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Fractions

EXAMPLE 4

Dividing Fractions

Find each quotient, and write it in lowest terms.

Objective

Add and subtract fractions.

Adding Fractions:

If and are fractions, then .

That is, to find the sum, the result of adding the numbers,
having the same denominator, add the numerators and keep the
same denominator.

If the fractions do not share a common denominator. The least
common denominator (LCD) must first be found as follows:

Step 1:Factor each denominator.

Step 2:
Use every factor that appears in any factored form. If
a factor is repeated, use the largest number of repeats
in the LCD.

Step 3:
Find the number that can be multiplied by the
denominator to get the LCD and multiply the numerator
and denominator by that number.

Subtracting Fractions:

If and are fractions, then ..

That is, to find the difference, the result of subtracting the
numbers, between two fractions having the same denominator
subtract the numerators and keep the same denominator.

If fractions have different denominators, find the LCD using
the same method as with adding fractions.

EXAMPLE 5

Adding Fractions with the
Same Denominator

Find the sum , and write it in lowest terms.