   23 × 3 = 20 × 3 + 3 × 3 = 60 + 9 = 69
3. Multiply by 4. Use the 4 times table and partition if you need to.
   69 × 4 = 60 × 4 + 9 × 4 = 240 + 36 = 276
4. Write the answer.
   23 × 12 = 276

Check. Estimate: 23 is about 20; 12 is about 10. 20 × 10 = 200. Our answer, 276, is a bit more than 200. ✓

Watch out. Multiply by each factor, one after the other. Do not add the factors: 12 is 3 × 4, not 3 + 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 double is to multiply by 2. To halve is to divide by 2.

Method. 18 is 2 × 9. Multiply 31 by each factor in turn.

1. Split 18 into factors. A factor pair gives two easier multiplications that make the same answer.
   18 = 2 × 9
2. Multiply by 2. Double it.
   31 × 2 = 30 × 2 + 1 × 2 = 60 + 2 = 62
3. Multiply by 9. Use the 9 times table and partition if you need to.
   62 × 9 = 60 × 9 + 2 × 9 = 540 + 18 = 558
4. Write the answer.
   31 × 18 = 558

Check. Estimate: 31 is about 30; 18 is about 20. 30 × 20 = 600. Our answer, 558, is close to 600. ✓

Watch out. Multiply by each factor, one after the other. Do not add the factors: 18 is 2 × 9, not 2 + 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 double is to multiply by 2. To halve is to divide by 2.

Method. Multiplying by 5 is the same as multiplying by 10 and then halving, because 5 is half of 10.

1. Multiply by 10. 5 is half of 10, so first multiply by 10: move the digits one place to the left.
   64 × 10 = 640
2. Halve the answer. We multiplied by a number that was 2 times too big, so halve it.
   640 ÷ 2 = 320
3. Write the answer.
   64 × 5 = 320

Check. Estimate: 64 is about 60. 60 × 5 = 300. Our answer, 320, is close to 300. ✓

Watch out. Remember to halve at the end. 10 is twice as big as 5.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Multiplying by 25 is the same as multiplying by 100 and then dividing by 4 (halving twice), because 25 is a quarter of 100.

1. Multiply by 100. 25 is a quarter of 100, so first multiply by 100: move the digits two places to the left.
   48 × 100 = 4,800
2. Halve the answer. To divide by 4, halve twice. First halve.
   4,800 ÷ 2 = 2,400
3. Halve again. A quarter is half of a half.
   2,400 ÷ 2 = 1,200
4. Write the answer.
   48 × 25 = 1,200

Check. Estimate: 48 is about 50; 25 is about 30. 50 × 30 = 1,500. Our answer, 1,200, is close to 1,500. ✓

Watch out. Halve TWICE. Dividing by 4 means halving, then halving 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 double is to multiply by 2. To halve is to divide by 2.

Method. Multiplying by 50 is the same as multiplying by 100 and then halving, because 50 is half of 100.

1. Multiply by 100. 50 is half of 100, so first multiply by 100: move the digits two places to the left.
   36 × 100 = 3,600
2. Halve the answer. We multiplied by a number that was 2 times too big.
   3,600 ÷ 2 = 1,800
3. Write the answer.
   36 × 50 = 1,800

Check. Estimate: 36 is about 40. 40 × 50 = 2,000. Our answer, 1,800, is close to 2,000. ✓

Watch out. Use 100 (not 10) and halve once.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Multiplying by 20 is the same as doubling and then multiplying by 10, because 20 = 2 × 10.

1. Multiply by 2 (double). 20 is 2 × 10. Double the number first.
   73 × 2 = 146
2. Multiply by 10. Move every digit one place to the left.
   146 × 10 = 1,460
3. Write the answer.
   73 × 20 = 1,460

Check. Estimate: 73 is about 70. 70 × 20 = 1,400. Our answer, 1,460, is close to 1,400. ✓

Watch out. Do both steps: double AND multiply by 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 double is to multiply by 2. To halve is to divide by 2.

Method. 15 = 10 + 5. Work out 10 lots, then 5 lots (half of 10 lots), then add.

1. Multiply by 10. 15 is 10 + 5, so work out 10 lots first.
   26 × 10 = 260
2. Find 5 lots. 5 lots is half of 10 lots.
   260 ÷ 2 = 130
3. Add them. 15 lots = 10 lots + 5 lots.
   260 + 130 = 390
4. Write the answer.
   26 × 15 = 390

Check. Estimate: 26 is about 30; 15 is about 20. 30 × 20 = 600. Our answer, 390, is a bit less than 600. ✓

Watch out. Halve the 10 lots to get 5 lots. Do not halve the original number.

Key words. To compensate is to make up for a change. Here we multiply by an easy number that is a little too big or too small, then correct the answer.

Method. 9 is close to 10. Multiply by 10, then take away 1 lot of 46.

