Write ratios as fractions

A ratio comparing one quantity to another can be written as a fraction: $a$ to $b$ or $a:b$ is represented by $\frac{a}{b}$ , with the first quantity in the numerator and the second in the denominator. This fraction expresses a multiplicative comparison, not automatically a part of a whole; reversing the terms changes the relationship. The focus is on positive whole-number quantities, without more advanced algebraic generalizations.

Detailed Explanation: 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.

Learn by doing: Write ratios as fractions

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Ratios - Calculate Item Ratio from Values

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