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!


 

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.

 

 


 

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]


 

 

 

 

 

Google Matched Ad