A ratio is a way to compare two quantities by using division. It shows how many times one value contains or is contained within the other.

A part to part ratio compares two different parts of a whole. For example, if there are 3 red apples and 2 green apples, the part to part ratio of red to green is 3:2.

Additive reasoning is when you think about how much more or less one quantity is compared to another. For example, if you have 5 apples and get 3 more, you think about 5 + 3.

Multiplicative reasoning is when you think about how many times one quantity is compared to another. For example, if you have 3 times as many pencils as your friend, you think about 3 x the number of pencils your friend has.

A ratio can be written in three ways: using a colon (e.g., 4:3), as a fraction (e.g., 4/3), or with the word 'to' (e.g., 4 to 3).

The ratio is 4:3.

The part to part ratio is 53:42.

The ratio is 3:5.

This is additive reasoning.

This is multiplicative reasoning.