# Operations with Fractions. Adding and Subtracting Fractions.

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Operations with Fractions

Rewrite the problem with equivalent fractions  List the multiples of both denominators.  Find the least common multiple (LCM).  Write new fractions with the LCM as the new denominator.  Find the factor you multiply by to get from your original denominator to your new denominator.  Use that same factor, and multiply it by your original numerator to get a new numerator.  Finally add and/or subtract from left to right as normal.

WHAT DOES THAT MEAN? Let’s illustrate the steps with an example. 3 4 + 1 6

3 4 + 1 6 Multiples of 4: 4, 8, 12, 16, 20 Multiples of 6: 6, 12, 18, 24, 30 + 12 x 3 9 x 2 2 12 11

Example 2 9 10 2 5 10, 20, 30, 40, 50 5, 10, 15, 20, 25 10 x 1 9 x 2 4 = 10 5 = 1 2

Example 3 

Example 4 improper fractions 

Practice  ½ + 1/3  1/5 + ¼  5/6 – 1/5  4/7 – 1/3

Homework Time!

Multiplying With Fractions

Just Follow These Easy Steps!  Multiply the numerators and write down the answer as your new numerator.  Multiply the denominators and write down the answer as your new denominator.  Simplify.

Example 1 5 8 x 3 4 = 15 32 There are no common factors for 15 and 32, so this fraction cannot be simplified.

Example 2 3 4 x 2 9 = 6 36 This fraction can be reduced. Divide the numerator and denominator by the GCF, which is 6. = 1 6

Multiplying by a Whole Number If you want to multiply a fraction by a whole number, turn your whole number into a fraction by placing a 1 as the denominator. If your answer is improper, divide the bottom into the top. 4 5 x 20 1 = 80 5 = 16

Another Example 15 x 1 61 = 6 15 and 6 have a GCF of 3. = 5 2 Five halves is improper, so we divide the bottom into the top. 25 2 4 1 2 1 2

Practice

Multiplying Fractions 1 Must simplify  

Homework Time!

Review Multiplying Fractions 

Dividing Fractions

To Divide Fractions:  Rewrite the first fraction.  Change the division sign to a multiplication sign.  Flip the second fraction upside down.  Multiply.

Reciprocal  When you flip the second fraction, you are writing that fraction’s reciprocal. 3 5 5 3

Example 1 1 3 ÷ 1 2 Rewrite: 1 3 x 2 1 = 2 3

Example 2 4 5 ÷ 4 9 Rewrite: 4 5 x 9 4 = 36 20 = 1 4 5

Example 3 12 ÷ 3 5 1 Rewrite: 12 1 x 5 3 = 60 3 = 20

Example 4 1 6 ÷ 2 1 Rewrite: 1 6 x 1 2 = 1 12

Homework Time