Mathematics Notes by Success Tutorials: Working with Fractions

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1. Make sure that both fractions have the same denominator.

3. Reduce the answer if we can.

example: 1/3 + 2/5; We want to add these two fractions together.

1. The lowest common denominator is 15.

Result: 5/15 + 6/15; We multiply 1/3 by 5/5 and 2/5 by 3/3.

Result: 11/15; We add 5 + 6 to get 11. The denominator is still 15.

3. Reduce the fraction if we can.

11/15 is already in simplest terms.

Exercise - add the following fractions:

1. 1/2 + 2/3 =               5. 3/4 + 2/7 =

2. 3/4 + 2/3 =               6. 1/4 + 2/5 =

3. 2/2 + 3/3 =               7. 1/3 + 2/3 =

4. 1/5 + 2/3 =               8. 3/5 + 2/3 =

Mathematics Notes by Success Tutorials: Working with Fractions

B. How to Multiply Fractions

To multiply fractions we must:

1. Multiply the numerators together.

2. Multiply the denominators together.

3. Reduce the fraction if we can.

4. We DO NOT need to have the same denominators for the fractions before we begin.

example: 1/3 x 2/5; We want to multiply these two fractions.

1. Multiply the numerators together.

Result: 1 x 2 = 2

2. Multiply the denominators together.

Result: 3 x 5 = 15

Fraction is: 2/15

3. Reduce the fraction if we can. The fraction 2/15 is already in simplest terms.

Exercise - multiply the following fractions:

1. 1/2 x 2/3 =               5. 3/4 x 2/7 =

2. 3/3 x 2/2 =               6. 1/3 x 2/9 =

3. 2/7 x 3/7 =               7. 1/3 x 2/3 =

4. 1/5 x 2/3 =               8. 3/5 x 2/3 =

Mathematics Notes by Success Tutorials: Working with Fractions

C. How to Divide Fractions

To divide fractions we must:

1. Invert the bottom fraction.

2. Multiply the top fraction by the inverted bottom fraction.

3. Reduce the fraction if we can.

4. We DO NOT need to have the same denominators for the fractions before we begin.

example: 1/3 divided by 3/7

This can also be written as:

1/3 / 3/7

1. Invert the bottom fraction and multiply it by the top fraction:

Result: 1/3 x 7/3

2. Multiply the numerators together.

Result: 1 x 7 = 7

3. Multiply the denominators together.

Result: 3 x 3 = 9

4. Reduce the fraction if we can. The fraction 7/9 is already in simplest terms.

Exercise - divide the following fractions:

1. 1/2 divided by 2/3 =               5. 3/4 divided by 2/7 =

2. 3/2 divided by 2/3 =               6. 1/4 divided by 2/7 =

3. 2/2 divided by 3/3 =               7. 1/3 divided by 2/3 =

4. 1/5 divided by 2/3 =               8. 3/5 divided by 2/3 =