Arithmetic and pre-algebra
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Fractions
Understanding fractions conceptually, using operations with fractions, and converting 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).
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!
- Equivalent fractions
- Equivalent Fractions Example
- Comparing Fractions
- Fractions in lowest terms
- Finding Common Denominators
- Simplifying fractions
- Ordering Fractions
- Comparing Fractions 2
- Comparing fractions 1
- Equivalent fractions
- Equivalent fractions 2
- Comparing fractions 2
- Ordering fractions
- Fractions cut and copy 1
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.
- Adding Fractions with Like Denominators
- Adding fractions with common denominators
- Subtracting Fractions
- Subtracting fractions with common denominators
- Adding and subtracting fractions
- Adding Fractions with Unlike Denominators
- Adding fractions (ex 1)
- Adding fractions
- Subtracting fractions
- Adding and subtracting fractions
- Adding fractions with different signs
- Adding fractions examples
Multiplying and dividing fractions
What is 2/3 of 2/3? If I divide a dozen donuts into donut thirds, how many donut pieces will I have?
Multiplying and dividing fractions is not only super-useful, but super-fun as well.
- Multiplying Fractions
- Multiplying fractions 0.5
- Multiplying fractions by integers
- Multiplying fractions
- Multiplying Fractions Word Problem
- Multiplying fractions word problems
- Dividing fractions
- Dividing Fractions Example
- Dividing fractions 0.5
- Dividing fractions
- Dividing Fractions Word Problem
- Dividing fractions 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!
- Proper and Improper Fractions
- Fractions on the number line 2
- Comparing improper fractions and mixed numbers
- Mixed numbers and improper fractions
- Comparing improper fractions and mixed numbers
- Converting Mixed Numbers to Improper Fractions
- Changing a Mixed Number to an Improper Fraction
- Changing an Improper Fraction to a Mixed Number
- Converting mixed numbers and improper fractions
- Ordering improper fractions and mixed numbers
- Ordering improper fractions and mixed numbers
- Fractions cut and copy 2
- Points on a number line
- Fractions on the number line 3
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!
- Adding Mixed Numbers
- Adding Mixed Numbers with Unlike Denominators
- Adding Mixed Numbers Word Problem
- Subtracting Mixed Numbers
- Subtracting Mixed Numbers 2
- Subtracting Mixed Numbers Word Problem
- Adding subtracting mixed numbers 0.5 (ex 1)
- Adding subtracting mixed numbers 0.5 (ex 2)
- Adding subtracting mixed numbers 0.5
- Adding subtracting mixed numbers 1 (ex 1)
- Adding subtracting mixed numbers 1 (ex 2)
- Adding subtracting mixed numbers 1
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).
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!
- Decimals and Fractions
- Converting Fractions to Decimals Example
- Converting fractions to decimals (ex1)
- Converting fractions to decimals (ex2)
- Converting fractions to decimals
- Converting fractions to decimals
- Representing a number as a decimal, percent, and fraction 2
- Representing a number as a decimal, percent, and fraction
- Converting decimals to fractions 1
- Converting decimals to fractions 2
- Ordering numeric expressions
- Ordering numbers
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.