Comparing – Adding – Subtracting Fractions

Fractions can be compared, added or subtracted only if they have the same denominator, called the common denominator.

To find the common denominator, find the multiples of each denominator.

Example: Find the common denominators of 2/4 and 5/8:

• Multiples of 4: 4,8,12,16,20,24,28,32…
• Multiples of 8: 8,16,24,32…
• Common denominators are: 8,16,24,and 32

The least common denominator is the smallest common denominator .

• The least common denominator in the example above is: 8

To compare, add or subtract fractions, change all the fractions so they have the same least common denominator. Then:

To add fractions – add up all the numerators.

To subtract fractions – subtract one numerator from the other numerator.

Compare 2/3 and 3/5:

• Find the least common denominator.
• The common denominators for 2/3 are: 3,6,9,15,18…
• The common denominators for 3/5 are: 5,10,15,20,25,…
• The least common denominator for 2/3 and 3/5 is: 15

15 is 5 times 3, and 3 times 5)

• The equivalent fraction for 2/3 with a denominator of 15 is: 10/15

(multiply the numerator and the denominator by 5)

• The equivalent fraction for 3/5 with a denominator of 15 is: 9/15

(multiply the numerator and denominator by 3)

Conclusion: 10/15 > 9/15 which means 2/3 > 3/5.

We could also add these fractions: (2/3 + 3/5) = (10/15 + 9/15) = 19/15.

And we could subtract them: (2/3 – 3/5) = (10/15 – 9/15) = 1/15.

Notice: when we add or subtract the fractions, the common denominator stays the same, and we add or subtract the numerators.