Common Denominators

Common Denominators for Adding and Subtracting Fractions

Least Common Multiple

• A multiple is the product when you multiply a number by any other number. For example, the multiples of 5 are 5x1=5, 5x2=10, 5x3=15,etc.

• The least common multiple (LCM) is the smallest multiple that two numbers have in common

• Example: the LCM of 4 and 5 is 20 (4, 8, 12, 16, 20 and 5, 10, 15, 20)

Multiple Choice

What is the least common multiple of 3 and 4?

• 24

• 12

• 7

• 6

Multiple Choice

What is the least common multiple of 2 and 8?

• 16

• 8

• 10

• 24

Least Common Denominator

We can use the least common multiple to find the least common denominator of two (or more) fractions. Remember, we HAVE to find common denominators before we can add or subtract fractions.

Multiple Choice

What is the least common denominator of 1/3 and 4/9?

• 12

• 3

• 27

• 9

Multiple Choice

What is the least common denominator for 3/5 and 1/6?

• 30

• 11

• 40

• 25

Multiple Choice

What is the least common denominator for 3/5 and 1/6?

• 30

• 11

• 40

• 25

What do we do once we find a common denominator?

• Multiply the fractions by a WHOLE fraction (like 2/2 or 4/4 or 6/6) to change them to fractions with our common denominator without changing the value or amount. (Multiplying by 1 doesn't change the amount, right?)

• Use the new fractions with the same denominator to add or subtract the numerators!

Multiple Choice

What would you multiply 2/3 by the rename it with the denominator 12?

• 3/3

• 2/2

• 4/4

• 12/12

Multiple Choice

What would you multiply 6/7 by to rename it with the denominator 35?

• 5/5

• 6/6

• 7/7

• 35/35

Multiple Choice

What is the least common denominator of 1/2 and 3/7?

• 2
• 14
• 7
• 28

Multiple Choice

What is the least common denominator of 1/9 and 2/3?

• 6
• 3
• 9
• 21

Multiple Choice

What is the least common denominator of 3/5 and 5/7?

• 35
• 25
• 7
• 30

Multiple Choice

What is the least common denominator of 2/4 and 4/7?

• 24
• 7
• 42
• 28

Multiple Choice

What is the least common denominator of 2/6 and 7/8?

• 36
• 8
• 18
• 24