Equivalent ratios and equivalents fractions are used to demonstrate that 2 quantities are the same. We can create equivalent ratios by multiplying the numerator and denominator by the same factor. This is true with ratios written in all forms including fractions.

## Finding Equivalent Ratios

If two ratios have the same value, they are equivalent. We can use a scale factor to test whether 2 ratios are in fact equivalent. If the ratios are written as fractions, cross multiplication can be used to test whether are not the ratios are equivalent.

## Different Numbers but Same Relationship

Even though the numbers are different, the relationship between the numbers is the same. The ratio is the expression of the relationship, not the individual numbers that make the ratio or fraction.

## The Purpose of Equivalent Ratios

When it is difficult or impossible to find quantities directly through measurement or some other means, equivalent ratios allow for finding the quantities indirectly.

## Equivalent Ratios in Real Life

Equivalent ratios are helpful when comparing prices when items are priced dynamically. They are helpful in calculating travel time. They are commonly used with measurement when direct measurement is impossible. Equivalent ratios are used by professionals in financial, medical, and engineering fields.

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