# Fractions

Contents

## Understanding fractions

If you don't understand fractions, you won't be even 1/3 educated. Glasses will seem half empty rather than half full. You'll be lucky to not be duped into some type of shady real-estate scheme or putting far too many eggs in your cake batter.
Good thing this tutorial is here. You'll see that fractions allow us to view the world in entirely new ways. You'll see that everything doesn't have to be a whole. You'll be able to slice and dice and then put it all back together (and if you order now, we'll throw in a spatula warmer for no extra charge).

5:41

Introduction to fractions

2:47

Identifying fraction parts

Identifying Fraction Parts

1:57

Recognizing fractions exercise

Exercise

Recognize fractions 1

Identify the fraction of a whole that is shaded.

2:31

Identifying numerators and denominators

Sal identifying numerators and denominators in fractions.

Exercise

Identify numerators and denominators

Practice identifying numerators and denominators in fractions.

3:53

Plotting basic fractions on the number line

Exercise

Fractions on the number line

Plot and spot fractions on the number line.

## Visualizing equivalent fractions

Do you want 2/3 or 4/6 of this pizza? Doesn't matter because they are both the same fraction. This tutorial will help us explore this idea by really visualizing what equivalent fractions represent.

3:45

Visualizing equivalent fractions

Sal uses fraction models to show equivalent fractions.

4:01

Equivalent fraction word problem example

Your teachers will tell you that being able to apply (or put to use) concepts helps you to learn them better. Here's a word problem in which you have to apply your knowledge of equivalent fractions.

2:01

Equivalent fraction word problem example 2

How do you find an equivalent fraction? If you know the denominator of both fractions, and the numerator of one of them...you can figure out the rest We'll show you in this word problem.

4:15

Equivalent fraction word problem example 3

We're comparing fractions using the info given in this word problem. Can you find the equivalent one?

Exercise

Equivalent fractions (fraction models)

Practice finding equivalent fractions. These problems show you pictures of fractions to help you out.

## Equivalent fractions and simplified form

There are literally infinite ways to represent any fraction (or number for that matter). Don't believe us? Let's take 1/3. 2/6, 3/9, 4/12 ... 10001/30003 are all equivalent fractions (and we could keep going)!
If you know the basics of what a fraction is, this is a great tutorial for recognizing when fractions are equivalent and then simplifying them as much as possible!

5:42

Fractions in lowest terms

Fractions in lowest terms

Exercise

Simplify fractions

Practice writing fractions in simplest form.

5:49

Equivalent fractions

Introduces the concept of equivalent fractions

4:50

Equivalent fraction word problem example 4

How may times have you been told, "Save your money!" We thought so. What if you wanted to save a fractional amount of your allowance? How would you go about figuring out how much to save?

4:42

Finding common denominators

Rewrite 2/8 and 5/6 to have the same denominator.

Exercise

Equivalent fractions

Practice making equivalent fractions by multiplying the numerator and denominator by the same number.

Exercise

Equivalent fractions 2

## Comparing fractions

In this tutorial, we'll practice understanding what quantities fractions actually represent and comparing those to each other.

5:19

Comparing fractions with > and < symbols

Sal shades visual fraction models to compare fractions.

4:48

Comparing fractions with like numerators and denominators

Exercise

Compare fractions with the same numerator or denominator

Compare two fractions that have either the same numerator or denominator.

2:30

Comparing fractions

Comparing Fractions

7:08

Comparing fractions 2 (unlike denominators)

Sal compares fractions by finding a common denominator.

Exercise

Compare fractions with different numerators and denominators

Practice comparing two fractions with different denominators with greater and less than symbols.

7:48

Comparing and ordering fractions

Finding common denominators of multiple fractions to order them

Exercise

Order fractions

Practice ordering 3 fractions from least to greatest.

## Decomposing fractions

In this tutorial, we'll see that a fraction can be broken up (or decomposed) into a bunch of other fractions. You might see the world in a completely different way after this.

4:59

Decomposing a fraction visually

Sal uses a tape diagram to decompose 7/9.

5:00

Decomposing a mixed number

Sal uses fraction models to decompose 2 1/4.

1:36

Adding up fractions

We need the sum of all the fractions to equal the given fraction. Can you help us choose which ones to use?

Exercise

Decompose fractions

Practice decomposing fractions (breaking fractions into parts that can be added together).

## Adding and subtracting fractions with unlike denominators

We've already had some good practice adding fractions with like denominators. We'll now add fractions with unlike denominators. This is a very big deal. After this tutorial, you'll be able to add, pretty much, any two (or three or four or... ) fractions!

4:25

Adding fractions (denominators 10 & 100)

Sal adds 3/10+7/100 by finding a common denominator.