1. Spot an easy number close by. 9 is just 1 less than 10. Multiplying by 10 is easy.
   9 = 10 − 1
2. Multiply by 10. Do the easy multiplication first.
   46 × 10 = 460
3. Work out the extra 1 lot of 46. We multiplied by 10, but we wanted 9. That is 1 lot of 46 too many.
   46 × 1 = 46
4. Correct the answer. Take away the extra lots.
   460 − 46 = 414
5. Write the answer.
   46 × 9 = 414

Check. Another way: 46 × 9 = 40 × 9 + 6 × 9 = 360 + 54 = 414

Watch out. Take away 1 lot of 46, not just 1.

Key words. To compensate is to make up for a change. Here we multiply by an easy number that is a little too big or too small, then correct the answer.

Method. 11 is close to 10. Multiply by 10, then add 1 lot of 52.

1. Spot an easy number close by. 11 is just 1 more than 10. Multiplying by 10 is easy.
   11 = 10 + 1
2. Multiply by 10. Do the easy multiplication first.
   52 × 10 = 520
3. Work out the extra 1 lot of 52. We multiplied by 10, but we wanted 11. We need 1 lot of 52 more.
   52 × 1 = 52
4. Correct the answer. Add the extra lots.
   520 + 52 = 572
5. Write the answer.
   52 × 11 = 572

Check. Another way: 52 × 11 = 10 × 52 + 1 × 52 = 520 + 52 = 572

Watch out. Add 1 lot of 52, not just 1.

Key words. To compensate is to make up for a change. Here we multiply by an easy number that is a little too big or too small, then correct the answer.

Method. 99 is close to 100. Multiply by 100, then take away 1 lot of 37.

1. Spot an easy number close by. 99 is just 1 less than 100. Multiplying by 100 is easy.
   99 = 100 − 1
2. Multiply by 100. Do the easy multiplication first.
   37 × 100 = 3,700
3. Work out the extra 1 lot of 37. We multiplied by 100, but we wanted 99. That is 1 lot of 37 too many.
   37 × 1 = 37
4. Correct the answer. Take away the extra lots.
   3,700 − 37 = 3,663
5. Write the answer.
   37 × 99 = 3,663

Check. Another way: 37 × 99 = 90 × 37 + 9 × 37 = 3,330 + 333 = 3,663

Watch out. Take away 1 lot of 37, not just 1.

Key words. To compensate is to make up for a change. Here we multiply by an easy number that is a little too big or too small, then correct the answer.

Method. 19 is close to 20. Multiply by 20, then take away 1 lot of 24.

1. Spot an easy number close by. 19 is just 1 less than 20. Multiplying by 20 is easy.
   19 = 20 − 1
2. Multiply by 20. Do the easy multiplication first.
   24 × 2 = 48, then × 10: 48 × 10 = 480
3. Work out the extra 1 lot of 24. We multiplied by 20, but we wanted 19. That is 1 lot of 24 too many.
   24 × 1 = 24
4. Correct the answer. Take away the extra lots.
   480 − 24 = 456
5. Write the answer.
   24 × 19 = 456

Check. Another way: 24 × 19 = 10 × 24 + 9 × 24 = 240 + 216 = 456

Watch out. Take away 1 lot of 24, not just 1.

Key words. To compensate is to make up for a change. Here we multiply by an easy number that is a little too big or too small, then correct the answer.

Method. 21 is close to 20. Multiply by 20, then add 1 lot of 31.

1. Spot an easy number close by. 21 is just 1 more than 20. Multiplying by 20 is easy.
   21 = 20 + 1
2. Multiply by 20. Do the easy multiplication first.
   31 × 2 = 62, then × 10: 62 × 10 = 620
3. Work out the extra 1 lot of 31. We multiplied by 20, but we wanted 21. We need 1 lot of 31 more.
   31 × 1 = 31
4. Correct the answer. Add the extra lots.
   620 + 31 = 651
5. Write the answer.
   31 × 21 = 651

Check. Another way: 31 × 21 = 20 × 31 + 1 × 31 = 620 + 31 = 651

Watch out. Add 1 lot of 31, not just 1.

Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. It does not mean “the answer comes next”.

Method. Work out the value of the side with no missing number. The other side must have the same value.

1. Work out the left side. The equals sign means both sides are worth the same. Find the value of the side with no missing number.
   3 × 8 = 24
2. Say what the right side must be. It has to balance the left side.
   6 × ? = 24
3. Ask: how many 6s make 24? Count in steps, or use the inverse operation.
   24 ÷ 6 = 4
4. Spot the pattern. If one number gets bigger, the other must get smaller by the same factor to keep the answer.
   6 is 2 times 3, so the missing number must be 2 times smaller than 8: 8 ÷ 2 = 4.
5. Read the sentence back. Both sides must be equal.
   3 × 8 = 6 × 4 (both are 24)

Check. 6 × 4 = 24 and 3 × 8 = 24. ✓

Watch out. If you double one number you must halve the other to keep the same answer. The two sides need the same VALUE, not the same numbers.

Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. It does not mean “the answer comes next”.

Method. Work out the value of the side with no missing number. The other side must have the same value.

1. Work out the left side. The equals sign means both sides are worth the same. Find the value of the side with no missing number.
   5 × 8 = 40
2. Say what the right side must be. It has to balance the left side.
   10 × ? = 40
3. Ask: how many 10s make 40? Count in steps, or use the inverse operation.
   40 ÷ 10 = 4
4. Spot the pattern. If one number gets bigger, the other must get smaller by the same factor to keep the answer.
   10 is 2 times 5, so the missing number must be 2 times smaller than 8: 8 ÷ 2 = 4.
5. Read the sentence back. Both sides must be equal.
   5 × 8 = 10 × 4 (both are 40)

Check. 10 × 4 = 40 and 5 × 8 = 40. ✓

Watch out. If you double one number you must halve the other to keep the same answer. The two sides need the same VALUE, not the same numbers.

Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. It does not mean “the answer comes next”.

Method. Work out the value of the side with no missing number. The other side must have the same value.

1. Work out the left side. The equals sign means both sides are worth the same. Find the value of the side with no missing number.
   6 × 7 = 42
2. Say what the right side must be. It has to balance the left side.
   3 × ? = 42
3. Ask: how many 3s make 42? Count in steps, or use the inverse operation.
   42 ÷ 3 = 14
4. Spot the pattern. If one number gets bigger, the other must get smaller by the same factor to keep the answer.
   3 is 6 ÷ 2, so the missing number must be 2 times bigger than 7: 7 × 2 = 14.
5. Read the sentence back. Both sides must be equal.
   6 × 7 = 3 × 14 (both are 42)

Check. 3 × 14 = 42 and 6 × 7 = 42. ✓

Watch out. If you double one number you must halve the other to keep the same answer. The two sides need the same VALUE, not the same numbers.

Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. It does not mean “the answer comes next”.

Method. The two sides of an equals sign must have the same value. Work out the side you can, then find the missing number that makes the other side match.

1. Work out the side with no missing number. The equals sign means both sides have the same value, so we need this value first.
   4 × 15 = 60
2. Say what the other side must be. The other side has to balance, so it must also be worth the same.
   ? × 30 = 60
3. Ask the question the missing number answers. Use the inverse (opposite) operation or a fact you know.
   What do I multiply by 30 to make 60?
   60 ÷ 30 = 2
4. Write the missing number and read the sentence back. Both sides must be the same.
   2    (2 × 30 = 60)

Check. Put 2 in the box: 4 × 15 = 60 and 2 × 30 = 60. Both sides are equal. ✓

Watch out. The equals sign does not mean “now write the answer”. It means “is the same as”, so there can be a calculation on both sides.

Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. It does not mean “the answer comes next”.

Method. The two sides of an equals sign must have the same value. Work out the side you can, then find the missing number that makes the other side match.

1. Work out the side with no missing number. The equals sign means both sides have the same value, so we need this value first.
   5 × 6 = 30
2. Say what the other side must be. The other side has to balance, so it must also be worth the same.
   20 + ? = 30
3. Ask the question the missing number answers. Use the inverse (opposite) operation or a fact you know.
   What do I add to 20 to make 30?
   30 − 20 = 10
4. Write the missing number and read the sentence back. Both sides must be the same.
   10    (20 + 10 = 30)

Check. Put 10 in the box: 5 × 6 = 30 and 20 + 10 = 30. Both sides are equal. ✓

Watch out. The equals sign does not mean “now write the answer”. It means “is the same as”, so there can be a calculation on both sides.

Key words. The equals sign (=) means “is the same value as”. The two sides of an equals sign balance, like the two sides of a see-saw. It does not mean “the answer comes next”.

Method. The two sides of an equals sign must have the same value. Work out the side you can, then find the missing number that makes the other side match.

1. Work out the side with no missing number. The equals sign means both sides have the same value, so we need this value first.
   3 × 4 = 12
2. Say what the other side must be. The other side has to balance, so it must also be worth the same.
   ? − 8 = 12
3. Ask the question the missing number answers. Use the inverse (opposite) operation or a fact you know.
   What number, take away 8, leaves 12?
   12 + 8 = 20
4. Write the missing number and read the sentence back. Both sides must be the same.
   20    (20 − 8 = 12)

Check. Put 20 in the box: 3 × 4 = 12 and 20 − 8 = 12. Both sides are equal. ✓

Watch out. The equals sign does not mean “now write the answer”. It means “is the same as”, so there can be a calculation on both sides.

