If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: 6th grade (Eureka Math/EngageNY)>Unit 1

Lesson 1: Topic A: Representing and reasoning about ratios

# Ratio review

Learn how to find the ratio between two things given a diagram.
A ratio compares two different quantities.
For example, those two quantities could be monkeys and bananas:
Notice that there are start color #11accd, 4, end color #11accd monkeys and start color #e07d10, 5, end color #e07d10 bananas.
Here are a few different ways we can describe the ratio of monkeys to bananas:
1. There are start color #11accd, 4, end color #11accd monkeys for every start color #e07d10, 5, end color #e07d10 bananas.
2. The ratio of monkeys to bananas is start color #11accd, 4, end color #11accd to start color #e07d10, 5, end color #e07d10.
3. The ratio of monkeys to bananas is start color #11accd, 4, end color #11accd, colon, start color #e07d10, 5, end color #e07d10.
Order matters in ratios. Here are a few different ways to describe the ratio of bananas to monkeys:
1. There are start color #e07d10, 5, end color #e07d10 bananas for every start color #11accd, 4, end color #11accd monkeys .
2. The ratio of bananas to monkeys is start color #e07d10, 5, end color #e07d10 to start color #11accd, 4, end color #11accd.
3. The ratio of bananas to monkeys is start color #e07d10, 5, end color #e07d10, colon, start color #11accd, 4, end color #11accd.

## Let's practice!

Problem 1
• Current
Dana loves rocks! She has 6 pieces of granite, 3 pieces of marble, 14 pieces of sandstone, and 1 piece of slate.
What is the ratio of pieces of sandstone to pieces of marble in Dana's collection?

## Want to join the conversation?

• Do you always need to simplify every ratio?
• If the ratios can have a way of being simplified you should.
• How do you compare two ratios? Well... let me tell you. There are still other ways to make the same comparison, by using equal ratios. To find an equal ratio, you can either multiply or divide each term in the ratio by the same number (but not zero). For example, if we divide both terms in the ratio 3:6 by the number three, then we get the equal ratio, 1:2.
• You compare two ratios by using the butterfly method. If you dont know what the butterfly method is then you can you the criss cross method.
• Why do ratios have olny two numbers
• so they can compare both the numbers
• if you have 2 apples and 3 toys is the ration 2:3
• you can also do it as a fraction
• How big can a ratio get?
• A ratio is basically a comparison of two numbers and an ratio can get as big as ∞:∞, because after all a ratio is an comparison of two numbers and that is indeed endless.
• Hey I have a question for you can you help me. Well what are the difference of a rate and a ratios I always get confused. Plz comment and help. thanks you
• Hi 🤩SOPHIALIU🌸🌺

A rate is something that allows you to express one thing in terms of another thing, this is easiest to demonstrate with an example:

Imagine you are walking to the park, the park might be 100 meters away from your house, and it may take you 1 minute to get there, the rate associated with this problem would be 100 meters per 1 second (this is the rate you are travelling at and we may write this as 100m/1sec)

A ratio is very similar to a rate, we are comparing how an amount of one thing compares to an amount of another thing, again an example may be useful:

Imagine you are making chocolate milk (by mixing chocolate powder with milk), if you mix 2 spoons of chocolate powder in 1 glass of milk this will give you a ratio of 2 spoons of chocolate powder to 1 cup of milk (we might write this as 2:1, this is our ratio)
• Can you have decimals in ratios?
• Although ratios are often given as fractions, they can also be expressed as decimals.