Introduction to multiplication Multiplication is a way of adding a number to itself a number of times. For example: 2 + 2 + 2 + 2 + 2 + 2 = 12

is the same as

6 × 2 = 12

5 + 5 + 5 + 5 + 5 = 25

is the same as

5 × 5 = 25

Multiplication is the same as repeated addition. When you multiply numbers you use the multiplication sign (×) When you’re multiplying numbers together it doesn’t matter what order you use. For example: 3 × 4 = 12

is the same as

4 × 3 = 12

2 × 8 = 16

is the same as

8 × 2 = 16

Multiplication is a quicker method of repeated addition. With repeated addition it doesn’t matter in what order you add up the numbers. For example: 4 + 4 + 4 = 12

is the same as

4 + 4 + 4 = 12

8 + 8 = 16

is the same as

8 + 8 = 16

We use different words to describe multiplication. For example, 3 × 7 = 21 can also be described as: 3 times 7 = 21 3 lots of 7 = 21 3 sets of 7 = 21 3 multiplied by 7 = 21 Checking your calculations Multiplication and division are linked. They are the opposite action of each other: 10 × 5 = 50

50 ÷ 5 = 10

or

50 ÷ 10 = 5

When you carry out a multiplication you can check your answer using division. You’ll recognise some of the calculations above from knowing your times tables. Knowing your times tables helps you to work out multiplication questions far more quickly. There are many different ways of multiplying numbers, read about them in the factsheets in this topic. You can use some of these to help you do mental maths (ie working out the answers in your head). You can use other methods when you need to write down calculations to work answers out. The important thing to remember is that everyone is different. Which multiplication method do you prefer?

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N1/E3.4

Multiplication revision Learn your times tables to help you with multiplication and division. Multiplication is a method of adding a number to itself a number of times. 2 + 2 + 2 + 2 + 2 + 2 = 12 is the same as 6 × 2 = 12 When you multiply numbers you use the multiplication sign: 6 × 2 = 12. When you’re multiplying numbers together it doesn’t matter what order you use. 3 × 4 = 12 is the same as 4 × 3 = 12 There are many different ways of multiplying numbers:

Traditional method

Lattice method

Grid or splitting method

Multiplication and division are linked. They are the opposite action of each other: 10 × 5 = 50 50 ÷ 5 = 10 or 50 ÷10 = 5

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N1/E3.4 N1/E3.5

Multiplication: splitting method There are many different ways of multiplying numbers. The method described here is the splitting (or grid) method. You can use this method to do mental multiplication. Have a read through these examples and then try them yourself. The best way to learn is to have a go. Example 1: what is 32 × 3? Steps: 1. Split 32 into tens and units: 32 = 30 + 2. 2. Multiply each number by 3: 30 × 3 = 90 and 2 × 3 = 6. 3. Add the numbers together: 90 + 6 = 96. This method can also be shown using a grid. Have a look at the next example. Example 2: you’re having a barbecue for your birthday and want to check how many vegetable burgers you have in the freezer. You have 12 boxes of 4 burgers. How many burgers do you have?

Steps:

×

10

2

1. Split 12 into tens and units and put these along the top of the grid. Put the 4 down the side of the grid.

4

2. Multiply each number in the row by each number in the column: 4 × 10 and 4 × 2.

×

10

2

4

40

8

3. Add each of the answers together: 40 + 8 = 48. You have 48 burgers - enjoy the barbecue!

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N1/E3.4 N1/E3.5

Multiplication tips When multiplying numbers you’ll start to notice lots of patterns. Here are some common patterns and other ways of multiplying that will help you become a multiplication wizard. Multiplying by 2 Multiplying by 2 is the same as doubling a number. A quick method is to split the number into tens and units and double: 2 × 13 is double 10, which is 20 plus double 3 which is 6 = 26. Tip: when you multiply by 2 you always end up with an even number. Multiplying by 4 Remember that 2 × 2 = 4. Multiplying by 4 is the same as doubling and doubling again: 4 × 15 is double 15 which is 30 and double 30 = 60. Multiplying by 10 To multiply by 10 move all the numbers one place value to the left: 10 × 8 = 80 Tens

units 8

move the number one place value to the left

tens

units

8

0

Tip: when you multiply a whole number by 10 it always ends in 0. Multiplying by 5 To multiply by 5, multiply by 10 and then halve: 5 × 62 is half of 10 × 62 which is half of 620 = 310 Tip: when you multiply a number by 5 it always ends in 0 or 5. Adjusting numbers You can round numbers up or down and then adjust to make them easier to multiply: 4 × 29 = (4 × 30) - 4 = 120 - 4 = 116 3 × 22 = (3 × 20) + 6 = 60 + 6 = 66 Splitting into factors You can split numbers into factors to make them easier to multiply: 17 × 6 = 17 × 2 × 3 = 34 × 3 = 102 Splitting into the numbers added together You can split numbers into addition facts and then multiply: 7 × 52 = 7 × (50 + 2) = (7 × 50) + (7 × 2) = 350 + 14 = 364 Checking your calculations Multiplication and division are linked. They are the opposite action of each other: 10 x 5 = 50

50 ÷ 5 = 10

or

50 ÷ 10 = 5

After multiplying you can check your answer using division.

© BBC 2011

N1/L1.3

Multiplication glossary Here are some of the words that will crop up when you do multiplication sums:

Have a look below to see how they can be used in the simple sum 2 x 2 = 4. Factors 2 is a factor of 4. One number is a factor of another number if it divides or goes into it exactly. Groups of 2 groups of 2 make 4. Lots of 2 lots of 2 make 4. Multiple 4 is a multiple of 2. Multiply If you multiply 2 by 2 you get 4. Product The product of 2 and 2 is 4. Sets of 2 sets of 2 make 4. Times 2 times 2 is 4. To find out more about maths words look in the Skillswise Glossary.

© BBC 2011

N1/L1.4

Multiplication shortcuts When multiplying by 10, 100 and 1,000 there’s a pattern that can help you get the right answer very quickly. This method moves the decimal point rather than the digits. Multiplying number

Number of places to move the decimal point

10

1

100

2

1,000

3

10,000

4

The zeros in the multiplying number tell you how many places to move the decimal point. Remember you’re making the number bigger. Make sure you move the digits (or the decimal point) in the correct direction!

When multiplying by 10, 100, 1,000 etc count the zeros to find out how much bigger your number must be.

Example Multiply 2.341 by 100: 100 has two zeros. Make 2.341 bigger by moving the decimal point two places.

© BBC 2011

N1/L1.4

Multiplying by 10, 100 and 1,000 Multiplying by 10 When you multiply a decimal number by 10 you move all the digits one place to the left. The number becomes 10 times bigger. Example: 2.63 × 10 = 26.3 You can see from the answer that the digits move to the left - units move to tens and the others follow like this:

H

T

U

2

1 10

1 100

3

2

.

6

6

.

3

H = hundreds T = tens U = units

Multiplying by 100 When you multiply a decimal number by 100 you move all the digits two places to the left. The number becomes 100 times bigger. Example: 2.63 × 100 = 263

Th

H

T

U 2

2

6

.

1 10

1 100

6

3

Th = thousands H = hundreds T = tens U = units

3

Multiplying by 1,000 When you multiply a decimal number by 1,000 you move all the digits three places to the left. The number becomes 1,000 times bigger. Example: 2.63 × 1,000 = 2,630

TTh

Th

H

T

U 2

2

6

3

.

1 10

1 100

6

3

TTh = tens of thousands Th = thousands H = hundreds T = tens U = units

0

© BBC 2011