Lowest Common Denominators (LCD)

Objective

Know how to convert two fractions into LCD form.

Example

Convert the following fractions into LCD form.

5

9

-

1

2

Answer:

10

18

-

9

18

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Explanation

Lowest Common Denominator (LCD)

  • Lowest: smallest

  • Common: for both

  • Denominator: the bottom number in a fraction

The bottom line is, you can't add or subtract two fractions if they have different denominators. Putting fractions. Putting fractions into LCD form solves this problem.

5

9

-

1

2

If you can't tell what the LCD is just by looking, you can create a table.

Put you two denominators on top. Then, start listing multiples (times 1, times 2, times 3, etc.)

Once you see the same number come up, you can stop. This is your LCD

  • For 9, the LCD was the 2nd multiple (9x2).

  • For 2, the LCD was the 9th multiple (2x9).

So, for 9, multiply the numerator and denominator by 2

5 x 2

9 x 2

=

10

18

For 2, multiply the numerator and denominator by 9

1 x 9

2 x 9

=

9

18

That's all. Notice that if both denominators aren't now the LCD, you did something wrong.

10

18

-

9

18

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Examples

Example 1

Convert the following fractions into LCD form

2

6

+

7

8

2 x 4

6 x 4

7 x 3

8 x 3

=

8

24

=

21

24

Answer:

8

24

+

21

24

~~~~~~~~~~~~~~~~~~~

Example 2

Convert the following fractions into LCD form

2

4

+

7

8

2 x 2

4 x 2

7 x 1

8 x 1

=

4

8

=

7

8

Answer:

4

8

+

7

8

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Practice your skills

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Ready?