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
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

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.

2 gallon jugs of juice

  • 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.

equivalent ratio

This will give us the answer to how many cups are in 1 gallon.

cups in a 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.

cups 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.

multiply by 5

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?

48 cups

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.

what times 16 equals 48

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.

ratios as fractions

Now you are ready to practice on your own!

Click NEXT to visit the Got It? section to practice using ratios to convert measurements.

Elephango's Philosophy

We help prepare learners for a future that cannot yet be defined. They must be ready for change, willing to learn and able to think critically. Elephango is designed to create lifelong learners who are ready for that rapidly changing future.