## Multiplying Larger Whole Numbers

#### Introduction

Multiplying large numbers follows the same principles as multiplying small numbers. However, all of the different values (for example, if you're multiplying four or five digit numbers) can be confusing, so most people instinctively reach for a calculator. However, if you break the numbers down, you can make the process simple, so that there are no numbers you can't multiply without a calculator.

#### Terms

## Lesson

To multiply large numbers you can break them down into their separate units. For example, 287 is 200, 80, and 7.

*One key rule to remember is that if you're multiplying numbers ending in one or more zero (e.g. 400) you can just multiply the first digit and then add the zeros back on the end of the answer. For example, to do 400 x 3, you can multiply 4 x 3 (which equals 12) then put the two zeroes back on the answer (1200).*

To multiply two large numbers make a multiplication table. Let's take the following multiplication:

789 x 64 = ?

We would begin by breaking the numbers up. 789 becomes 700, 80, and 9; 64 becomes 60 and 4. Then we enter the numbers into a table. One number goes across the top row, and one number goes down the first column.

60 | 4 | |
---|---|---|

700 | ||

80 | ||

9 |

Now we fill in the table, multiplying each square by the number at the top of its row and column. Let's start with the square with a * in it:

60 | 4 | |
---|---|---|

700 | * | |

80 | ||

9 |

The two numbers we are multiplying here are 60 (at the top of the column) and 700 (on the left of the row). To do 60 x 700, we can use the principle above. There are three zeroes in the equation, so we make a note of that, and then multiply 6 and 7.

6 x 7 = 42

Then we add the three zeroes back on to give us 42,000. We can then enter that in the square.

60 | 4 | |
---|---|---|

700 | 42,000 | |

80 | ||

9 |

We can then go through the rest of the table and fill in the values.

60 | 4 | |
---|---|---|

700 | 42,000 | 2,800 |

80 | 4,800 | 320 |

9 | 540 | 36 |

Now we've filled in the table, we add up the results of each row. For example, the results of the top row are 42,000 and 2,800. Adding them together gives us 44,800. We can put this in the 'Total' column.

60 | 4 | Total | |
---|---|---|---|

700 | 42,000 | 2,800 | 44,800 |

80 | 4,800 | 320 | |

9 | 540 | 36 |

Now we repeat the process for the other two rows:

60 | 4 | Total | |
---|---|---|---|

700 | 42,000 | 2,800 | 44,800 |

80 | 4,800 | 320 | 5,120 |

9 | 540 | 36 | 576 |

The final step is to add up all the values in the 'Total' column:

44,800 + 5,120 +576 $overline{50,496}$

Therefore:

**789 x 64 = 50,496**

## Examples

2 | 9 | |||

* | 4 | 4 |