FRACTION REVIEW
Welcome Back! Let’s recap our fraction work!
ADDING AND SUBTRACTING FRACTIONS
STEP 1. Make sure the denominators are the same or common.
If they aren’t the same find the least common multiple each of the denominators share.
For example:
1+3
2 8
The 2 and 8 are different denominators.
STEP 2: We must find a multiple they have in common to be able to add. So I must look:
2x1=2
2x2=4 2x3=6 2x4=8 2x5=10
8x1=8
8x2=16 8x3=24 8x4=32
The least common multiple is 8.
STEP 3: So I change the fractions- what you do to the numerator you MUST do to the denominator , then
STEP 4: perform the operation (ADD OR SUBTRACT).
CHANGE
THEN ADD:
4x 1 + 3 x1
4x 2
8 x1
New fractions 4 + 3
8
8
=
7
8
SIMPLIFYING OR REDUCING FRACTIONS
STEP 1: Check and find if there are any common factors that will go into (or divide into) BOTH the numerator
and denominator.
STEP 2: Divide both the numerator and the denominator by the common factor.
EXAMPLE 1:
12 12 is divisible by 12, 1, 2, 6, 3, and 4
20 20 is divisible by 20, 1, 2, 10, 4 and 5
12
20
÷4
÷4
3
5
There are several common factors- BUT- 4 is the HIGHEST
divide both the numerator and the denominator by 4 . Check to see if 3/5 is as low as this
fraction can go. Both 3 and 5 are prime so this fraction is simplified!!!!
EXAMPLE 2:
Let’s use the answer from above:
7 7 is a prime number- it is only divisible by 7 and 1
8 8 is divisible by 8, 1, 2 and 4
There are no common factors that can go into
both numbers. SO the fraction is already simplified!
FRACTIONS (CONTINUED)
MULTIPLYING FRACTIONS- Easy as pie!!
STEP 1 Multiply the numerator by the other numerator
STEP 2 Multiply the denominator by the denominator.
STEP 3 Check and see if the fraction can be simplified.
4 x
7
3 =
5
12
35
12 is divisible by 12, 1, 2, 6, 3, and 4
35 is divisible by 35, 1, 5, 7
There are no common factors
The answer is simplified
DIVIDING FRACTIONS- Tricky but not too hard
STEP 1 Find the RECIPROCAL of (or flip) the divisor fraction.
STEP 2 MULTIPLY the numerator by the numerator.
STEP 3 MULTIPLY the denominator by the denominator.
STEP 4 simplify if you can
4
7
÷ 3
=
5
4
7
X
5
3
20
21
=
****NOTE****
If it’s a mixed number
fraction you must
change it to an
improper fraction
before MULTIPLYING
OR DIVIDING!!!!!
MIXED NUMBERS
(1) Convert to improper
1
3
5
X
2 3=
4
8 x 11
5
4
(2) multiply or divide
=
88 = 88 ÷ 20 =
20
4
(3) Simplify
8 =
20
4
2
5