Problem Set 20 – Adding Like FractionsClass 5 Maths · Chapter 5 Fractions · Problem Set 20 – Maharashtra Board

Summary: Problem Set 20 – Adding Like Fractions

Like fractions have the same denominator, so their pieces are all the same size.

To add like fractions, add the numerators and keep the same denominator: 3/7 + 2/7 = 5/7.

Three or more like fractions are added the same way: 2/9 + 4/9 + 1/9 = 7/9.

When the numerator and the denominator are equal, the fraction is one whole: 5/5 = 1, 9/9 = 1.

A whole that is not cut at all can be written as 1/1, and 1 = 2/2 = 3/3 and so on.

Key points to remember

• Like fractions → same-size pieces
• Add the numerators
• Keep the denominator the same
• Never add the denominators
• 3/7 + 2/7 = 5/7
• Equal numerator and denominator = 1
• 4/9 + 5/9 = 9/9 = 1
• 1 = 1/1 = 2/2 = 3/3 …

Problem Set 20 – Adding Like Fractions – Notes

1. Why we add only the numerators

• In 3/7, the 7 tells the size of each piece (sevenths) and the 3 tells how many pieces.
• 3 sevenths and 2 more sevenths make 5 sevenths — the size of the pieces does not change.
• So 3/7 + 2/7 = (3 + 2)/7 = 5/7.

2. Adding three like fractions

• Add all the numerators and write the common denominator once.
• It works just like adding counts of the same thing: 2 apples + 4 apples + 1 apple = 7 apples.

3. When the sum is one whole

• If a cake is cut into 6 equal parts and all 6 are taken, the whole cake is taken: 6/6 = 1.
• So 4/9 + 5/9 = 9/9 = 1 and 3/8 + 5/8 = 8/8 = 1.
• Any fraction whose numerator equals its denominator is equal to 1.

4. Writing 1 as a fraction

• A whole that is not cut can be written 1/1.
• 1 = 2/2 = 3/3 = 10/10 — all show the full whole.
• Dividing top and bottom of 7/7 by 7 gives 1/1, which is 1.

5. Word problems

• 'Altogether' or 'in all' means add.
• A girl reads 2/10 of a book on Monday and 5/10 on Tuesday: 2/10 + 5/10 = 7/10 of the book.
• Check that the fractions are like fractions before adding.

Formulas at a glance

Key terms

Problem Set 20 – Adding Like Fractions – Flashcards

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

Problem Set 20 – Adding Like Fractions – MCQ Quiz

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

How to study Problem Set 20 – Adding Like Fractions

⏱ About 20 minutes

1. See it (5 min)
   Shade 3 of 7 parts of a strip in one colour and 2 in another. Count: 5/7.
2. Practise (10 min)
   Do the worked example and the 4 'Try it yourself' sums.
3. Review (5 min)
   Go through the flashcards, take the quiz and play 🎮 Play.