A ratio is used to describe how two or more quantities are related.

For example, we might say that a fruit drink calls for sugar crystals to be mixed with water in a ratio of 2:6. This means that for every 2 scoops sugar crystals, there will need to be 6 ounces of water. If there were 200 scoops of sugar crystals, there would need to be 600 ounces of water.

Finding equivalent ratios

The ratio of sugar crystals to water in the example above was 2:6, but this could be written as 200:600, or 10:30, or 6:18. These ratios are equivalent because they have the same meaning - the amount of water is three times the amount of sugar crystals.

You can find equivalent ratios by multiplying or dividing both sides by the same number. This is similar to finding equivalent fractions. Some examples of finding equivalent ratios are shown on the right. All the ratios in the diagram are equivalent.

When equivalent ratios are graphed, they always form a straight line that goes through the origin.

Writing a ratio in its simplest form
A ratio is in its simplest form when both sides are whole numbers and there is no whole number that both sides can be divided by. In the fruit drink example above, 2:6 was the original ratio given, but 1:3 is the simplest form of the ratio.

To write a ratio in its simplest form, keep dividing both sides by the same number until you cannot go any further without going into decimals.

Example: write 160:240 in it's simplest form

160:240

(divide both sides by 4)

40:60

(divide both sides by 2)

20:30

(divide both sides by 5)

4:6

(divide both sides by 2)

2:3

SIMPLEST FORM

Directions:

Create a ratio of your choosing. Notice the point moving as you create your ratio.

Use the "reveal" slider to show equivalent ratios to the one you created.

Equivalent ratios ALWAYS form a line going through the origin!

Self-Check

Q1: Are $\frac{10}{12}\mbox{ and }\frac{35}{42}$ equivalent ratios? Yes/No [show answer]

Yes...because both ratios reduce to $\frac{5}{6}$

Q2: Are $\frac{4}{6}\mbox{ and }\frac{12}{24}$ equivalent ratios? Yes/No [show answer]

No...because 4x3=12, but 6x4=24. Since 4 and 6 are not multiplied by the same number, the two ratios are NOT equivalent.

Q3: Which ratio is NOT equal to all the others? $\frac{4}{6}\mbox{ , }\frac{6}{9}\mbox{ , }\frac{8}{12}\mbox{ , }\frac{10}{12}\,\,\,$ [show answer]

$\frac{10}{12}$ because it reduces to $\frac{5}{6}$, but all the other ratios reduce to $\frac{2}{3}$.