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Maths

Long multiplication and division

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For both long multiplication and long division, there is an alternative to the traditional method. You can use whichever you prefer.

# Long multiplication

There are two main methods for long multiplication:

2. Boxes method

Choose one method to revise.

This is where we multiply by the units and the tens separately, then add the two rows together.

To calculate 158 × 67:

First, multiply by 7 (units):

•  158
• x 67
• ____
• 1106

Then add a zero on the right-hand side of the next row. This is because we want to multiply by 60 (6 tens), which is the same as multiplying by 10 and by 6.

Now multiply by 6:

•  158
• x 67
• ____
• 1106
• 9480

•   158
•  x 67
• _____
•  1106
•  9480
• _____
• 10586

Question

A box contains 36 tins of sweetcorn. Each tin weighs 475 grams. What is the total weight of the tins in the box.

You needed to multiply by 6, add a zero on the line below and then multiply by 3, before adding the two rows together.

If you had a problem you may need to practise your times tables. Here is a worked solution:

•   475
•  x 36
• ______
•  2850
• 14250
• ______
• 17100

## Boxes method

This is where we split each number into its parts.

To calculate 158 × 67:

158 is 100, 50 and 8.

67 is 60 and 7.

We arrange these in a rectangle and multiply each part by the others. You need to be able to understand multiplying with powers of 10 to know how many zeros to put on the end.

158 x 67
100508
6060003000480
770035056

We have worked out 100 × 60, 100 × 7, 50 × 60, 50 ×7, 8 × 60 and 8 × 7.

When this has all been done, you have to write out all the answers and add them together:

•  6000
•  3000
•   480
•   700
•   350
•     56
• ______
•  10586

Question

A box contains 36 tins of sweetcorn. Each tin weighs 475 grams. What is the total weight of the tins in the box?

Did you get the answer 17100 grams?

You needed to work out 400 × 30, 400 × 6, 70 × 30, 70 × 6, 5 × 30, 5 × 6, and add them together.

If you had a problem, perhaps you need to revise both your times tables and multiplying by 10.

For example 400 × 30 is the same as 4 × 3 = 12 followed by 3 zeros, because there are 3 zeros altogether in 400 and 30. So 400 × 30 = 12000.

Here is a worked solution using the boxes method:

475 x 36
400705
30120002100150
6240042030

• 12000
•  2100
•    150
•  2400
•    420
•     30
• _____
• 17100

So the answer is 17100 grams.

Remember that you are not allowed to use a calculator in one of your written GCSE papers, so you will need to be able to solve long multiplication and division problems on paper, showing all your workings out.

Check with your teacher to make sure you know which paper is the non-calculator exam.

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