Exercise

Add fractions (denominators 10 & 100)

Practice adding fractions that have denominators of 10 and 100.

9:48

Adding and subtracting fractions

How to add and subtract fractions.

4:06

How to add fractions that have different denominators

To solve this problem, we need to find the least common multiple to get at the common denominator. Can you help? We bet you can!

2:33

Example of adding fractions with unlike denominators

To add these fractions we need to find a common denominator. The answer can be expressed as a mixed number. Let's try together.

Exercise

Add fractions with unlike denominators

Practice adding fractions that have different denominators.

4:24

Example of subtracting fractions with unlike denominators

If you conquered adding fractions with different denominators, then subtracting fractions will be a snap. Don't worry...we'll take it slow and explain every step.

Exercise

Subtracting fractions with unlike denominators

Practice subtracting fractions that have different denominators.

6:22

Adding fractions with different signs

Use a number line to add fractions with different signs.

Exercise

Adding & subtracting negative fractions

Practice adding and subtracting positive and negative fractions.

## Adding and subtracting fractions

You've already got 2 cups of sugar in the cupboard. Your grandmother's recipe for disgustingly-sweet-fudge-cake calls for 3 and 1/3 cups of sugar. How much sugar do you need to borrow from you robot neighbor?
Adding and subtracting fractions is key. It might be a good idea to look at the equivalent fractions tutorial before tackling this one.

3:18

Adding fractions with like denominators

Sal adds 3/15+7/15.

Exercise

Add fractions with common denominators

Add two fractions with the like denominators.

2:26

Subtracting fractions with like denominators

Sal subtracts 8/18-5/18.

Exercise

Subtract fractions with common denominators

Solve a subtraction problem with two fractions with like denominators.

1:45

Fraction word problem: spider eyes

Sal solves a fraction word problem about spider eyes. The fractions have common denominators.

3:04

Fraction word problem: piano

Sal solves a fraction word problem about practicing piano. The fractions have common denominators.

2:29

Fraction word problem: lizard

Sal solves a fraction word problem about the length of a lizard. The fractions have common denominators.

Exercise

Add and subtract fractions: word problems 2

Practice solving word problems by adding and subtracting fractions. The fractions used in these problems have like (common) denominators.

## Adding and subtracting with unlike denominator word problems

You know what a fraction is and are now eager to apply this knowledge to real-world situations (especially ones where the denominators aren't equal)? Well, you're about to see that adding and subtracting fractions is far more powerful (and fun) then you've ever dreamed possible!

5:47

Adding fractions word problem: paint

Sal solves a word problem by adding mixed numbers with unlike denominators.

3:19

Subtracting fractions word problem: tomatoes

Sal solves a word problem by subtracting mixed numbers with unlike denominators.

Exercise

Add and subtract fractions word problems

Practice solving fraction addition and subtraction word problems. The fractions in these problems have unlike denominators.

## Multiplying fractions

What is 2/3 of 2/3? If 4/7 of the class are boys, how many boys are there?
Multiplying fractions is not only super-useful, but super-fun as well.

3:08

Multiplying unit fractions and whole numbers

Sal multiplies 1/2x5 using repeated addition and fraction models.

Exercise

Multiply fractions and whole numbers 1

Practice multiplying a whole number times a fraction.

5:06

Intro to multiplying 2 fractions

Sal introduces multiplying 2 fractions.

2:26

Multiplying 2 fractions: 5/6 x 2/3

Sal multiplies 5/6x2/3.

Exercise

Multiplying fractions

Practice multiplying two fractions.

4:33

Multiplying positive and negative fractions

See examples of multiplying and dividing fractions with negative numbers.

Exercise

Multiplying positive and negative fractions

Practice multiplying fractions. Fractions in these problems may be positive or negative.

5:06

Multiplication as scaling with fractions

Sal compares the following expressions by thinking about multiplication as scaling: 2/3x7/8, 8/7x2/3, and (5x2)/(3x5)

Exercise

Fraction multiplication as scaling

Interpret how multiplying by a fraction greater or less than 1 affects the product.

## Multiplying fractions word problems

Multiplying fractions is useful. Period. That's all we really have to say. Believe us don't believe us. You'll learn eventually.
This tutorial will have you multiplying in real-world scenarios (which is almost as fun as completely artificial, fake scenarios).

3:42

Multiplying fractions word problem: movies

Sal solves a multiplication fraction word problem about movies.

2:19

Multiplying fractions word problem: milk

Sal solves a multiplication fraction word problem about milk.

4:36

Multiplying fractions word problem: pigging out on pumpkin pie

Oops! Someone tried to solve this problem and made a mistake. See if you can spot the error.

Exercise

Multiply fractions and whole numbers word problems

Practice solving multiplication word problems that include whole numbers and fractions.

