Fraction Review Fraction Review

LCM/LCD The LCD or LCM is the smallest multiple that two numbers have in common. For example: If you were comparing the numbers 2 and 3:  2 = 2, 4, 6, 8, 10  3 = 3, 6, 9, 12  The smallest number in both lists (LCM) is the #6

When do we use the LCD? WHENEVER we ADD or SUBTRACT we must find a common denominator for our two fractions. There are 3 ways to do this.

1st Way Ask your self if one of the denominators can divide evenly into the other denominator. If so, the BIGGER number is your LCD For example, ½ and ¼ Ask yourself can 2 go into 4…YES it can (twice) so 4 is your LCD.

2nd Way Make a list of the multiples of both denominators and pick out the smallest number that appears on BOTH lists. For example: ½ and ¼  2 = 2, 4, 6, 8  4 = 4, 8, 12 4 is the smallest number on both lists, so 4 is the LCM or LCD.

3rd Way Multiply both denominators by each other. For example: ½ and ¼ 2 x 4 = 8 so 8 is our common denominator BE CAREFUL …if you use this method you may have to reduce large numbers at the end of the problem

Now that you have your LCD what do you do? Rewrite the fractions using the least common denominator or least common multiple. Then add or subtract. ALWAYS reduce! 1 x2= 2 5 x = /10 = 2/5

Multiplying Fractions You must have a numerator AND a denominator to multiply. If you do not have one, put that number over 1. Then Multiply across the top and the bottom. REDUCE!!! Example:  6 x 2 3  6 x 2 = 12 = 4 1 x 3 3

Multiplying Fractions We CANNOT multiply mixed numbers, so you must change your mixed numbers into improper fractions (improper= numerator bigger than denominator)

Changing mixed numbers into improper fractions Multiply the denominator by the whole number Add the numerator to that Put that number over your denominator = (3x1) + 2 = 5 x 3 3

Changing improper fractions into mixed numbers Ask yourself how many times the denominator can go into the numerator evenly. That becomes your whole #. Then ask how many you have left over. The number left over, goes over your denominator.

Changing improper fractions into mixed numbers For example:  32 = 6 goes into 32 5 times because 6 6 x 5 = becomes my whole number. I have 2 left over because 32-30= 2. Therefore, 2 goes over my denominator. The answer is : 5 2/ /3 when you reduce!!!

Dividing Fractions When dividing, multiply the 1 st fraction by the reciprocal (flipped version) of the 2 nd fraction. For example:  1 ÷ 2 = 1 x 3 = 3/

Things to Remember REDUCE!!! (any even numerator and denominator can be reduced by 2). If you do not reduce, your answer is WRONG! If your answer is improper, you must turn it into a mixed number.