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Fraction Competency Packet

Least Common Multiple (LCM)
Used to find the Least Common Denominator (LCD)

Example: Find the LCM of 30 and 45

Note: There are four common methods; DO NOT mix the steps of the methods!

Method 1

30, 60, 90, 120, … 45, 90, 135, …	Remember that multiples are equal to or larger than the given number. List the multiples of each of the given numbers, in ascending order.
LCM = 90	The LCM is the first multiple common to both lists.

Method 2

45, 90, 135, …	List the multiples of the larger number.
45 ÷ 30 remainder	Divide each in turn by the smaller.
90 ÷ 30 no remainder LCM = 90	The LCM is the multiple that the smaller number divides without leaving a remainder.

Method 3

30 ÷ 5 = 6 ; 45 ÷ 5 = 9 6 ÷ 3 = 2 ; 9 ÷ 3 = 3	Divide both numbers by any common factor, (5 then 3). Continue until there are no more common factors. Note: 2 and 3, the results of the last division have no common factors.
LCM = 5× 3× 2× 3 = 90	The LCM equals the product of the factors, (5 and 3) and the remaining quotients, (2 and 3).

Method 4

	Find the prime factors of each the given numbers.
or	Write each number as a product of primes using exponents, if required.
	LCM equals the product of all the factors to the highest power.

In each exercise, find the LCM of the given numbers.

1) 4 and 18

2) 16 and 40

3) 20 and 28

4) 5 and 8

5) 12 and 18

6) 12 and 16

7) 50 and 75

8) 24 and 30

9) 36 and 45

10) 8 and 20

11) 16 and 20

12) 28, 35, and 21

Addition and Subtraction of Fractions
with the Same Denominator

To add or subtract fractions, the denominators MUST be the same.

Example 1:

Because both fractions have the same denominator,
you may subtract the numerators and keep the
denominator.

Example 2:

	Because both fractions have the same denominator, you may add the numerators and keep the denominator.
	Always change improper fractions to a mixed number.
	Reduce, when possible.

Add or Subtract as indicated.

Addition and Subtraction of Fractions
with Different Denominators

Remember: In order to add or subtract fractions, the denominators MUST be the same.

Example:

LCM = 24	Find the LCM Write the problem vertically.
	Find the equivalent fractions with the LCM as a denominator.
	Add the fractions with the same denominator.
	Remember to write as a mixed number and reduce when possible!