In this figure, it is easy to see that the ratio of yellows to greens is $\frac{6}{8}$. If we put circles around each column of tiles

we can see that the ratio of yellow columns to green columns is $\frac{3}{4}$.

Since the number of tiles never changed - only how we looked at them - this shows that the ratios $\frac{6}{8}$ and $\frac{3}{4}$ are equivalent to each other. In other words, $$\frac{6}{8}\,=\,\frac{3}{4}$$

Ratios can be reduced just like fractions!

Example 1

There are 12 boys and 16 girls in a class.

• What is the ratio of boys to girls in simplest form?
• What is the ratio of boys to girls to total in simplest form?

Example 2

What is the ratio of spoons to glasses in simplest form?

Directions:

1. The ratio is randomly created and plotted on the graph.
2. Reduce the blue ratio.
3. Use the sliders to create the ratio in simplest form. Point B moves as you create the ratio.
4. The ratio in simplest form will ALWAYS lie somewhere on the dotted line.