Skill: Write ratios as fractions

A ratio compares two quantities in a specific order.

• The first quantity goes in the numerator.
• The second quantity goes in the denominator.

So,

$$a\text{ to }b=a:b=\frac{a}{b}$$

Example

A box has $6$ green pencils and $(10)$ yellow pencils. Write the ratio of green pencils to yellow pencils as a fraction.

Step 1: Identify the quantities in order.

The ratio is green to yellow:

• Green pencils: $6$
• Yellow pencils: $(10)$

Step 2: Put the first quantity on top and the second quantity on the bottom.

$$\text{green to yellow}=\frac{6}{10}$$

So, the ratio of green pencils to yellow pencils as a fraction is

$$\boxed{\frac{6}{10}}$$

The order matters. The ratio of yellow pencils to green pencils would be $\frac{10}{6}$, which describes a different comparison.