3:39

Multiplying fractions word problem: muffins

Sal solves a word problem by multiplying 2 fractions.

1:20

Multiplying fractions word problem: laundry

Sal solves a word problem by multiplying 2 fractions.

3:51

Multiplying fractions word problem: bike

Sal solves a word problem by multiplying a fraction by a mixed number.

Exercise

Multiply fractions word problems

Solve and interpret fraction multiplication word problems.

## Mixed numbers and improper fractions

We can often have fractions whose numerators are not less than the denominators (like 23/4 or 3/2 or even 6/6). These top-heavy friends are called improper fractions. Since they represent a whole or more (in absolute terms), they can also be expressed as a combination of a whole number and a "proper fraction" (one where the numerator is less than the denominator) which is called a "mixed number." They are both awesome ways of representing a number and getting acquainted with both (as this tutorial does) is super useful in life!

4:54

Comparing improper fractions and mixed numbers

Worked examples comparing improper fractions and mixed numbers

9:13

Mixed numbers and improper fractions

Converting mixed numbers to improper fractions and improper fractions to mixed numbers

1:41

Proper and improper fractions

Proper and Improper Fractions

4:26

Converting mixed numbers to improper fractions

Converting Mixed Numbers to Improper Fractions

6:43

Rewriting mixed numbers as improper fractions

Sal rewrite 5 1/4 as an improper fraction.

4:02

Rewriting improper fractions as mixed numbers

Sal rewrite 7/4 as a mixed number.

Exercise

Rewrite mixed numbers and improper fractions

Practice writing a fraction as a mixed number and vice versa.

2:12

Mixed number or improper fraction on a number line

Fraction or mixed number...either way you should end up on the same spot on the number line. Give it a try with us.

Exercise

Unit fractions on the number line

Use unit fractions to think about the location of other fractions on the number line.

Exercise

Compare fractions and mixed numbers

Practice comparing fractions and mixed numbers that have unlike denominators.

1:58

Decimals & fractions on the number line

We're mixing it up by placing both fractions and decimals on the same number line. Great practice because you need to move effortlessly between the two.

Exercise

Rational numbers on the number line

Practice placing positive and negative fractions and decimals on the number line.

## Mixed number addition and subtraction

You know the basics of what mixed numbers are. You're now ready to add and subtract them. This tutorial gives you plenty of examples and practice in this core skill!

2:06

Adding mixed numbers

Adding Mixed Numbers

5:16

Adding mixed numbers with unlike denominators

Adding Mixed Numbers with Unlike Denominators

3:22

Adding mixed numbers word problem

Adding Mixed Numbers Word Problem

3:59

Subtracting mixed numbers

Subtracting Mixed Numbers

4:54

Subtracting mixed numbers 2

Subtracting Mixed Numbers 2

4:41

Subtracting mixed numbers word problem

Subtracting Mixed Numbers Word Problem

1:35

Adding mixed numbers with like denominators

Think of a mixed numbers as a number AND a fraction. You can add numbers....you can add fractions with like denominators. Therefore, you can add mixed numbers! Watch.

2:31

Subtracting mixed numbers with like denominators

Think of a mixed numbers as a number AND a fraction. You can subtract numbers....you can subtract fractions with like denominators. Therefore, you can subtract mixed numbers! Watch.

Exercise

Add and subtract mixed numbers 1

Practice adding and subtracting mixed numbers with common (like) denominators.

2:21

Adding mixed numbers: 19 3/8 + 18 2/3

Sal adds 19 3/8 + 18 2/3 by rewriting each mixed number to have a common denominator.

2:31

Subtracting mixed numbers: 7 6/9 - 3 2/5

Sal subtracts 3 2/5 from 7 6/9 by rewriting each mixed number to have a common denominator.

Exercise

Add and subtract mixed numbers with unlike denominators 1

Practice adding and subtracting mixed numbers with different denominators. No regrouping required.

## Mixed number multiplication and division

My recipe calls for a cup and a half of blueberries and serves 10 people. But I have 23 people coming over. How many cups of blueberries do I need?
You know that mixed numbers and improper fractions are two sides of the same coin (and you can convert between the two). In this tutorial we'll learn to multiply and divide mixed numbers (mainly by converting them into improper fractions first).

4:03

Multiplying fractions and whole numbers 2

Sal multiplies 6x1/4.

4:21

Multiplying mixed numbers

Sal introduces multiplying mixed numbers.

Exercise

Multiply mixed numbers

Practice multiplying mixed numbers.

