## Simplifying ratios 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? [show answer]   $\large\frac{\mbox{spoons}}{\mbox{glasses}}=\frac{2}{6}=\frac{1}{3}$

Ratios can be reduced or scaled up just like fractions!

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

# Self-Check

Q1: What is the ratio of yellows to the total number of tiles in simplest form? [show answer]

Q2: In the word "PROPORTION" what is the ratio of consonants to vowels in simplest form? [show answer]

Q3: The chess club at school has 18 boys and 15 girls in it. What is the ratio of girls to boys in simplest form? [show answer]