The ten things you'll need to learn about fractions

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There is more explanation of these rules in my article: "A Year of Learning Fractions in Ten Simple Rules".

Writing and Naming Fractions 
The number on the top of the fraction is called the NUMERATOR and the number on the bottom is called the DENOMINATOR.
Reducing a fraction to it's simplest form 
Find the biggest number that will divide EXACTLY into both the top and bottom of the fraction. Divide both top and bottom of your fraction by that number and it's as simple as it can ever be.
Turning a fraction into a 'mixed' number 
Divide the top of the fraction by the bottom. You'll get an answer - usually with some remainder. The result of the division is the 'whole number' part of the mixed number - and the remainder from the division becomes the top part of the fraction. The number that was on the bottom of the fraction just stays there.
Multiplying two fractions 
Multiply the two numbers on the tops of the fractions together and put them on the top of the answer, multiply the two numbers on the bottom of the fractions together and put them on the bottom of the answer.
Dividing two fractions 
Turn the second fraction upside-down - then multiply them.
Unsimplifying 
You can "un-simplify" a fraction by multiplying it top and bottom by the same number.
Adding two fractions 
The numbers on the BOTTOM of the two fractions have to be the same before we can add them. Once the numbers on the bottom ARE the same, we can just add the numbers on the top and leave the numbers on the bottom alone.
Subtracting two fractions 
You have to get the bottom halves of the two fractions to be the same - then you can subtract the numbers on the top.
Adding, Subtracting, Multiplying and Dividing 'mixed' numbers 
Multiply the whole number part by the bottom of the fraction - and then add that to the top part of the fraction.
A fraction can't have Zero underneath 
It's not OK to have a fraction with zero underneath.