0
0

Fractions Simplification

Introduction

Fraction simplification वाले questions आपकी ratios को जल्दी handle करने की ability को test करते हैं। Exams में ये common होते हैं और reciprocals का सही इस्तेमाल और step-by-step cancelation सीखने पर बहुत आसान हो जाते हैं।

Pattern: Fractions Simplification

Pattern

मुख्य idea: Division को हमेशा reciprocal से multiplication में बदलें। फिर common factors cancel करके fraction को step-by-step simplify करें।

Step-by-Step Example

Question

Simplify: (3/4 ÷ 2/5) × (5/6)

Options:

  • A) 25/16
  • B) 16/25
  • C) 15/18
  • D) 75/48

Solution

  1. Step 1: Division को multiplication में बदलें

    Division को reciprocal लेकर multiplication में बदलें। (3/4 ÷ 2/5) = (3/4 × 5/2).

  2. Step 2: तीसरी fraction को शामिल करें

    अब तीसरी fraction को शामिल करें: (3/4 × 5/2 × 5/6).

  3. Step 3: Numerators और denominators multiply करें

    Numerator = 3 × 5 × 5 = 75, Denominator = 4 × 2 × 6 = 48.

  4. Step 4: Fraction को simplify करें

    75/48 को 3 से divide करके simplify करें। 75 ÷ 3 = 25, 48 ÷ 3 = 16 → 25/16.

  5. Final Answer:

    25/16 → Option A.

  6. Quick Check:

    Decimals में देखें → (3/4 ÷ 0.4) × 0.833 ≈ 1.5625, और 25/16 = 1.5625 ✅

Quick Variations

1. Addition/Subtraction → common denominator लें।

2. Mixed numbers → improper fractions में बदलें।

3. Whole numbers के साथ division → whole number को n/1 लिखें।

Trick to Always Use

  • Step 1 → Division को हमेशा reciprocal लेकर multiplication में बदलें।
  • Step 2 → Multiply करने से पहले common numbers cancel कर दें।
  • Step 3 → Final fraction को पूरी तरह simplify करें।

Summary

Summary

  • Division को हमेशा reciprocals की मदद से multiplication में बदलें।
  • Common factors को पहले cancel करें ताकि calculation आसान हो जाए।
  • Addition या subtraction में ही common denominator का उपयोग होता है।
  • Final fraction को lowest terms में simplify करें।

याद रखने वाला example:
(3/4 ÷ 2/5) × (5/6) = 25/16

Practice

(1/5)
1. Simplify: (2/3 ÷ 4/9)
easy
A. 3/2
B. 2/9
C. 9/8
D. 1/6

Solution

  1. Step 1: Change division into multiplication by reciprocal

    Change division to multiplication by reciprocal: (2/3 ÷ 4/9) = (2/3 × 9/4).

  2. Step 2: Multiply numerators and denominators

    Multiply numerators and denominators: numerator = 2 × 9 = 18, denominator = 3 × 4 = 12.

  3. Step 3: Simplify the fraction

    Simplify 18/12 = 3/2.

  4. Final Answer:

    3/2 → Option A.

  5. Quick Check:

    As decimals: 0.6667 ÷ 0.4444 ≈ 1.5 ✅
Hint: Flip the second fraction and multiply.
Common Mistakes: Multiplying denominators without flipping the second fraction.
2. Simplify: (5/8 × 16/15)
easy
A. 2/3
B. 3/4
C. 4/5
D. 8/15

Solution

  1. Step 1: Cancel common factors before multiplying

    Cancel before multiplying: 16/8 = 2, so expression becomes (5 × 2) / 15.

  2. Step 2: Compute numerator and denominator

    Compute numerator and denominator: 10/15.

  3. Step 3: Simplify the fraction

    Simplify 10/15 = 2/3.

  4. Final Answer:

    2/3 → Option A.

  5. Quick Check:

    0.625 × 1.0667 ≈ 0.6667 ✅
Hint: Always cancel common factors first to keep numbers small.
Common Mistakes: Multiplying fully first and forgetting to reduce early.
3. Simplify: (7/9 ÷ 14/27)
easy
A. 2/3
B. 3/2
C. 9/14
D. 27/126

Solution

  1. Step 1: Flip the divisor and multiply

    Flip and multiply: (7/9 ÷ 14/27) = (7/9 × 27/14).

  2. Step 2: Cancel common factors before multiplying

    Cancel 27/9 = 3 → expression becomes (7 × 3) / 14 = 21/14.

  3. Step 3: Simplify the fraction

    Simplify 21/14 = 3/2.

  4. Final Answer:

    3/2 → Option B.

  5. Quick Check:

    0.7778 ÷ 0.5185 ≈ 1.5 ✅
Hint: Look for easy cancellations like 27/9 before multiplying.
Common Mistakes: Multiplying denominators without cancelling common factors first.
4. Simplify: (3/4 ÷ 9/8)
medium
A. 3/4
B. 4/3
C. 2/3
D. 3/2

Solution

  1. Step 1: Flip the divisor and convert to multiplication

    Flip and multiply: (3/4 ÷ 9/8) = (3/4 × 8/9).

  2. Step 2: Cancel factors before multiplying

    Cancel 8/4 = 2 → expression becomes (3 × 2) / 9 = 6/9.

  3. Step 3: Simplify the fraction

    Simplify 6/9 = 2/3.

  4. Final Answer:

    2/3 → Option C.

  5. Quick Check:

    0.75 ÷ 1.125 = 0.6667 ✅
Hint: Flip the divisor and cancel before multiplying.
Common Mistakes: Forgetting to flip the second fraction or not cancelling 8/4 early.
5. Simplify: (7/8 ÷ 7/16) × (3/5)
medium
A. 3/8
B. 5/6
C. 7/16
D. 6/5

Solution

  1. Step 1: Divide by multiplying with reciprocal

    First divide: (7/8 ÷ 7/16) = (7/8 × 16/7).

  2. Step 2: Cancel identical factors

    Cancel the 7s → becomes 16/8 = 2.

  3. Step 3: Multiply by the third fraction

    Now multiply by 3/5 → 2 × 3/5 = 6/5.

  4. Final Answer:

    6/5 → Option D.

  5. Quick Check:

    (7/8 ÷ 7/16) = 2, and 2 × 0.6 = 1.2 = 6/5 ✅
Hint: Cancel identical factors (7) early to simplify the division.
Common Mistakes: Multiplying incorrectly before cancelling or forgetting to flip the divisor.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes