Fractions, decimals and ratio
Class 6 Maths · Fractions, decimals and ratio · 34 questions with answers
Class 6 treats fractions and decimals as two ways of writing the same quantity rather than as two topics, and introduces ratio - which compares two quantities without producing a third. The unitary method learned here reappears as percentage, speed and most word problems for years.
- Simplifies a fraction by spotting a common factor
- Converts between a fraction and a decimal
- Uses the unitary method on an unfamiliar problem
Exercise 1 of 3 · 12 questions
Write each fraction in its simplest form.
Write the answer · Warm-up
Here’s one done for you
18/24 → divide both by 6, giving 3/4. Six is the HCF of 18 and 24, so one step is enough. A child dividing by 2 and then by 3 gets the same answer more slowly - and that is fine, but spotting the HCF is what the Class 6 factors chapter was for. Five of these six simplify to 3/4, which is worth noticing.
- 1)18/24
- 2)45/60
- 3)36/48
- 4)27/36
- 5)50/75
- 6)42/56
- 7)30/45
- 8)64/80
- 9)21/28
- 10)60/72
- 11)35/63
- 12)48/54
Answers
- 1) 3/4
- 2) 3/4
- 3) 3/4
- 4) 3/4
- 5) 2/3
- 6) 3/4
- 7) 2/3
- 8) 4/5
- 9) 3/4
- 10) 5/6
- 11) 5/9
- 12) 8/9
Exercise 2 of 3 · 12 questions
Convert between fractions and decimals.
Write the answer · Guided
Here’s one done for you
3/4 as a decimal → 3 ÷ 4 = 0.75. A fraction is a division waiting to happen, which is the whole idea Class 6 is trying to establish. For 0.6 as a fraction: 0.6 is six tenths, so 6/10, which simplifies to 3/5 - and the simplifying step is where marks are lost.
- 1)1/2 as a decimal
- 2)3/4 as a decimal
- 3)0.25 as a fraction
- 4)0.6 as a fraction
- 5)1/5 as a decimal
- 6)0.75 as a fraction
- 7)1/4 as a decimal
- 8)2/5 as a decimal
- 9)0.8 as a fraction
- 10)0.05 as a fraction
- 11)3/10 as a decimal
- 12)1.5 as a fraction
Answers
- 1) 0.5
- 2) 0.75
- 3) 1/4
- 4) 3/5
- 5) 0.2
- 6) 3/4
- 7) 0.25
- 8) 0.4
- 9) 4/5
- 10) 1/20
- 11) 0.3
- 12) 3/2 (or 1 1/2)
Exercise 3 of 3 · 10 questions
Use the unitary method. Show the 'one' step.
Write the answer · Practice
Here’s one done for you
5 pens cost 60 → one pen costs 60 ÷ 5 = 12, so 8 pens cost 12 × 8 = 96. Always find the value of one first. The second question is the tricky kind - more workers means fewer days, so one worker takes 4 × 12 = 48 days, and 6 workers take 48 ÷ 6 = 8. Ask 'should the answer be bigger or smaller?' before calculating.
- 1)If 5 pens cost 60 rupees, what do 8 pens cost?
- 2)If 4 workers finish a job in 12 days, how long for 6 workers?
- 3)A recipe for 6 people needs 300 g of rice. How much for 10 people?
- 4)If 3 books weigh 1.2 kg, what do 7 books weigh?
- 5)If 5 pens cost 60 rupees, what do 15 pens cost?
- 6)If 8 identical bricks weigh 12 kg, what do 20 bricks weigh?
- 7)A car travels 240 km on 16 litres. How far on 25 litres?
- 8)If 6 shirts need 9 m of cloth, how much cloth for 10 shirts?
- 9)If 4 taps fill a tank in 30 minutes, how long would 5 taps take?
- 10)If 9 kg of rice costs 630 rupees, what does 4 kg cost?
Answers
- 1) One pen costs 12, so 8 pens cost 96 rupees.
- 2) One worker would take 48 days, so 6 workers take 8 days.
- 3) One person needs 50 g, so 10 people need 500 g.
- 4) One book weighs 0.4 kg, so 7 books weigh 2.8 kg.
- 5) One pen costs 12, so 15 pens cost 180 rupees.
- 6) One brick weighs 1.5 kg, so 20 bricks weigh 30 kg.
- 7) One litre gives 15 km, so 25 litres give 375 km.
- 8) One shirt needs 1.5 m, so 10 shirts need 15 m.
- 9) One tap would take 120 minutes, so 5 taps take 24 minutes.
- 10) One kg costs 70, so 4 kg costs 280 rupees.
While your child works
- The 'find one first' step must be written down, not done mentally. It is where the method mark is and where errors become visible.
- For the workers question, ask 'more workers - should it take longer or less time?' before any calculation. That check catches the commonest ratio error.
- If simplifying is slow, the gap is factors and HCF from earlier in Class 6, not fractions.