# Multiplication

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BRAIN-TEASER!

Calculate the following in the same way as the Egyptians did thousands of years ago:

15 × 241

• Is there an easier way of doing it? Discuss this with your friend. Check your answer with a calculator.

DID YOU KNOW?

Thus we can also make use of DOUBLING when we want to multiply:

2 × 280 = (200 + 200) + (80 + 80)

= 400 + 160

= 560

## To use a series of techniques to do computations with whole numbers [lo 1.10.4]

1. If you looked carefully at the example above, you would have seen that this method of doubling differs from that of the Egyptians. Can you calculate the following by doubling it in exactly the same way?

1.1 2 × 1 430 =

1.2 2 × 2 315 =

2. We would very much like to use the shortest possible method in Mathematics, because it saves a lot of time, trouble and paper. Calculate the product again by doubling, but this time use a shorter method if you can.

2.1 2 × 14 820 =

2.2 2 × 36 947 =

3. There is another technique that you can use to calculate the product. You can double and halve ! This makes it easier to multiply with the “big” numbers. Look carefully at the following:

126 × 5= 63 × 10 (halve 126 ; double 5)= 630

Can you find the following answers by doubling and halving ?

 3.1 50 × 24 3.2 5 × 346

BRAIN-TEASER!

Can you fill in the missing numbers/factors WITHOUT using your calculator?

 48 × 12 = 576 64 × 10 = 640 ........... × 24 = 576 32 × ........... = 640 12 × ........... = 576 ........... × 40 = 640 6 × ........... = 576 8 × ........... = 640 ........... × ........... = 576 ........... × ........... = 640

Did you discover a pattern?

## To calculate by using selected computations [lo 1.9.2]

1. Now let us look at multiplication with multiples of 10 and 100. As we work through the examples, you will see that there are certain rules that you must follow in order to calculate the product. If you apply these rules, you will be able to calculate the answers without doing long computations on paper. Work with a friend and write down the product of the following:

1.1 10 × 6 = ......................... ; 10 × 60 = ......................... ;

10 × 600 = ......................... and 10 × 6 000 = .........................

1.2 10 × 9 = ......................... ; 10 × 90 = ......................... ;

10 × 900 = ......................... and 10 × 9 000 = .........................

1.3 10 × 15 = ......................... ; 10 × 150 = ......................... ;

10 × 1 500 = .........................

1.4 10 × 26 = ......................... ; 10 × 260 = ......................... ;

10 × 2 600 = .........................

Can you now write down a rule for multiplying any number by 10?

Does this “work” for 0,5 × 10?

2. Let us look at multiplication with multiples of 100. Work with the same friend and write down the product of:

2.1 100 × 8 = ......................... ; 100 × 80 = ......................... ;

100 × 800 = .........................

2.2 100 × 13 = ......................... ; 100 × 130 = ......................... ;

100 × 1 300 = .........................

2.3 100 × 27 = ......................... ; 100 × 270 = ......................... ;

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