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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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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

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.   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!    Subtraction of Fractions with Borrowing

 Example 1: Example 2: Note: There are two common methods; DO NOT mix the steps of the methods!

Method 1 Example 1 Subtraction with Borrowing
Write problem vertically
Cannot subtract fraction from whole without finding
common denominator.
Borrow one whole from 7 and express as Subtract numerators and whole numbers.
Example 2 Write problem vertically and find LCD
Cannot subtract 5 from 2.
Borrow one whole from 5, and add Subtract numerators and whole numbers; reduce as
needed.
Method 2 Example 1: Subtraction Using Improper Fractions
Write the problem vertically.
Convert the whole numbers and mixed numbers to
improper fractions using the LCD.
Subtract and convert improper fraction to
mixed number.
Example 2: Write problem vertically and find the LCD.
Change the mixed numbers to improper fractions.
Subtract the numerators.
Convert to a mixed number.
Reduce.