Main content

## Praxis Core Math

### Course: Praxis Core Math > Unit 1

Lesson 2: Number and quantity- Rational number operations | Lesson
- Rational number operations | Worked example
- Ratios and proportions | Lesson
- Ratios and proportions | Worked example
- Percentages | Lesson
- Percentages | Worked example
- Rates | Lesson
- Rates | Worked example
- Naming and ordering numbers | Lesson
- Naming and ordering numbers | Worked example
- Number concepts | Lesson
- Number concepts | Worked example
- Counterexamples | Lesson
- Counterexamples | Worked example
- Pre-algebra word problems | Lesson
- Pre-algebra word problems | Worked example
- Unit reasoning | Lesson
- Unit reasoning | Worked example

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Ratios and proportions | Lesson

## What are ratios and proportions?

A

**ratio**is a comparison of two quantities. The ratio of a to b can also be expressed as a, colon, b or start fraction, a, divided by, b, end fraction.A

**proportion**is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.### What skills are tested?

- Identifying and writing equivalent ratios
- Solving word problems involving ratios
- Solving word problems using proportions

## How do we write ratios?

Two common types of ratios we'll see are

**part to part**and**part to whole**. For example, when we make lemonade:- The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
- The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.

To write a ratio:

- Determine whether the ratio is part to part or part to whole.
- Calculate the parts and the whole if needed.
- Plug values into the ratio.
- Simplify the ratio if needed. Integer-to-integer ratios are preferred.

**Equivalent ratios**are ratios that have the same value. Given a ratio, we can generate equivalent ratios by multiplying both parts of the ratio by the same value.

## How do we use proportions?

If we know a ratio and want to apply it to a different quantity (for example, doubling a cookie recipe), we can use

**proportional relationships**, or equations of equivalent ratios, to calculate any unknown quantities.To use a proportional relationship to find an unknown quantity:

- Write an equation using equivalent ratios.
- Plug in known values and use a variable to represent the unknown quantity.
- If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
- If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.

## Your turn!

## Things to remember

A

**ratio**is a comparison of two quantities.A

**proportion**is an equality of two ratios.To write a ratio:

- Determine whether the ratio is part to part or part to whole.
- Calculate the parts and the whole if needed.
- Plug values into the ratio.
- Simplify the ratio if needed. Integer-to-integer ratios are preferred.

**Equivalent ratios**are ratios that have the same value.

To use a proportional relationship to find an unknown quantity:

- Write an equation using equivalent ratios.
- Plug in known values and use a variable to represent the unknown quantity.
- If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
- If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.

## Want to join the conversation?

- Writing
**equivalent ratios**is mentioned in the "What Skills Are Tested?" section of this article.

What does writing an equivalent ratio of a given ratio mean? Is it the same as converting an a:b ratio to a fraction—a/b—and reducing the fraction to its simplest form, where the denominator and numerator have no common factors?

Conversely, can an equivalent ratio of a given ratio also mean multiplying the numerator and denominator of the fraction with the same number?

In other words, are the following two examples of equivalent ratios correct?

Example A:

24:3 = 24/3 = 8 = 8:1

Example B:

1:2 = 1/2 = 4/8 = 4:8(7 votes)- Both of your examples of equivalent ratios are correct. Good job!(13 votes)

- Why does it have to be hard?(10 votes)
- Why does it have to be hard?(5 votes)

- Hello! Why does Sal always do easy examples and hard questions?(6 votes)
- I think that it is because he shows you the skill in a simple way first, so you understand it, then he takes it to a harder level to broaden the variety of levels of understanding.(2 votes)

- hard i dont understand this(5 votes)
- why is this ratio HA:RD(3 votes)
- do non understand that much(2 votes)
- I'm kind of stuck not gonna lie on the last one(2 votes)
- what do the letters a and b represent?(1 vote)
- Nothing, they're just showing the positions of numbers(2 votes)

- Can you explain how a ratio without fractions works?(1 vote)
- I need help pls... PLSSS(1 vote)