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Working with Fractions
ADDITION/SUBTRACTION
LCD
It is necessary to find a Least Common Denominator (LCD) when adding or subtracting fractions.
The Least Common Multiple (LCM) of the denominators is called the LCD.
Example:
Add
3
8
1
.
6
Finding the LCD
Method 1
List the multiples of each denominator and find the smallest one common to both lists.
Multiples of 8: 8, 16, 24, 32…
Multiples of 6: 6, 12, 18, 24, 30…
Method 2
LCD = 24
Find the prime factorization* of each denominator. Compare and list each prime factor
without duplicating or leaving any out. Multiply to obtain the LCD.
8
2
6
2
2
2
3
2
6=2
3
8 = 2 2 2=23
Use a chart to compare factors without duplicating or leaving any out:
8= 2 2 2
6 = 2
3
2
2
2
3 = 24
LCD = 24
*The Fundamental Theorem of Arithmetic states that every positive integer greater
than 1 can be written as a unique product of prime numbers.
Using the LCD to Add Fractions
3 1
8 6 24 24
1) Write two equivalent fractions with the LCD.
3 3 1 4 9
8 3 6 4 24
More Examples
1.
1
2
1
3
3
6
1
3
2.
3.
2
5
4.
2
3
2
6
4
24
5
6
2
3
1
4
2) Find the number each original denominator
needs to multiply to equal the LCD.
Multiply the numerator by the same number.
3
3
8
20
1
9
13
24
1
8
5
20
6
9
1
9
5
3
20
20
7
9
MULTIPLICATION/DIVISION
No LCD is needed when multiplying and dividing fractions.
Multiply straight across and simplify if possible.
Multiplication
1 1
2 3
Examples:
1
6
2
5
3
2 5
3 1
3 8
4 9
1
10
3
3 82
93
14
1 2
1 3
2
3
Division (Multiplication by Reciprocal)
Change division to multiplication by “flipping” the second fraction.
(Multiply the first fraction by the reciprocal of the second).
3
8
Examples:
2
3
2
5
3 5
8 2
3
4
2
3
15
16
4
3
8
9
LSC-Montgomery Learning Center: Working With Fractions
Updated April 7, 2011
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