Fractions

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.

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 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.

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!

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