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### Course: 7th grade foundations (Eureka Math/EngageNY)>Unit 1

Lesson 1: Topic A: Foundations

# 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 $4$ monkeys and $5$ bananas.
Here are a few different ways we can describe the ratio of monkeys to bananas:
1. There are $4$ monkeys for every $5$ bananas.
2. The ratio of monkeys to bananas is $4$ to $5$.
3. The ratio of monkeys to bananas is $4:5$.
Order matters in ratios. Here are a few different ways to describe the ratio of bananas to monkeys:
1. There are $5$ bananas for every $4$ monkeys .
2. The ratio of bananas to monkeys is $5$ to $4$.
3. The ratio of bananas to monkeys is $5:4$.

## Let's practice!

Problem 1
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?
• You need to simplify the ratios that are able to be multiplied by each other. For example, if John had 4 apples and Susie had 12 oranges, what would the ratio apples to oranges be? The answer is or 4/12. You can see here that 12 can divide by 4, so we can simplify it easily to become 1:3. But if John had 2 apples and Susie had 11 oranges the apple to orange ratio would be or 2/11. 11 cannot be divided by two, so you cannot simplify it. Therefore only simplify the ones that can be divided by each other.
• 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.
• if you have 2 apples and 3 toys is the ration 2:3
• you can also do it as a fraction
• Why do ratios have olny two numbers
• so they can compare both the numbers
• 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?
• yes a ratio can be 3.25 apples for every 6.64 bananas :)