Exercise 7.4 - Q6
Textbook Exercise Problem
Compare the fractions: 5/6 and 13/15. Which fraction is greater?
Step-by-Step Verified Solution:
- Step 1: Find LCM of denominators 6 and 15: 6 = 2 × 3, 15 = 3 × 5. LCM = 2 × 3 × 5 = 30.
- Step 2: Convert to like denominators: 5/6 = (5 × 5)/(6 × 5) = 25/30.
- Step 3: 13/15 = (13 × 2)/(15 × 2) = 26/30.
- Step 4: Compare numerators: 26 > 25, therefore 26/30 > 25/30 => 13/15 > 5/6.
Final Answer: 13/15 is greater than 5/6
Key Concept / Exam Strategy: Always convert unlike fractions to like fractions using the LCM of their denominators.
Generated Exercise #1
Foundation
Question: Convert 17/5 into a mixed fraction.
Core Concept Tested: Improper to mixed fraction conversion
Mentor Hint: Divide 17 by 5. Quotient is the whole number part; remainder is numerator.
Step-by-Step Solution:
- Step 1: Divide 17 by 5: 17 = 5 × 3 + 2.
- Step 2: Quotient = 3, Remainder = 2, Divisor = 5.
- Step 3: Mixed fraction = 3 2/5.
Verified Answer: 3 2/5
Generated Exercise #2
Intermediate
Question: Evaluate: 3 1/4 + 2 2/3 - 1 1/6.
Core Concept Tested: Addition and subtraction of mixed fractions with unlike denominators
Mentor Hint: Convert each to improper fractions, find LCM of 4, 3, 6 (which is 12).
Step-by-Step Solution:
- Step 1: Convert: 3 1/4 = 13/4; 2 2/3 = 8/3; 1 1/6 = 7/6.
- Step 2: Denominators 4, 3, 6 have LCM = 12.
- Step 3: 13/4 = 39/12; 8/3 = 32/12; 7/6 = 14/12.
- Step 4: (39 + 32 - 14)/12 = 57/12 = 19/4 = 4 3/4.
Verified Answer: 19/4 or 4 3/4
Generated Exercise #3
Intermediate
Question: Express 45 mm in cm, m, and km using decimal notation.
Core Concept Tested: Decimal unit conversions in metric length
Mentor Hint: 1 cm = 10 mm; 1 m = 100 cm; 1 km = 1000 m.
Step-by-Step Solution:
- Step 1: mm to cm: 45 / 10 = 4.5 cm.
- Step 2: mm to m: 45 / 1000 = 0.045 m.
- Step 3: mm to km: 45 / 1,000,000 = 0.000045 km.
Verified Answer: 4.5 cm, 0.045 m, 0.000045 km
Generated Exercise #4
JEE-NEET Foundation
Question: A car covers 43.2 km in 2.4 liters of petrol. How much distance will it travel in 1 liter of petrol?
Core Concept Tested: Unitary method with decimal division
Mentor Hint: Divide total distance by total liters of fuel.
Step-by-Step Solution:
- Step 1: Distance for 1 L = 43.2 ÷ 2.4.
- Step 2: Eliminate decimals by multiplying both by 10: 432 ÷ 24.
- Step 3: 432 / 24 = 18 km.
Verified Answer: 18 km per liter
Generated Exercise #5
Advanced HOTS
Question: Ramesh bought a notebook for ₹ 45.75, a pen for ₹ 18.50, and 2 pencils for ₹ 6.25 each. He handed a ₹ 100 note to the shopkeeper. How much change does he receive?
Core Concept Tested: Multi-step financial decimal arithmetic
Mentor Hint: Find cost of 2 pencils first, sum all purchases, then subtract from ₹ 100.
Step-by-Step Solution:
- Step 1: Cost of pencils = 2 × 6.25 = ₹ 12.50.
- Step 2: Total expenditure = 45.75 + 18.50 + 12.50 = ₹ 76.75.
- Step 3: Change returned = 100.00 - 76.75 = ₹ 23.25.
Verified Answer: ₹ 23.25