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]


Ratios can be reduced or scaled up just like fractions!



  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.





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]





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