Number - Ratio and Proportion

A ratio compares the sizes of two or more quantities of the same kind, written in the form $a:b$ or as a fraction $\frac{a}{b}$. Visually, if you have a bag with 3 red marbles and 5 blue marbles, the ratio of red to blue is $3:5$.

Equivalent ratios are ratios that represent the same relationship. You can find them by multiplying or dividing both terms of a ratio by the same non-zero number. For example, $1:2$ is equivalent to $2:4$ and $5:10$, which can be visualized as different sized groups that maintain the same proportion of items.

Simplifying a ratio involves dividing all numbers in the ratio by their Greatest Common Factor (GCF) until they cannot be divided further. For instance, $12:18$ simplifies to $2:3$ after dividing both sides by $6$.

A proportion is an equation that states two ratios are equal, such as $\frac{a}{b} = \frac{c}{d}$. This can be visualized as a balanced scale where the relationship on the left side is identical to the relationship on the right side.

The Unit Rate is a ratio that compares a quantity to exactly one unit of another quantity, such as $60$ kilometers per $1$ hour. In a graph, the unit rate is often represented by the slope of a line passing through the origin $(0,0)$.

Sharing in a given ratio involves dividing a total amount into parts. To do this, add the terms of the ratio to find the 'total number of parts,' then divide the whole amount by this total to find the value of 'one part.' This is often visualized using a bar model where a single bar is segmented into equal blocks representing the ratio terms.

Scale Drawings use ratios to represent real-world objects at a smaller or larger size. The scale $1:100$ means $1$ unit on the drawing represents $100$ units in real life. Visually, a map is a scaled-down version of a geographic area where distances remain proportional.