# Repeated addition

Repeated addition is the process of adding equal groups of objects together. It can be visualized by counting up by a specific number on a number line. For example, the number line below shows the repeated addition of 2 from 0 to 10.

This can be written in the form of a number sentence as:

2 + 2 + 2 + 2 + 2 = 10

Below are a few other examples of repeated addition.

Examples

1. 8 + 8 + 8 = 24

2. 35 + 35 + 35 + 35 = 140

Another way to visualize repeated addition is by using multiple groups of identical objects. Below, the problem 2 + 2 + 2 + 2 + 2 = 10 can be demonstrated as there being 5 groups of 2 objects that make up 1 group of 10.

## Multiplication as repeated addition

Repeated addition can be used to help teach multiplication. This is because the concept of multiplication is closely related to that of repeated addition. In the example above, we added 2 objects 5 times to get 10 objects. This is equivalent to multiplying groups of 2 objects by 5. In other words:

2 + 2 + 2 + 2 + 2 = 2 × 5 = 10

Below are some other examples equating repeated addition and multiplication.

Examples

1. 3 × 8 = 8 + 8 + 8 = 24

2. 4 × 35 = 35 + 35 + 35 + 35 = 140

We can also use repeated addition to demonstrate the commutative property of multiplication, a property of real numbers. The multiplication problem, 5 × 3 = 15, can be written in the form of repeated addition in one of two ways: 5 groups of 3, or 3 groups of 5.

(1) | 3 + 3 + 3 + 3 + 3 = 15 |

(2) | 5 + 5 + 5 = 15 |

In either case, the result is the same, which shows that the order in which the factors of a multiplication problem are multiplied does not have an effect on the final result.