Fractions Study Guide
ADD/SUBTRACT/MULTIPLY/DIVIDE/SIMPLIFY FRACTIONS
The Basics
Fraction – Part of a whole
Numerator – Top number;
the parts of a whole
Denominator – Bottom
number; number of parts
the whole is divided into
Factors
What are factors? – A whole number that divides exactly into another whole
number; two numbers that multiply together to get another number
Ex. 4 × 3 = 12  4 and 3 are factors of 12
A number can have many factors
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
12 (1, 2, 3, 4, 6, 12)
Prime Numbers – A number that has exactly two factors—1 and itself; a
number that can only be divided evenly by 1 and itself.
Ex. 2 3 5 7 11 13 17 19 23 29 31 37 39
A Prime Number Will NEVER be EVEN with the EXCEPTION of 2
Simplifying Fractions
Simplify – To divide the largest number both the numerator and denominator have in common out to
make the fraction as small as possible.
Greatest Common Factor (GCF) – The largest factor that both the numerator and denominator have the
same.
24
Ex.
36
Step 1: List the factors of both the numerator and denominator.
24 (1, 2, 3, 4, 6, 8, 12, 24)
36 (1, 2, 3, 4, 6, 9, 12, 18, 36)
Step 2: Identify the GCF.
12
Step 3: Divide both the numerator and denominator by the GCF.
24 ÷ 12
2
=
36 ÷ 12
3
Equivalent Fractions
Adding and Subtracting Fractions with the Same
What are Equivalent Fractions – Can be simplified
Denominator
to the same fraction; two fractions with the same
Add/Subtract the numerators and put it over the
value.
common denominator. Then SIMPLIFY.
4
5
9÷3
3
3
6
3
12
Ex.
+
=
=
Ex. =
=
=
12
12
12 ÷3
4
4
8
12
15
9 (1 ,3, 9)
3
is in simplest terms.
4
12 (1, 2, 3, 4, 6, 12)
GCF – 3
Adding and Subtracting Fractions with Different Denominators
Least Common Denominator (LCD) – Is the least common multiple of the denominator.
Least Common Multiple (LCM) – The smallest number that is a multiple of two (or more) numbers
(Multiples – Skip Counting  2, 4, 6, 8, 10… or 3, 6, 9, 12, 15…).
1
Ex.
4
+
3
6
Step 1: Find the LCD by listing the multiples of the denominator and identifying the LCM
4, 8, 12, 16, 24, 30, 36….
Step 2: The LCM becomes the new LCD
+
1
4
12
3
6
12
6, 12, 18, 24, 36….
LCM = 12
Fractions Study Guide
Step 3: Figure out what you multiplied the original denominator by to get the new
denominator. Then multiply the numerator by the same number. (Hint: Count your multiples)
1
4
×3
×3
3
12
3
×2
6
+
6
×2
12
Step 4: Add/Subtract the numerators and put it over the common denominators then
simplify.
3+ 6
9 ÷ 3
𝟑
=
=
12
12 ÷ 3
𝟒
Multiplying Fractions
DO NOT CROSS MULTIPLY!!!!!
Ex.
3
4
×
6
10
Three Easy Steps:
Step 1: Multiply the Numerators (top number)
3
6
18
×
=
4
10
Step 2: Multiply the Denominators (bottom numbers)
3
6
4
×
10
=
18
40
Step 3: Simplify the Fraction
18 ÷ 2
=
𝟗
18 (1, 2, 3, 6, 9, 18)
40 (1, 2, 4, 5, 8, 10, 20, 40)
40 ÷ 2
𝟐𝟎
Dividing Fractions
In math terms, we say we divide fractions by MULTIPLYING BY THE RECIPROCAL
Reciprocal – Turn the fraction upside down; swap the numerator and denominator
𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
 reciprocal 
𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
We can also say we KCF the fraction or KEEP CHANGE FLIP
2
4
Ex.
÷
3
5
Three Easy Steps  K C F then SOLVE AND SIMPLIFY
Step 1: Keep the first fraction the same. Don’t Flip this one!
2
3
Step 2: Change the division sign to multiplication.
2
×
3
Step 3: Flip the second fraction. Change the second fraction to its reciprocal.
2
5
×
3
4
USE MULTIPLICATION AND SIMPLIFICATION STEPS FROM ABOVE
2
5
10
𝟓
×
=
=
3
4
12
𝟔