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# Using the Multiplication Table

by Ron Kurtus (updated 18 January 2022)

A * Multiplication Table*is a tool to help in learning the multiplication of two single digit whole numbers. A whole number is a counting number (

**1**,

**2**,

**3**...) along with

**0**. Single-digit means that the number only has one digit. For example,

**7**is a single-digit number, while

**27**has two digits.

It is worthwhile to memorize the multiplication of any two single-digit whole numbers between **0** and **9**.

Questions you may have include:

- What is the product of any two single-digit numbers?
- What are some examples?
- How does counting by a number help?

This lesson will answer those questions.

## Multiplying two numbers

A single-digit number consists of only one digit. These are the whole numbers between **0** and **9**. For example, **3** is a single digit number, while **23** is not because it consists of two digits

(**2** and **3**).

It is important to memorize the product of every two single digit numbers, because that knowledge is used in so many arithmetic calculations. The following table can be used to aid in learning those products.

× | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

2 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |

3 | 0 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |

4 | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |

5 | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |

6 | 0 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 |

7 | 0 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 |

8 | 0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 |

9 | 0 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 |

Pick a number along the top row and multiply it times to a number from the first column.

## Example of using the table

For example, use the table to multiply **6** times **4**.

Pick **6** from the top row and go down to **4** in the first column. The product of the two numbers,** 6 × 4**, equals **24**. You should memorize that.

× | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

2 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |

3 | 0 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |

4 | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |

5 | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |

6 | 0 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 |

7 | 0 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 |

8 | 0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 |

9 | 0 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 |

### Notes

Note that multiplication does not depend on the order of the numbers. In other words **6 × 4 = 4 × 6 = 24**. Check to verify that.

Also note that **0** times any number is **0**.

### 3 × 9

Now use the table to multiply **3 × 9** and **9**** × 3**. Your answer should be **27**. You should memorize those products.

## Counting exercises

A way to help you learn the multiplication of single digit numbers is by counting by a number. Some examples are below.

### By 2

Count by **2** (skipping **0**): **2**, **4**, **6**, **8**, **10**, **12**, **14**, **16**, **18**... That is easy, but you can also note that this series corresponds to the numbers in the **2** row and column.

### By 9

Now try counting by **9** (skipping **0**): **9**, **18**, **27**, **36**, **45**, **54**, **63**, **72**, **81**...

This will help you multiplying by **9**.

Some interesting things about multiples of **9** can be seen from this series.

First of all, the sum of the digits equals **9**. For example, for **72**: **7 + 2 = 9**. This is even true for larger numbers in this series. **13 × 9 = 117** and **1 + 1 + 7 = 9**.

Also in the series above, the first digits go up by **1** and the second digits go down by **1**.

## Summary

You can use a multiplication table to multiply single digit numbers together. This is a handy way to learn your multiplication. Note that the order of the numbers in multiplication does not matter. **2 × 3 = 3 × 2**. Finally, practicing counting by a number is a good way to get a feeling of the products.

Use tools to learn

## Resources and references

### Websites

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## Students and researchers

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**www.school-for-champions.com/arithmetic/
multiplication_table.htm**

Please include it as a link on your website or as a reference in your report, document, or thesis.

## Where are you now?

## Using the Multiplication Table