## What Ratio is the Same as 2/3?

*A ratio equivalent to 2/3 is 4/6. Ratios are equivalent if they can be obtained by multiplying or dividing both the numerator and denominator by the same nonzero number. In this case, you can multiply both 2 and 3 by 2 to get 4/6, which is still in the same proportion as 2/3.*

## Understanding Equivalent Ratios

A ratio shows the relative sizes of two or more values. A ratio can be written in different forms but still represent the same relationship. Identifying ratios that are equivalent to a given ratio is an important skill in algebra and beyond.

Let’s look at finding ratios equal to 2/3.

## Defining a Ratio

A ratio compares two quantities using division. For example, if a bowl contains 2 apples and 3 oranges, the ratio of apples to oranges is:

Apples:Oranges 2:3

This shows the relative amount of apples is 2/3 the amount of oranges.

A ratio is unitless – it simplifies a comparison between numbers.

## Equivalent Ratios

An equivalent ratio shows the same relationship but in different numerical form.

Some ways to write ratios equivalent to 2/3 are:

- 4/6
- 6/9
- 8/12

These all reduce to 2/3 by dividing the numerator and denominator by 2.

We can also scale up:

- 20/30
- 1200/1800

These express the same 2:3 relationship as 2/3.

## Putting Ratios in Simplest Form

To find equivalent ratios, we want to reduce them to the simplest integer fraction:

8/12 = 2/3 30/45 = 2/3

Reducing by dividing out common factors gives the simplest ratio form.

Word Problems

## Equivalent ratios help solve word problems:

If a recipe uses 2 cups flour to 3 cups sugar, and I want to triple the recipe, I need a 6:9 flour:sugar ratio.

Recognizing and generating ratios equivalent to a given ratio is useful across math and real-world applications. Focusing on the underlying relationship rather than just the numbers allows us to apply ratios flexibly.

In summary, equivalent ratios express a proportion relationship in different numerical forms. Finding these aids in abstracting the meaning of ratios and using them in algebraic contexts.

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