Add and subtract fractions with unlike denominators: word problems

Key notes :-

Identify Fractions with Unlike Denominators:

  • Fractions with different denominators cannot be added or subtracted directly. They must be converted to equivalent fractions with the same denominator.

Find the Least Common Denominator (LCD):

  • The Least Common Denominator (LCD) is the smallest number that is divisible by both denominators.
  • Example: For 1/4​ and 1/6, the LCD is 12.

Convert Fractions to Equivalent Fractions:

  • Multiply both the numerator and denominator of each fraction by a number that makes the denominators equal.
  • Example: To convert 1/4​ and 1/6​ to fractions with denominator 12:
    • 1/4=3/12
    • 1/6=2/12

Add or Subtract Fractions:

  • Once the fractions have the same denominator, add or subtract the numerators, keeping the denominator the same.
  • Example (Addition): 3/12+2/12=5/12
  • Example (Subtraction): 3/12−2/12=1/12

Simplify the Result:

  • After adding or subtracting, simplify the fraction if necessary. This can be done by dividing both the numerator and denominator by their greatest common divisor (GCD).

Learn with an example

Last week Sharon and her roommates ate 1/2 of a carton of yoghurt, and this week they ate 5/6 of a carton.

How much more yoghurt did they eat this week compared to last week?

Find how many more cartons they ate this week by subtracting 1/2 from 5/6.

You can use 6 as the common denominator.
Multiply the numerator and the denominator of 1/2 by 3 to find an equivalent fraction.

1 × 3 = 3
2 × 3 6

Now subtract the fractions. Subtract the numerators and keep the denominators the same.

5/6 -3/6 = 2/6

Sharon and her roommates ate 2/6 of a carton more yoghurt this week.

At Jill’s Boutique, 1/12 of the trousers are denim. Another 1/2 is khaki.

What fraction of the trousers are either denim or khaki?

Find the fraction of the trousers that are either denim or khaki by adding 1/12 and 1/2.

You can use 12 as the common denominator.

Multiply the numerator and the denominator of 1/2 by 6 to find an equivalent fraction.

1×6 / 2×6 = 6/12

Now add the fractions. Add the numerators and keep the denominators the same.

1/12+6/12 = 7/12

The fraction of the trousers that are either denim or khaki is 7/12.

While making desserts for a bake sale, Zane used 2/5 of a scoop of brown sugar as well as 3/10 of a scoop of white sugar.

How much more brown sugar did Zane use?

Find how much more brown sugar was used by subtracting 3/10 from 2/5.

You can use 10 as the common denominator.
Multiply the numerator and the denominator of 2/5 by 2 to find an equivalent fraction.

2×2 / 5×2 = 4/10

Now subtract the fractions. Subtract the numerators and keep the denominators the same.

4/10 – 3/10 = 1/10

Zane used 1/10 of a scoop more brown sugar.

let’s practice: