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# Equivalent Ratios

Finding equivalent ratios can help us make many math problems much simpler to understand. But when might this skill be useful to us? How do we find equivalent ratios? Let''s find out:

## What are equivalent ratios?

We can use equivalent ratios to solve math problems based on proportionality. In other words, if the ratios remain the same, we can solve problems with greater ease.

Here''s a fairly easy example of equivalent ratios:

2:5
and
4:10

Consider this multiplication table:

1*3 = 32*3 = 63*3 = 93*4 = 125*3 = 15

Now let''s graph these numbers on a coordinate plane:

We can see that the line joining these points passes through the origin. This almost always tells us that the ratios of the coordinates are equivalent or "in proportion" to one another.

## Examples of equivalent ratios

a. Are the ratios

3:4
and
75:100
equivalent?

Yes, because we can simplify
75:100
using the greatest common factor of both 75 and 100, which is 25, to get
3:4
for both values.

b. Are the ratios
8:32
and
13:52
equivalent?

Yes, because the cross products
8*52
and
13*52
both equal 416. Both ratios are equivalent to
1:4
.

## Topics related to the Equivalent Ratios

Ratios

Word Problems: Ratios

Partitioning a Segment in a given Ratio

## Flashcards covering the Equivalent Ratios

Common Core: 6th Grade Math Flashcards

## Practice tests covering the Equivalent Ratios

MAP 6th Grade Math Practice Tests