Problem Set 19 – Comparing FractionsClass 5 Maths · Chapter 5 Fractions · Problem Set 19 – Maharashtra Board

Summary: Problem Set 19 – Comparing Fractions

Like fractions (same denominator): the one with the bigger numerator is bigger. 5/9 > 2/9.

Fractions with the same numerator: the one with the bigger denominator is smaller, because the whole is cut into more, smaller pieces. 2/3 > 2/5.

Unlike fractions with different numerators: first change them into like fractions, then compare the numerators.

A quick common denominator is the product of the two denominators: for 3/5 and 5/8 use 40.

If the two like fractions have equal numerators, the fractions are equal, so use =.

Key points to remember

• Same denominator → bigger numerator wins
• Same numerator → bigger denominator is smaller
• Different both → make like fractions first
• 1/2 > 1/3 > 1/4 > 1/5
• < means 'is less than', > means 'is greater than'
• Equal like fractions → use =
• 3/5 = 24/40 and 5/8 = 25/40, so 3/5 < 5/8
• Open side of the sign faces the bigger number

Problem Set 19 – Comparing Fractions – Notes

1. Comparing like fractions

• Cut a strip into 9 equal parts. 5 parts are more than 2 parts.
• So 5/9 > 2/9. With equal denominators, compare only the numerators.
• Order 1/7, 6/7, 4/7 from small to big: 1/7 < 4/7 < 6/7.

2. Comparing fractions with equal numerators

• Cut equal strips into 3, 4 and 5 parts. Each third is bigger than each quarter, and each quarter is bigger than each fifth.
• So 2 thirds > 2 quarters > 2 fifths: 2/3 > 2/4 > 2/5.
• With equal numerators, the fraction with the smaller denominator is the bigger one.

3. Comparing unlike fractions

• Think of two children standing on stools of different heights — to compare them fairly they must stand on the same level.
• In the same way, give both fractions the same denominator first.
• Then the one with the bigger numerator is the bigger fraction.

4. Using the signs

• > means 'is greater than'; < means 'is less than'; = means 'is equal to'.
• The open mouth of the sign always faces the bigger number: 7/10 > 3/10.
• Equal like fractions get =: 20/30 = 20/30, so 4/6 = 10/15.

5. Which rule should I use?

• Look at the denominators first. Same? Compare numerators.
• Not the same? Look at the numerators. Same? The smaller denominator wins.
• Both different? Make a common denominator, then compare.

Formulas at a glance

Key terms

Problem Set 19 – Comparing Fractions – Flashcards

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

Problem Set 19 – Comparing Fractions – MCQ Quiz

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

How to study Problem Set 19 – Comparing Fractions

⏱ About 25 minutes

1. Learn (5 min)
   Learn the three rules: same denominator, same numerator, and making like fractions.
2. Practise (15 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.