A ratio is a comparison of two quantities that describes how much of one thing there is compared to another. Ratios are commonly represented using colon notation or as fractions. They are read as the ratio of $a$ to $b,$ where $b$ is a non-zero number.

The ratio $a:b$ means that for every $a$ units of one quantity, there are $b$ units of another quantity. Ratios can be part-to-part or part-to-whole.

	Part-To-Part	Part-To-Whole
Explanation	Describes how two different groups are related	Describes the relationship between a specific group to a whole
Example $1$	The number of sophomores to freshmen on the basketball team is $7:15.$	The number of sophomores to all basketball team members is $7:22.$
Example $2$	The number of mangoes to jackfruits the vendor has is $10:20.$	The number of mangoes to all fruits the vendor has is $10:42.$

Ratios that express the same relationship between quantities are called equivalent ratios. For instance, consider the ratios of pages read per minute by Tearrik and by Zain. These ratios can be simplified by finding the greatest common factor of their numerator and denominator. That factor can then be used to rewrite each ratio.

	Fraction Form	Greatest Common Factor	Rewrite	Simplify
Tearrik	$\frac{27}{15}$	$\text{GCF}(27,15)=3$	$\frac{9\cdot \cancel{3}}{5\cdot \cancel{3}}$	$\frac{9}{5}$
Zain	$\frac{45}{25}$	$\text{GCF}(45,25)=5$	$\frac{9\cdot \cancel{5}}{5\cdot \cancel{5}}$	$\frac{9}{5}$

These ratios are equivalent because both simplify to $\frac{9}{5}.$ Equivalent ratios can be created by multiplying or dividing the numerator and denominator of a ratio by the same number.