Operations with Fractions

Adding and Subtracting 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.

34

+ 16

34

+ 16

Multiples of 4: 4, 8, 12, 16, 20

Multiples of 6: 6, 12, 18, 24, 30

+12 12

x 3 9 x 22

1211

Example 2

9

1025

10, 20, 30, 40, 50

5, 10, 15, 20, 25

10 10

x 1

9x 2

4 =105

= 12

Example 3

Example 4 improper fractions

Practice

½ + 1/3 1/5 + ¼5/6 – 1/54/7 – 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

58

x 34 =

1532

There are no common factors for 15 and 32, so this fraction cannot be simplified.

Example 2

3

4x

29 =

636

This fraction can be reduced. Divide the numerator and denominator by the GCF, which is 6.

= 16

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.

45

x 201 = 80

5 = 16

Another Example

15 x 161 = 15

615 and 6 have a GCF of 3.

=52

Five halves is improper, so we divide the bottom into the top.

2 52

41

2 12

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.

35

53

Example 1

1

3÷

12

Rewrite:

13

x 21 = 2

3

Example 2

4

5÷

4

9Rewrite:

45

x 94 =

3620

=1 45

Example 3

12 ÷ 351

Rewrite:

121

x 53

=60

3= 20

Example 4

16

÷21

Rewrite:

16

x 12

=112

Homework Time