QUICK LINKS


Introduction

QUICK LINKS


Introduction

INTRO
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A ratio is a comparison of two quantities, and a proportion is an equation that lets us know two ratios are equal to each other.

So when we solve a proportion, weโ€™re really just solving an equation, and we find that itโ€™s easiest to do this when the ratios are written as fractions.

The top and bottom of each side of the equation form the 4 corners of an x, which means we can cross-multiply to solve for the unknown.

Remember, we can only cross-multiply when we have two ratios or fractions that are equal to each other - x marks the spot!

We can also use cross-multiplication to double check that two ratios are equivalent and form a proportion:

Cross-Multiply
Resultโœ… Equal / ProportionNot equal / Not a proportion
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about solving proportions problems.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR
โ€”

Proportions Calculator



KEY STEPS
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How to Solve a Proportion

Step 1. Write the ratios as fractions.

If the ratios are already in fraction format, continue to Step 2.

Step 2. Cross-multiply if x marks the spot.

The top and bottom of each side of the equation form the 4 corners of an x.
This means we can multiply across the diagonals, and the products are equal.

Step 3. Divide.

If solving for an unknown, divide both sides of the equation by the number itโ€™s being multiplied by.
LESSON
โ€” Solving Proportions

Solving Proportions

A proportion is an equation that lets us know two ratios are equal to each other.

When we write the ratios as fractions, we can use cross-multiplication to a proportion.

x marks the spot!

Do we have to cross-multiply when the unknown variable is in the top?

While we can never go wrong with using cross-multiplication to solve proportions, if the unknown variable is in the top, we can just multiply both sides of the equation by its bottom.

Letโ€™s walk through some example problems!

EXAMPLE 1

Let's start by solving for if

Step 1. Write the ratios as fractions.

Since the ratios are already in fraction form, we just continue to Step 2.

EXAMPLE 2

Nice work! Now, solve for if

Step 1. Write the ratios as fractions.

EXAMPLE 3

Amazing! Last problem - if we know there are bad Netflix movies for every good Netflix movies, how many good Netflix movies are there if there are bad Netflix movies?

Step 1. Write the ratios as fractions.

Awesome! If youโ€™d like to practice additional problems solving proportions, expand the
Practice
below before closing out this lesson! โšก
PRACTICE
โ€” Solving Proportions

Practice: Solving Proportions

Question 1 of 10: Solve for if .

Step 1. Write the ratios as fractions.

Since our ratios are already in fraction form, we can just continue to Step 2.

Step 2. Cross-multiply.

Step 3. Divide.

Awesome job! The answer is ย .

CONCLUSION
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Incredible job, look at you go! Thanks for checking out this lesson โ˜บ๏ธ๐Ÿ™. Where to next?
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