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This is a cheat sheet for the fractions chapter in the Canadian curriculum of British Colombia of grade 8.
How to multiply fractions1. If you have a mixed number fraction, turn it into an improper fraction  Example: 1 1/3 x 3/6  2. Multiply your denominators  1. 1 1/3 becomes 4/3  3. Multiply your numerators  2. 3 x 6 = 18  4. Put your new numerator over your new denominator  3. 4 x 3 = 12  5. Simplify your (im)proper fraction  4. 12/18  6. Now you're done  5. 12/18 becomes 1 1/2 
How to divide fractions1. If you have a mixed number fraction, turn it into an improper fraction  Example: 1 1/4 ÷ 4/5  2. Find the reciprocal of your second fraction  1. 1 1/4 becomes 5/4  3. Now multiply your new numerators  2. 4/5 becomes 5/4  4. And...multiply your new denominators  3. 5 x 5 = 25  5. Put your new numerator over your new denominator  4. 5 x 5 = 25  6. Simplify the (im)proper fraction  5. 25/25  7. You're done  6. 1 
Mixed numbers into improper fractions1. Divide the numerator by the denominator  Example: 6/4  2. Write down the whole number answer  1. 6 ÷ 4 = 1.5  3. Write down any remainder above the denominator  2. 1  4. Simplify your fraction (if necessary)  3. 2/4  5. Put your whole number in front of your new fraction  4. 1/2  6. You're done  5. 1 1/2 
  How to add fractions1. Make your denominators the same. To do this, find the lowest common multiple of both denominators  Example: 3/4 + 7/8  2. Add your numerators  1. 4 + 4 = 8. New denominator = 8  3. Put that answer over your denominator  2. 6 + 7 = 13  4. Simplify your fraction (if necessary)  3. 13/8  5. You're done!  4. 1 3/4 
How to subtract fractions1. Make your denominators the same. To do this, find the lowest common multiple of both denominators  Example: 1/2  1/4  2. Subtract your second numerator from your first numerator  2 + 2 = 4, new denominator = 4  3. Put your new numerator over your denominator  2. 2  1 = 1  4. Simplify your fraction (if necessary)  3. 1/4  5. You're done!  4. 1/4 
Improper fractions into mixed numbers1. Multiply the whole number by the denominator  Example: 1 5/10  2. Add this number to your numerator  1. 1 x 10 = 10  3. Put that number over your denominator  2. 10 + 5 = 15  4. Simplify your improper fraction if possible  3. 15/10  5. You're done!  4. 3/2 
  Fraction termsReciprocal = the result of flipping the number upside down  1/2 = proper fraction because the numerator is smaller than the denominator  The first or top number is the numerator. Ex. 1 in 1/4  3/2 = improper fraction because the numerator is bigger than the denominator  The second or lower number is the denominator  1 1/2 = mixed number fraction because there's a whole number and a fraction combined to make one fraction  When a shape is divided into equal sections of which some have been shaded, the amount of shaded sections is the numerator and the total amount of sections, unshaded or shaded is your denominator  When there is a numerator over another fraction, you divide the lower number, top number divided by bottom number and then you divide the numerator by the new denominator 
How to simplify fractions1. Write down the factors of the numerator and the denominator until you find the lowest common multiple  Example: 6/4  2. Determine what the lowest common multiple is  1. 2, 6, 12 2, 4, 8, 12  3. Divide the numerator and the denominator by their lowest common multiple  2. 2  4. Write down the new simplified fraction  3. 6 ÷ 2 = 3 and 4 ÷ 2 = 2  5. You're done!  4. 3/2 

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