Fractions

Addition and Subtraction of Similar Fractions

1. Add or subtract the numerators.

2. Keep the common denominator the same.

3. Simplify the fraction if necessary.

Example 1. 3/5 + 1/5 = 4/5

Example 2. 5/7 + 1/7 = 6/7

Addition and Subtraction of Dissimilar Fractions

1. Determine the Least Common Denominator (LCD).

2. Adjust the fractions to have the same denominator.

3. Perform the addition or subtraction on the fractions.

4. Simplify the result if necessary.

Example 1. 3/6 + 1/2 = 3/6 + 3/6 = 6/6 or 1

Example 2. 3/6 + 3/4 = 6/12 + 9/12 = 15/12 or 1 3/12 or 1 1/4

Application

Solve the following

1. 8/12 – 4/12 =

2.7/10 – 3/10 =

3. 4/9 + 2/9 =

4. 7/8 + 1/4 =

5. 7/8 + 1/3 =

Addition of Whole Numbers and Fractions

Subtraction of Whole Numbers and Fractions

Mixed Fractions

Multiplication of Fractions

1. When multiplying fractions, simply multiply the numerators together and the denominators together.

Example 1. 3/5 x 2/3 = 6/15 or 3/5

Example 2. 4/7 x 1/2 = 4/14

Example 3. 5/9 x 3/4 = 15/36 or 5/12

2. If there are common factors between the numerator of one fraction and the denominator of another, you can divide by those factors to simplify the calculation. It’s also a good idea to simplify the fractions before multiplying them to make the process easier and to avoid simplifying later.

Example 1. 2/3 x 33/9 = 2/1 x 11/9 = 22/9 or 2 4/9

Example 2. 4/5 x 60/9 = 4/1 x 12/9 = 36/9 or 4

Example 3. 3/4 x 32/7 = 3/1 x 8/7 = 24/7 or 3 3/7

Division of Fractions

Dividing fractions is similar to multiplying fractions, with a couple of extra steps:

Copy the dividend (the first fraction).
Change the division sign to multiplication.
Reciprocate the divisor (flip the second fraction).
Perform the multiplication to find the answer.

Example 1. 4/5 ÷ 1/2 = 4/5 x 2/1 = 8/5 or 1 3/5

Example 2. 5/8 ÷ 4/3 = 5/8 x 3/4 =15/32

Example 3. 4/9 ÷2/3 = 4/9 x 3/2 = 4/3 x 1/2 = 4/6 or 2/3

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