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Introduction

QUICK LINKS


Introduction

Adding and Subtracting Fractions

We've always found that the easiest way to understand adding and subtracting fractions is by seeing 👀 fractions in action.

Pick whichever you vibe with more:

INTRO
Think of a fraction like this:
The
denominator
,
, tells us the size of the slice. The
numerator
,
, tells us how many slices we have of that size.
So, let's say we have
big pizza, and we eat
of it.
Peep 👀 how the sizes of the slices (denominators) don’t match. So we need to do some extra work before we can subtract.
We can split up the
whole pizza into
equal slices.
See how the amount of pizza hasn’t changed, we still have
whole pizza, but now it’s split into
slices.
Nice! Now, we can easily take the
“sixth-sized” slices and subtract the
“sixth-sized” slice we ate.
Yum! Looks like we still have
“sixth-sized” slices or
of pizza left to eat! 🤤
We only subtracted the numerators, and left the common denominator alone! That’s because we needed to subtract the number of slices (numerator) not the size of the slices (denominator).
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the area of triangles and test your understanding.

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

Adding & Subtracting Fractions Calculator

Use the LCM



KEY STEPS

How to Add & Subtract Fractions

Use the LCM

Step 1. Check the denominators. If they match, skip to Step 4.

Step 2. Multiply the numerator and denominator of fraction 1 by the denominator of fraction 2.

Step 3. Multiply the numerator and denominator of fraction 2 by the denominator of fraction 1 from the original equation.

Step 4. Add/subtract the numerators, and keep the denominator the same.

LESSON
Multiplying by the Denominators

Multiplying by the Denominators

A reliable way to find the common denominator is to multiply the two denominators together.

But, when we do this, we have to make sure we multiply both the top and bottom by the same thing. Look what happens if we only multiply the denominators:

Original
Multiply by Denominator
New
Y’all see what we see?! 👀 What happened to all our pizza?! When we only multiply the denominators, the amount of pizza changes, and we end up solving an entirely different problem.
Original
Multiply by Denominator
New
Much better. 😌 We multiply the numerator and denominator, so that they change by the same factor, and the value of our fractions stay the same. That's why we have to multiply both the top and bottom.
Now let's try an example problem!

EXAMPLE 1

Let’s say we need to find the sum of
of a pizza and
of a pizza:

Step 1. Check the denominators to see if they're the same.

Looks like our denominators are NOT the same. If we think in terms of pizzas, this means that the sizes of our slices are DIFFERENT in the two fractions.
So we can't add them yet.
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore how we use the LCM to find a common denominator.
PRACTICE
Multiplying by the Denominators

Practice: Multiplying Denominators

Question 1 of 3:

Step 1. Check the denominators to see if they're the same.

Are the denominators the same?
That's right! So, we need to make the denominators the same.

Step 2. Multiply the numerator and denominator of fraction 1 by the denominator of fraction 2.

Original
Multiply by Denominator
---
New

---
Great! And now we can add/subtract.

Step 4. Add/subtract the numerators, and keep the denominator the same.


Nice work! Our answer is .
LESSON
Using the LCM

Using the LCM

We can also find a common denominator by finding the LCM, or least common multiple, of the two denominators.

Is Using the LCM Better than Multiplying by the Denominators? 🤔

Tbh… it depends on what comes more naturally to you. 🤷🏻
Both methods will always get you to the correct answer, but you may end up having to deal with larger numbers when multiplying by the denominators.
In addition, using the LCM can come in pretty handy when solving problems that involve more than two fractions.
Let's try an example!

EXAMPLE 1

Let’s try an example where we use the LCM:

Step 1. Check the denominators to see if they're the same.

Looks like our denominators are NOT the same. If we think in terms of pizzas, this means that the sizes of our slices are DIFFERENT in the two fractions.
So we can't subtract them yet.
Awesome! If you’d like to practice additional problems using the LCM, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
Using the LCM

Practice: Using the LCM

Question 1 of 3:

Step 1. Check the denominators to see if they're the same.

Are the denominators the same?
That's right! So, we need to make the denominators the same.

Step 2. Find the least common multiple (LCM) of the denominators.

Multiples
What is the LCM?
LCM:

Step 3. Multiply the numerator and denominator of fraction 1 by the number of times the denominator of fraction 1 goes into the LCM.

Original
Multiply to Get LCM
---
New

---
Great! And now we can add/subtract.

Step 5. Add/subtract the numerators, and keep the denominator the same.


Nice work! Our answer is
CONCLUSION
Sheesh, look at you go! Thanks for checking out this lesson ☺️🙏.
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