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Least Common Denominator

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Least Common Denominator

Find the least common denominator (LCD) by finding the smallest positive number that is a multiple of every denominator. When rewriting a fraction, multiply its numerator and denominator by the same number.

Find the LCD

1.Write the first five positive multiples of 3 and the first five positive multiples of 4. Then use the lists to find the LCD of 1/3 and 1/4.

2.What is the LCD of 1/6 and 1/8?

3.Find the LCD of 2/5 and 3/10.

4.Find the LCD of 3/4 and 5/6.

5.Find the LCD of 7/8 and 1/3.

6.Choose the LCD of 1/5 and 1/10.

Rewrite Fractions with Common Denominators

7.Rewrite 3/4 and 5/6 as equivalent fractions with the LCD as their denominator. Include the LCD.

8.Rewrite 1/3 and 3/8 as equivalent fractions with the LCD as their denominator. Include the LCD.

9.Rewrite 2/5 and 1/4 as equivalent fractions with the LCD as their denominator. Include the LCD.

10.Show how to find the LCD of 7/10 and 2/15, then rewrite both fractions using that denominator.

11.Match each pair of denominators to its LCD.

4 and 10
6 and 9
8 and 12
5 and 7
3 and 4

Use the LCD

12.Madison ate 1/4 of a pie, and Brianna ate 1/6 of the same-sized pie. Find the LCD, then write both amounts as fractions with that denominator.

13.Find the LCD of 1/2, 1/3, and 1/4. Then rewrite each fraction using that denominator.

14.Mark each statement True or False: (a) The LCD is the smallest positive number that is a multiple of every denominator. (b) The LCD of two denominators is always their product. (c) Equivalent fractions have the same value. (d) To add fractions with different denominators, first rewrite them with a common denominator.

TrueFalse

15.In your own words, explain why fractions need a common denominator before you can add them. Give one example using 1/3 and 1/6.