Multiplication '×' | Basics of Arithmetic

See also: Numbers

This page covers the basics of Multiplication (×).

See our other arithmetic pages, for discussion and examples of: Addition (+), Subtraction (-) and Division (÷).

Multiplication

When writing, the common sign for multiplication is ‘×’.  In spreadsheets and some other computer applications the ‘*’ symbol (or asterisk) is used to indicate a multiplication sum.

In order to perform multiplication sums without a calculator or spreadsheet you will need to know how to add numbers.  See our Addition page for help with adding.

When you ‘multiply’ or ‘times’ a number you add it to itself a number of times, for example 3 multiplied by 3 is the same as saying 3 + 3 + 3 = 9.  Multiplication however is a quicker way of adding the same number many times 3 × 3 =9.  This calculation is the same as saying, if I have 3 lots of 3 widgets, how many widgets do I have in total?

Basic Rules of Multiplication:


  • Any number multiplied by 0 is 0.  200 × 0 = 0
  • Any number multiplied by 1 stays the same.  200 × 1 = 200.
  • When a number is multiplied by two we are doubling the number.  200 × 2 = 400.
  • When a whole number is multiplied by 10 we can simply add a 0 to the end (there is one zero in 10).  200 × 10 = 2000.  When multiplying by 100 we add two zeros to the end, by a thousand we add three zeros to the end and so on.  4 × 2000 for example is 4 × 2 = 8 plus 3 zeros: 8000.

For simple and quick multiplication it is useful to memorise the multiplication or 'times table’ as shown below.   This table gives the answers to all multiplication sums up to 10 × 10.  To find the answer to 4 × 6 for example find 4 on the top (red shaded) line and find 6 on the left hand (red shaded) column – the point where the two lines intercept is the answer:  24.

It doesn't matter which way around you search for the numbers, if you find 4 in the first column and 6 in the first row you get the same answer, 24.

Multiplication Table

× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100


By using the table above you can quickly calculate the answer to the following problem. Megan is taking her three brothers to the cinema, she needs to buy 4 tickets in total, and each ticket costs £8. How much will the total cost of the trip be? The sum here is 4 × 8.

Find 4 on the vertical red column and 8 on the horizontal red column, the answer is in the cell where the two lines intercept: 32. The cost of the trip to the cinema will therefore be £32.


Often it is necessary to multiply numbers that are bigger than 10 and therefore the above multiplication table cannot give an immediate answer. However we can still use the multiplication table to make the calculation easier.

Lisa runs a catering business, she has to deliver sandwiches to 23 businesses each with 14 employees – assuming each employee eats one sandwich how many sandwiches does Lisa have to make?

The sum we need to preform here is 23 × 14 (that is 23 businesses each needing 14 sandwiches). As we have already discovered we could write the sum the other way around 14 × 23 – the answer will be the same.

First write your numbers in columns representing hundreds, tens and units (See our Numbers page for help).


Hundreds Tens Units
  2 3
  1 4

Next, starting in the right hand column (units) multiply 4 and 3 – refer to the multiplication table above if needed. Write your answer underneath your sum.

The blue numbers are the ones we are currently working on and the pink numbers are the partial answer.

Hundreds Tens Units
  2 3
  1 4
  1 2

Next multiply the 4 by the next number across (in the tens column) 2 or 20. Write your answer underneath in the tens column. The answer is written into the tens column (8) as we are working in the tens column above. Add a zero to the units column for clarity.

Hundreds Tens Units
  2 3
  1 4
  1 2
  8 0

Next move to the tens column of the bottom number and repeat the steps above. However, as we have moved over a column we must remember to write zeros in the first column. Work out 1 × 3.

Hundreds Tens Units
  2 3
  1 4
  1 2
  8 0
  3 0

The final multiplication we need to preform is 1 × 2. Both the numbers from the tens column, this being so we need to write our answer in the hundred’s column and add zero’s (for clarity) to the tens and units column.

Hundreds Tens Units
  2 3
  1 4
  1 2
  8 0
  3 0
2 0 0

At this stage we have finished our multiplication; the only step that remains is to add up all our answers (pink numbers) to find the total number of sandwiches needed. (See our Addition page for help with adding up numbers)

Hundreds Tens Units
  2 3
  1 4
  1 2
  8 0
  3 0
2 0 0
Total: 3 2 2

12 + 80 + 30 + 200 = 322. We have calculated that Lisa needs to make a total of 322 sandwiches.

The above example shows how to perform a multiplication sum split into all possible parts, as confidence improves it is possible to skip steps.

We could for example multiply the 4 by 23 by breaking the sum down:

4 × 20 = 80
4 × 3 = 12
80 + 12 = 92

Hundreds Tens Units
  2 3
  1 4
  9 2

Then the same for the second column:

10 × 23 = 230

Hundreds Tens Units
  2 3
  1 4
  9 2
2 3 0

Finally we add our two answers:

  Hundreds Tens Units
  2 3
  1 4
  9 2
2 3 0
Total: 3 2 2

92 + 230 = 322.


Multiplying More Numbers

If you need to multiply more than two items together then it is usually easier to multiply the first two items, get a total and then multiply the next number to that. For example if Joe wanted to work out how many hours he had worked in a four week period then the calculation would look something like:

Joe works 7 hours a day, 5 days a week.

Step one:

7 × 5 = 35 (The number of hours Joe works in one week).

Step two:

To find how many hours Joe works in four weeks we can then multiply this answer (35) by 4. 35 × 4 = 140.

Furthermore, if we know that Joe gets paid £12 an hour then we can calculate how much money he earned in the four week period: 12 × 140.

The quick way to work this out is to calculate:
10 × 140 = 1400 (remember that if we multiply by 10 then we simply add a zero to the end of the number we are multiplying by).
2 × 140 = 280 the same as 2 × 14 (with a zero on the end) or 140 + 140.

We add our answers together: 1400 + 280 = 1680.

Joe therefore has earned £1,680 during the four week period.

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