   # Ratios to Convert Meausrements

Contributor: Ashley Nail. Lesson ID: 13892

Do you know how to convert between inches and feet, or pounds and ounces? Learn how to use equivalent ratios to figure out tricky conversions!

categories

## Middle School, Pre-Algebra, Ratios, Rates, Percentages, and Proportions

subject
Math
learning style
Kinesthetic, Visual
personality style
Lion, Otter, Beaver, Golden Retriever
Middle School (6-8)
Lesson Type
Quick Query

## Lesson Plan - Get It! Eilah is helping with her mom’s small business. Eilah’s mom makes orange juice to sell at the local farmers’ market.

Eilah and her mom make large batches of orange juice and then fill gallon jugs to sell. So far, Eliah has made 32 cups of orange juice, which fills 2 gallon jugs. • Is 84 cups enough orange juice to fill 5 gallon jugs?

In order to answer Eilah’s question, we need to really figure out how many cups are in 5 gallons.

Let’s look more closely at the information we know:

There are 32 cups of orange juice in 2 gallon jugs.

This can also be written as a ratio.

32 : 2

To answer Eilah’s question, we are looking for a ratio equivalent to 32 : 2.

First, let’s find out how many cups are in just 1 gallon. This simplified ratio will help us convert measurement later.

We can divide each part of the ratio by 2 to find an equivalent ratio. This will give us the answer to how many cups are in 1 gallon. 16 cups of orange juice will fit in a 1-gallon jug.

16 : 1 is equivalent to 32 : 2

Now, we can use this equivalent ratio to find how many cups are in 5 gallons. We know to get from 1 to 5, we need to multiply by 5. Then, we multiply the other side of the ratio by 5 also. Now we know that there are 80 cups in 5 gallons.

80 : 5 is equivalent to 16 : 1 and 32 : 2

• How can we convert 48 cups into gallons? We need to figure out what number, when multiplied by 16 multiplied, will give us 48. Then, we will multiply both sides of the ratio by that number to find an equivalent ratio. 3 gallons is equal to 48 cups

These are all equivalent ratios:

• 32 : 2
• 16 : 1
• 80 : 5
• 48 : 3

To further prove that these ratios are equivalent, we can look at them as fractions. 