Problem Set 40 – Half and Quarters as DecimalsClass 5 Maths · Chapter 9 Decimal Fractions · Problem Set 40 – Maharashtra Board

Summary: Problem Set 40 – Half and Quarters as Decimals

To write a fraction as a decimal, first make an equal fraction with denominator 10 or 100.

Half: 1/2 = (1 × 5)/(2 × 5) = 5/10 = 0.5. Also 1/2 = 50/100 = 0.50 — the same value.

10 cannot be divided by 4 exactly, but 4 × 25 = 100. So a quarter is 1/4 = 25/100 = 0.25.

Three quarters: 3/4 = 75/100 = 0.75.

With a whole number in front, write the whole number, then the decimal part: three and a half = 3.5, five and a quarter = 5.25, nine and three quarters = 9.75.

Key points to remember

• Half = 1/2 = 0.5 = 0.50
• Quarter = 1/4 = 0.25
• Three quarters = 3/4 = 0.75
• Make the denominator 10 or 100 first
• 2 × 5 = 10, so half → tenths
• 4 × 25 = 100, so quarters → hundredths
• One and a quarter = 1.25
• Two quarters = one half: 0.25 + 0.25 = 0.5

Problem Set 40 – Half and Quarters as Decimals – Notes

1. Half as a decimal

• 1/2 has denominator 2. Multiply top and bottom by 5: 1/2 = 5/10.
• 5/10 = 0.5. Or multiply by 50: 50/100 = 0.50.
• 0.5 and 0.50 are equal: 5 tenths = 50 hundredths. Half a rupee = 50 paise.

2. Quarter and three quarters

• 4 does not go into 10 exactly, so we cannot make tenths.
• But 4 × 25 = 100. So 1/4 = (1 × 25)/(4 × 25) = 25/100 = 0.25.
• 3/4 = (3 × 25)/(4 × 25) = 75/100 = 0.75. A quarter metre = 25 cm; three quarters of a metre = 75 cm.

3. Whole number and a part

• Write the whole number, put the point, then the decimal of the part.
• Three and a half = 3 + 0.5 = 3.5. Eleven and a half = 11.5.
• Five and a quarter = 5.25. Nine and three quarters = 9.75.

4. Seeing it with money

• ₹ 1 = 100 paise. Half = 50 paise = ₹ 0.50; quarter = 25 paise = ₹ 0.25; three quarters = 75 paise = ₹ 0.75.
• Two and a half rupees = ₹ 2.50; six and a quarter rupees = ₹ 6.25.
• So decimals for these parts are easy to remember using paise.

5. Quick checks

• Two quarters make a half: 0.25 + 0.25 = 0.50 = 0.5.
• Half + quarter = three quarters: 0.5 + 0.25 = 0.75.
• Four quarters make one whole: 0.25 × 4 = 1.00.

Formulas at a glance

Key terms

Problem Set 40 – Half and Quarters as Decimals – Flashcards

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

Problem Set 40 – Half and Quarters as Decimals – MCQ Quiz

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

How to study Problem Set 40 – Half and Quarters as Decimals

⏱ About 20 minutes

1. Learn (5 min)
   Learn 1/2 = 0.5, 1/4 = 0.25 and 3/4 = 0.75 and why.
2. Write (10 min)
   Turn 'and a half', 'and a quarter' and 'and three quarters' into decimals.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.