Fractions

ADDING AND SUBTRACTING FRACTIONS WITH "LIKE" DENOMINATORS

 * 1) add or subtract the numerators
 * 2) leave the denominator the same
 * 3) simplify your answer if necessary

EXAMPLES:

2/8 + 5/8 = 7/8

12/19 - 7/19 = 5/19

ADDING AND SUBTRACTING FRACTIONS WITH "UNLIKE" DENOMINATORS
OPTION #1


 * 1) find a common denominator you can use with both denominators; try to use the least common denominator (LCD)
 * 2) multiply the numerator of the fraction by the same factor you multiplied the denominator by
 * 3) once you have changed all the necessary fractions, they will all have common denominators
 * 4) add or subtract the numerators
 * 5) leave the denominator the same
 * 6) simplify your answer if necessary

EXAMPLES:

2/7 +3/14 = 4/14 + 3/14 = 7/14 = 1/2

12/24 - 3/8 = 12/24 - 9/24 = 3/24 = 1/8

OPTION #2
 * 1) find the cross products by cross multiplying the opposite numerators and denominators
 * 2) add or subtract the cross products you just calculated; this is the numerator of your answer
 * 3) multiply the unlike denominators together; this is the denominator of your answer
 * 4) simplify your final answer if necessary

EXAMPLES:

2/7 + 3/5 = 2 x 5 = **10** and 7 x 3 = **21** (cross products) 10 + 21 = 31 (numerator of answer) 7 x 5 = 35 (denominator of answer) final answer = 31/35

7/9 - 1/3 = 7 x 3 = **21** and 1 x 9 = **9** (cross products) 21 - 9 = 12 (numerator of your answer) 9 x 3 = 27 (denominator of your answer) final answer = 12/27

MULTIPLYING FRACTIONS AND MIXED NUMBERS
OPTON #1 OPTION #2
 * 1) change all mixed numbers into improper fractions
 * 2) multiply numerator x numerator
 * 3) multiply denominator x denominator
 * 4) simplify your answer
 * 1) change all mixed numbers to improper fractions
 * 2) cross simplify opposite (diagonal) numerators and denominators if possible
 * 3) multiply numerator x numerator
 * 4) multiply denominator x denominator

**DIVIDING FRACTIONS AND MIXED NUMBERS**
OPTION #1-using the reciprocal OPTION #2-cross products
 * 1) change any mixed numbers to improper fractions
 * 2) 1st fraction stays the same
 * 3) division becomes multiplication
 * 4) use the reciprocal of the second fraction
 * 5) multiply and simplify
 * 1) multiply cross products of opposite (diagonal) numerators and denominators
 * 2) the first cross product is the answer's numerator
 * 3) the second cross product is the answer's denominator
 * 4) simplify your answer