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Arabic Numbers --- Introduction --- Add --- Subtract --- Multiply --- Divide --- Practise sums --- Less than 1 --- Types of numbers

Multiply is sometimes also known as times.

Multiplication tables

Here are the multiplication tables laid out for you to look at. Click on numbers at the top and the side.

Patterns to help learning tables

You can spot patterns in these tables, which means that there is less to learn.

• Half the table looks the same as the other half, for example, 6 x 8 = 8 x 6.
• Certain tables are easy, such as 10x, 11x and 5x (and 1x!)
• If you look at the last digit of the 2x table, you will see that it goes 2, 4, 6, 8, 0, 2, 4, 6, 8, 0...
• 9 times a number is 10 times the number minus the number. So 9 x 7 = 10 x 7 - 7 = 70 - 7 = 63.
• 6 times an even number has the last digit the same as the number. So 6 x 8 = 48.
• I'm not quite sure why, but I found it easy to learn the squares (a number multiplied by itself). These are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. This meant that there was at least one number in each table that I knew!
• The 7x and 8x times give trouble. 56 = 7 x 8 which you can remember as it goes 5678!
• There are other rules - see the section on factors (the 3 and 9 rules are particularly clever!)
• There are finger techniques to help with 6x, 7x, 8x, 9x.

Commutative, associative and distributive

Multiplication is commutative, as 2x3 = 3x2. It is also associative, as 2x(3x4)=(2x3)x4. Multiplication is also distributive over both addition and subtraction. This means that a(b+c)=ab+ac, and a(b-c)=ab-ac.

For example:    2 x (3 + 5) = 2 x 8 = 16   and   2 x 3 + 2 x 5 = 6 + 10 = 16

For example:   7 x (4 - 2) = 7 x 2 = 14   and   7 x 4 - 7 x 2 = 28 - 14 = 14

Order of calculation

When you see a calculation with addition, subtraction, multiplication and division, you need to decide what order to do the calculation. 1+2x3 can do interpreted as (1+2)x3 which gives the answer 9, or 1+(2x3) which is 7. Simple calculators do the calculations from left to right, so give the answer 9. However, mathematicians have decided on a different order. They do anything inside brackets before aything else. Then they do division and multiplication. Finally they do addition and subtraction. So with 1+2x3, the 2x3 is done first, giving 6 and then the one is added afterwards, giving 7. This order is called BODMAS.

B - Brackets - perhaps Of (meaning division) - Division - Multiplication - Addition - Subtraction

Scientific calculators use this order. So does this arithmetic calculator. If you write down a formula for someone else to use, and you're not sure if they understand what order to do the calculation, then put in extra brackets to make sure!

Multiplication on paper

Here is how you multiply on paper rather than using a calculator.

 This example multiplies a long number 2698 by a single digit 6. You write the long number, then the single digit underneath, then draw two lines under that. Now you start the calculation. You multiply the last digit of the long number, which is 8, by 6. This gives 48. You write the units of this, the 8, between the lines in the end column. You write the tens, the 4, under the bottom line in the next column. This is called carrying the 4 forward. You can see that the red numbers do give 48. Now you move onto the next digit in the longer number, 9. If you multiply 9 by 6, you get 54. But you must also add the 4 which was carried forward. So you have 58. The 8 goes between the line and the 5 is carried forward. The next digit in the longer number is 6. You will have worked out by now that the digit we are working on is green! 6 x 6 = 36. Add 5 which was carried forward last time. You get 41 - 1 in the answer, and 4 to carry forward. Finally we multiply the first digit of the larger number, 2 by 6. This gives 12. Add the carry, 4, to give 16. No need to carry anything as we have finished the calculation, so just write 16 down. There is the answer 16188.

Practise multiplication

Click on Get sum for some practice in multiplication. When the sum appears, enter the answer in the boxes. There are boxes provided for carries, but you don't have to use them.

Long multiplication

Long multiplication, where you multiply two long numbers together, is more complicated. It depends on the fact that you can split a long number up into single digits.

234 = 2 x 100 + 3 x 10 + 4

So you can multiply a number by 234 by first multiplying it by 2 x 100, then 3 x 10, then 4, and then adding these together. Does this help? Yes, it does, because you can easily multiply by ten or a hundred. To multiply by ten, add a zero on the end of a number. To multiply by a hundred, add 2 zeroes, and so on.

Click on Get sum for a demonstration of how long multiplication works You will get different numbers each time.

Multiplication using fingers

You have to learn your multiplication tables to do multiplication on paper, and it's a good idea to learn them anyway, as simple multiplications come up all the time, in mathematics or in life, and it's much quicker to do them in your head. Most people find that they know their simple tables all right, but get confused around six, seven, eight and nine times tables. Here is a way of doing your nine times table using your fingers, and here is a way to do your six, seven, eight or nine times table using your fingers.

Multiplication using calculating machines

There have been machines which do multiplication for centuries. John Napier, a clever mathematician, invented Napier's bones to do his multiplication for him, which makes me wonder how good he was at his multiplication tables! Slide rules were used up to the 1970's. Now, of course, everyone uses calculators.

However, it's best to make sure that you can do simple sums in your head. Click here to learn to do mental arithmetic quickly and accurately!