1:41

Reciprocal of a mixed number

Reciprocal of a Mixed Number

2:41

Dividing mixed numbers

Dividing Mixed Numbers

3:22

Dividing mixed numbers and fractions

Dividing Mixed Numbers and Fractions

## Decimals and fractions

If you already know a bit about both decimals and fractions, this tutorial will help build a bridge between the two. Through a bunch of examples and practice, you'll be able operate in both worlds. Have fun!

2:42

Decimal to simplified fraction

Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you.

2:17

Fraction to decimal: 7/8

Sal writes 7/8 as a decimal.

3:15

Fraction to decimal with rounding

Sal writes 21/16 as a rounded decimal.

1:33

Fraction to decimal: 11/25

Sal writes 11/25 as a decimal.

Exercise

Converting fractions to decimals

Practice converting a fraction to a decimal.

9:22

Converting fractions to decimals

How to express a fraction as a decimal

3:32

Converting percents to decimals & fractions example

Sal writes 18% as a decimal and as a fraction.

1:56

Rewriting decimals as fractions: 0.15

Sal converts 0.15 to a fraction.

0:53

Rewriting decimals as fractions: 0.8

Sal converts 0.8 to a fraction.

1:14

Rewriting decimals as fractions: 0.36

Sal converts 0.36 to a fraction.

Exercise

Rewrite decimals as fractions

Practice rewriting decimals as fractions. These problems use decimals with tenths and hundredths.

1:14

Converting decimals to fractions 2 (ex 1)

2:11

Converting decimals to fractions 2 (ex 2)

Exercise

Rewriting decimals as fractions challenge

Practice rewriting decimals as fractions. These problems use decimals with up to four decimal places.

9:22

Ordering numeric expressions

Ordering numbers expressed as decimals, fractions, and percentages

4:25

Converting a fraction to a repeating decimal

Learn how to rewrite 19/27 as a repeating decimal. What's a repeating decimal? THAT is a great question. This video explains.

Exercise

Writing fractions as repeating decimals

Practice writing fractions as repeating decimals. Get ready to bust out those long division skills!

## Dividing fractions

This is one exciting tutorial. In it, we will understand that fractions can represent division (and the other way around). Then we will create fractions by dividing whole numbers and then start dividing the fractions themselves. We'll see that dividing by something is the exact same thing as multiplying by that thing's reciprocal!

2:45

Creating a fraction through division

Sal explains how 3 ÷ 2 is the same as 3 • 1/2, which is the same as 3/2.

2:31

Mixed numbers on a number line

Sal locates 3/2 on a number line.

Exercise

Fractions as division

Practice understanding that the fraction bar really means division.

2:32

Dividing whole numbers by fractions: potpourri

Sal solves a word problem that involves dividing a whole number by a unit fraction.

2:35

Dividing fractions by whole numbers: studying

Sal solves a word problem that involves dividing a unit fraction by a whole number.

2:08

Dividing whole numbers & fractions: t-shirts

Dividing a whole number by a fraction? Turn the tables and multiply by the reciprocal of the fraction. Boom!

Exercise

Dividing unit fractions by whole numbers

Divide a unit fraction by a whole number.

Exercise

Dividing whole numbers by unit fractions 2

Practice dividing a whole number by a unit fraction.

Exercise

Divide fractions and whole numbers word problems

Solve and interpret division word problems that include whole numbers and fractions.

## Dividing fractions by fractions

In this tutorial, we'll become fraction dividing experts! In particular, we'll understand what it means to divide a fraction by another fraction. Too much fun!!!

5:42

Understanding division of fractions

Using a number line, we'll explain the rule of "invert and multiply" when dividing two fractions.

Exercise

Understanding dividing fractions by fractions

1:17

Dividing fractions: 2/5 ÷ 7/3

This is a straightforward example of dividing two fractions. We'll make super clear!

3:36

Dividing fractions: 3/5 ÷ 1/2

Let's take another stab at dividing two fractions. This time the answer should be a mixed number.

Exercise

Dividing fractions

Practice dividing fractions by fractions. No negative numbers are used in this exercise.

2:08

Dividing whole numbers & fractions: t-shirts

Dividing a whole number by a fraction? Turn the tables and multiply by the reciprocal of the fraction. Boom!

2:32

Dividing whole numbers by fractions: potpourri

Sal solves a word problem that involves dividing a whole number by a unit fraction.

4:11

Dividing negative fractions

Exercise

Dividing positive and negative fractions

Practice dividing fractions. Fractions in these problems may be positive or negative.

## Number sets

The world of numbers can be split up into multiple "sets", many of which overlap with each other (integers, rational numbers, irrational numbers, etc.). This tutorial works through examples that expose you to the terminology of the various sets and how you can differentiate them.

5:17

Number sets

Number Sets

6:17

Number sets 1

Number Sets 1

6:52

Number sets 2

Number Sets 2

2:52

Number sets 3

Number Sets 3