Problem Set 23 – Fraction of a Collection or a NumberClass 5 Maths · Chapter 5 Fractions · Problem Set 23 – Maharashtra Board

Summary: Problem Set 23 – Fraction of a Collection or a Number

To find 1/4 of a group, share it into 4 equal parts and take one part: 1/4 of 20 = 20 ÷ 4 = 5.

To find 3/4 of a group, first find 1/4, then take 3 such parts: 20 ÷ 4 = 5 and 5 × 3 = 15.

Rule: a fraction of a number = (number ÷ denominator) × numerator.

Twice means two times and thrice means three times: twice 6 is 12. Half of 12 is 6, so halving undoes doubling.

Finding 4/5 of 20 km is the same as 20 × 4/5: take 1/5 of 20 (which is 4) four times to get 16 km.

Key points to remember

• 1/n of a number = number ÷ n
• a/n of a number = (number ÷ n) × a
• Divide by the denominator first
• Then multiply by the numerator
• 3/4 of 28 = 7 × 3 = 21
• Twice = × 2, thrice = × 3
• Improper fraction: numerator bigger than denominator (7/3)
• Mixed fraction = whole number + proper fraction: 7/3 = 2 1/3

Problem Set 23 – Fraction of a Collection or a Number – Notes

1. One part of a collection

• 1/3 of 24 pencils: make 3 equal groups of the 24 pencils. Each group has 24 ÷ 3 = 8 pencils.
• So 1/3 of 24 = 8. The denominator tells how many equal groups to make.
• 1/2 of 18 = 18 ÷ 2 = 9; 1/5 of 35 = 35 ÷ 5 = 7.

2. More than one part

• The numerator tells how many of the equal groups to take.
• 2/3 of 24 pencils = 2 groups of 8 = 16 pencils.
• So: divide by the denominator, then multiply by the numerator.

3. Twice, thrice and half

• Twice 6 = 6 × 2 = 12; thrice 7 = 7 × 3 = 21.
• Half of 12 = 12 ÷ 2 = 6. If Mina has twice as many stickers as Tara, Tara has half as many as Mina.
• 2/3 of 15 means: find 1/3 of 15 (that is 5), then take it twice (5 × 2 = 10).

4. A fraction of a quantity

• Keep the unit: 1/5 of ₹35 = ₹7; 1/5 of 45 km = 9 km; 1/4 of 20 litres = 5 litres.
• A boy walks 3/4 of a 24 km trip: 24 ÷ 4 = 6, 6 × 3 = 18 km.
• 'Number × fraction' means the same thing: 24 × 3/4 = 18.

5. Mixed fractions and improper fractions

• Shade half of each of 3 circles: that is 1/2 + 1/2 + 1/2 = 3/2, which is one whole and a half more.
• We write 1 + 1/2 as 1 1/2 and read it 'one and one by two'. 1 is the whole-number part and 1/2 is the fraction part. Such numbers are mixed fractions (mixed numbers).
• A fraction whose numerator is bigger than its denominator, like 3/2 or 7/3, is an improper fraction.
• To change an improper fraction into a mixed fraction, take out as many wholes as you can: 7/3 = 3/3 + 3/3 + 1/3 = 1 + 1 + 1/3 = 2 1/3. (Quick way: 7 ÷ 3 = 2, remainder 1.)

Formulas at a glance

Key terms

Problem Set 23 – Fraction of a Collection or a Number – Flashcards

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

Problem Set 23 – Fraction of a Collection or a Number – MCQ Quiz

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

How to study Problem Set 23 – Fraction of a Collection or a Number

⏱ About 25 minutes

1. See it (5 min)
   Take 20 buttons, share them into 4 equal heaps and count 1, 2 and 3 heaps.
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.