# Multiplication '×' | Basics of Arithmetic

See also: Ordering Mathematical Operations**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 operation.

In order to perform multiplication calculations 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 4 multiplied by 3 is the same as saying 4 + 4 + 4 = 12. Multiplication is therefore a quicker way of adding the same number many times, for example 3 × 4 = 12. This calculation is the same as saying, if I have 3 bags of 4 apples, how many apples 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 write a 0 at the end (there is one zero in 10 because it is 1 × 10). 200 × 10 = 2000.
- When multiplying by 100 we write two zeros at the end, by a thousand we write three zeros at the end and so on. 4 × 2000 for example is 4 × 2 = 8 with 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 multiplications up to 10 × 10. To obtain 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 intersect 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 |

The table above can help us 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? We need to calculate 4 lots of £8, which is written 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 intersect: **32**. The cost of the trip to the cinema will therefore be **£32**.

It is often necessary to multiply numbers that are bigger than 10. In this case the multiplication table above cannot give an immediate answer. However, we can still use it 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?

23 businesses each need 14 sandwiches, which is 23 lots of 14 or, in other words, 23 multiplied by 14. As we have already discovered, we could write the calculation the other way around. 14 × 23. The answer will be the same.

**We need to find the answer to the calculation 23 × 14.**

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

Hundreds | Tens | Units |

2 | 3 | |

1 | 4 |

**Step 1:** Starting in the right-hand column (units) multiply 4 and 3. You can refer to the multiplication table above if needed. Write the answer (12) underneath your calculation, taking care to put the 1 in the tens column and the 2 in the units column.

The blue numbers are the ones we are currently working on and the pink numbers are the first part of our answer.

Hundreds | Tens | Units |

2 | 3 | |

1 | 4 | |

1 | 2 |

**Step 2:** Next we multiply the 4 by the next number across, which is 2 (or 20, because it is in the tens column). Write your answer underneath in the tens column: We write 8 in the tens column (4 times 2 tens) and zero in the units column (4 times 2 tens is the same as 4 × 20 = 80).

Hundreds | Tens | Units |

2 | 3 | |

1 | 4 | |

1 | 2 | |

8 | 0 |

**Step 3:** In the steps above, we have multiplied the units of the bottom number (4) by the top number (23). Next we need to multiply the tens in the bottom number (1) by the top number (23). Now we are working with the digit in the tens column of the bottom number and we repeat the steps above. Looking back at our basic rules of multiplication above, we know that when we multiply a number by 10, we write a zero at the end. In this step, because we have moved over a column and we are working in tens, we must remember to write zeros in the first (units) column.

Work out 1 × 3. As above, we write our answer (3) in the tens column and (0) in the units column.

Hundreds | Tens | Units |

2 | 3 | |

1 | 4 | |

1 | 2 | |

8 | 0 | |

3 | 0 |

**Step 4:** The final multiplication we need to perform is 1 × 2. Both the numbers are in the tens column, so we are multiplying one lot of 10 by two lots of 10. Using the rules we have learned in the previous steps, we need to write a zero in the units column **and** a zero in the tens column. Our answer (1 × 2 = 2) is written in the hundreds column, because we have actually calculated 10 × 20 = 200.

Hundreds | Tens | Units |

2 | 3 | |

1 | 4 | |

1 | 2 | |

8 | 0 | |

3 | 0 | |

2 | 0 | 0 |

**Stage 5:** At this stage we have finished our multiplications; 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 if you need 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 split into all possible parts, but 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 Than Two Numbers

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

**Joe works 7 hours a day, 5 days a week for four weeks.**

**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.

If we know that Joe gets paid £12 an hour, we can then 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 has therefore earned £1,680 during the four week period.**

Multiplying Negative Numbers

Multiplying a negative number by a positive number always gives a negative answer:

15 × (−4) = −60

Multiplying a negative number by another negative number always gives a positive answer:

(−15) × (−4) = 60