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 double is to multiply by 2. To halve is to divide by 2.

Method. Multiplying by 20 is the same as doubling and then multiplying by 10, because 20 = 2 × 10.

1. Multiply by 2 (double). 20 is 2 × 10. Double the number first.
   45 × 2 = 90
2. Multiply by 10. Move every digit one place to the left.
   90 × 10 = 900
3. Write the answer.
   45 × 20 = 900

Check. Estimate: 45 is about 50. 50 × 20 = 1,000. Our answer, 900, is close to 1,000. ✓

Watch out. Do both steps: double AND multiply by 10.

Key words. To compensate is to make up for a change. Here we multiply by an easy number that is a little too big or too small, then correct the answer.

Method. 98 is close to 100. Multiply by 100, then take away 2 lots of 6.

1. Spot an easy number close by. 98 is just 2 less than 100. Multiplying by 100 is easy.
   98 = 100 − 2
2. Multiply by 100. Do the easy multiplication first.
   6 × 100 = 600
3. Work out the extra 2 lots of 6. We multiplied by 100, but we wanted 98. That is 2 lots of 6 too many.
   6 × 2 = 12
4. Correct the answer. Take away the extra lots.
   600 − 12 = 588
5. Write the answer.
   6 × 98 = 588

Check. Another way: 98 × 6 = 90 × 6 + 8 × 6 = 540 + 48 = 588

Watch out. Take away 2 lots of 6, not just 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 double is to multiply by 2. To halve is to divide by 2.

Method. Multiplying by 25 is the same as multiplying by 100 and then dividing by 4 (halving twice), because 25 is a quarter of 100.

1. Multiply by 100. 25 is a quarter of 100, so first multiply by 100: move the digits two places to the left.
   16 × 100 = 1,600
2. Halve the answer. To divide by 4, halve twice. First halve.
   1,600 ÷ 2 = 800
3. Halve again. A quarter is half of a half.
   800 ÷ 2 = 400
4. Write the answer.
   16 × 25 = 400

Check. Estimate: 16 is about 20; 25 is about 30. 20 × 30 = 600. Our answer, 400, is a bit less than 600. ✓

Watch out. Halve TWICE. Dividing by 4 means halving, then halving again.

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.
   Try 8 × 5 = 40, and 8 × 10 = 80, half of 80 is 40.
   Try 13 × 5 = 65, and 13 × 10 = 130, half of 130 is 65.
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   5 is half of 10, so a number times 5 is half of the same number times 10.
3. Decide.
   Always

Check. Each example gave the same answer both ways. ✓

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.
   Try 6 × 8 = 48 and double 6 and halve 8: 12 × 4 = 48.
   Try 15 × 4 = 60 and double 15 and halve 4: 30 × 2 = 60.
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Doubling one number makes the answer twice as big. Halving the other makes it half as big. Twice and half cancel, so the answer stays the same.
3. Decide.
   Never

Check. The answer was the same every time. It never gets bigger. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Split 253 into place-value parts (partition it). Multiply each part by 3, then add the answers.

1. Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.
   253 = 200 + 50 + 3
2. Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.

   ×	200	50	3
   3	?	?	?

3. Multiply each part. Use a times table fact, then put the zeros back.
   200 × 3: 2 × 3 = 6, then 2 zeros.  600
   50 × 3: 5 × 3 = 15, then 1 zero.  150
   3 × 3 = 9
4. Write each answer in the grid. These are the partial products.

   ×	200	50	3
   3	600	150	9

5. Add the partial products. Add them one at a time. Keep a running total.
   600 + 150 = 750
   750 + 9 = 759
6. Write the answer.
   253 × 3 = 759

Check. Estimate: 253 is about 300. 300 × 3 = 900. Our answer, 759, is close to 900. ✓

Watch out. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.

Key words. To partition a number is to split it into parts, such as 47 = 40 + 7. A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each one.

Method. Split 417 into place-value parts (partition it). Multiply each part by 5, then add the answers.

1. Partition the number you are multiplying. Split it into thousands, hundreds, tens and ones. Each part is easy to multiply.
   417 = 400 + 10 + 7
2. Draw the grid and write the parts across the top. The number on the side is 5. Every part gets multiplied by 5.

   ×	400	10	7
   5	?	?	?

3. Multiply each part. Use a times table fact, then put the zeros back.
   400 × 5: 4 × 5 = 20, then 2 zeros.  2,000
   10 × 5: 1 × 5 = 5, then 1 zero.  50
   7 × 5 = 35
4. Write each answer in the grid. These are the partial products.

   ×	400	10	7
   5	2,000	50	35

5. Add the partial products. Add them one at a time. Keep a running total.
   2,000 + 50 = 2,050
   2,050 + 35 = 2,085
6. Write the answer.
   417 × 5 = 2,085