6.1 Everyday multiplication
Just as with addition and subtraction, there are a number of ways that you can carry out multiplication, in your head, on paper or using a calculator. You’ll probably find for more complicated examples you will need a calculator, but if you don’t have one handy remembering how to multiply on paper will be a great help. Of course, a good knowledge of the multiplication (times) tables will also be a bonus!
To make sure that you are happy with multiplying on paper have a look at a couple of examples.
Suppose that you need to work out 9 lots of £32.50 when you are out shopping.
You need to set up the calculation so that the smaller number is on the bottom, as shown below (you have to do less work then!). Working from right to left multiply each number in turn, writing the result in line with the appropriate column. If the result is greater than 9, remember you will need to carry to the next column.
If you need to multiply by a number that is 10 or more, then follow the same procedure as described in the example above to set up the calculation. Then multiply each number in the top row by each digit in the lower number in turn, finally adding up the two results.
For example, when multiplying 3965 by 25, start with the 5 and then move onto the 2. But you are not really multiplying by 2 but by 20 (2 is in the 10s place). To take this into account, add a zero to the beginning of the 2nd line of working, as shown below.
The next activity will give you a chance to practise this. Here’s a reminder of your times tables.
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
If you like you can download [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] and print a version of this table.
Activity 5 Multiplication
On a piece of paper, perform the following operations by hand.
(a) 348 × 37
Answer
Thus, the answer is 12876. (This seems reasonable since 300 × 40 = 12000.)
(b) 560 × 23
Answer
Thus, the answer is 12880. (This seems reasonable since 600 × 20 = 12000.)
You might now be wondering about multiplying by a decimal. How do you calculate something like 30 × 0.6, for example, or even 1.2 × 0.7? One way to do it is to do the calculation first without the decimal points in, and then put the decimal point back afterwards. To work out where to put the decimal point afterwards, count how many digits after the decimal point there are altogether in the numbers you started with. Then put the decimal point in the answer to give the same number of digits after the point.
For example, to calculate 30 × 0.6, you would first do the calculation without the decimal points, so 30 × 6 = 180. You now need to put the decimal point back! In the numbers you started with, there was just one digit after the decimal point (the 6 in 0.6). So you need one digit after the decimal point in the answer. Therefore the answer is 18.0
To calculate 1.2 × 0.7, you would do the calculation without the decimal points: 12 × 7 = 84. As there are a total of two digits after the point in the numbers you started with (the ‘2’ in 1.2 and the ‘7’ in 0.7) you now need to move two digits after the point in the answer. Therefore the answer is 0.84.
Now you’ve looked at multiplication, it’s time for division, a close relation of multiplication.