Problem Set 22 – Adding and Subtracting Unlike FractionsClass 5 Maths · Chapter 5 Fractions · Problem Set 22 – Maharashtra Board

Summary: Problem Set 22 – Adding and Subtracting Unlike Fractions

Unlike fractions have pieces of different sizes, so we cannot add or subtract their numerators straight away.

First change them into like fractions with a common denominator (a common multiple of the denominators).

The smallest common multiple keeps the numbers small: for 4 and 6 it is 12.

Then add or subtract the numerators and keep the common denominator: 3/4 + 1/6 = 9/12 + 2/12 = 11/12.

If one denominator is a multiple of the other, change only the fraction with the smaller denominator: 3/10 + 2/5 = 3/10 + 4/10.

Key points to remember

• Unlike fractions: make them like first
• Common denominator = common multiple of the denominators
• Use the smallest common multiple if you can
• Change each fraction by multiplying top and bottom
• Then add or subtract the numerators only
• 1/2 + 1/3 is NOT 2/5 — it is 5/6
• 3/4 + 1/6 = 11/12
• 5/6 − 1/4 = 7/12

Problem Set 22 – Adding and Subtracting Unlike Fractions – Notes

1. Why we need a common denominator

• 1/2 of a strip and 1/3 of the same strip are pieces of different sizes.
• Cut both into sixths: 1/2 = 3/6 and 1/3 = 2/6. Now all pieces are sixths.
• 3 sixths + 2 sixths = 5 sixths, so 1/2 + 1/3 = 5/6.

2. Steps for adding unlike fractions

• Step 1: find the smallest common multiple of the denominators.
• Step 2: change each fraction to an equivalent fraction with that denominator.
• Step 3: add the numerators and keep the denominator.

3. Subtracting unlike fractions

• Use the same first two steps, then subtract the numerators.
• 5/6 − 1/4: common denominator 12; 5/6 = 10/12 and 1/4 = 3/12.
• 10/12 − 3/12 = 7/12.

4. When one denominator fits into the other

• In 3/10 + 2/5, 10 is a multiple of 5, so 10 is the common denominator.
• Change only 2/5: 2/5 = 4/10. Then 3/10 + 4/10 = 7/10.
• Likewise 5/8 − 1/4 = 5/8 − 2/8 = 3/8.

5. A common mistake to avoid

• Never add the tops and the bottoms separately: 1/2 + 1/3 is not 2/5.
• Check with sense: 1/2 + 1/3 must be more than 1/2, but 2/5 is less than 1/2.
• When the denominators have no easy common multiple, multiply them: 4/5 − 1/3 uses 15.

Formulas at a glance

Key terms

Problem Set 22 – Adding and Subtracting Unlike Fractions – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 22 – Adding and Subtracting Unlike Fractions – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 22 – Adding and Subtracting Unlike Fractions

⏱ About 30 minutes

1. Revise (5 min)
   Revise how to make like fractions (Problem Set 18).
2. Practise (20 min)
   Do the worked example and the 4 'Try it yourself' sums, writing all three steps.
3. Review (5 min)
   Go through the flashcards, take the quiz and play 🎮 Play.