In this guide, we'll walk through Fractions — Complete Guide with Examples step by step. Whether you're revising for an exam or practising fractions, this clear walkthrough will help you understand not just the answer, but the reasoning behind every step.

Quick Answer

See the step-by-step solution above for the complete answer.

Step-by-Step Solution

Step 1: Find common denominator: 6×6=36

Step 2: 5/6 = 30/36

Step 3: 5/6 = 30/36

Step 4: Add: 30/36 + 30/36 = 60/36

Step 5: Multiply across: 15/121

Step 6: Flip & multiply: 10/48

Step 7: Multiply across: 45/10

Step 8: Common denominator: 6

Step 9: = 8/6

Step 10: Common denominator: 9

Step 11: 6/9 - 6/9 = 0/9

Step 12: 7×7=49

Step 13: 49+2=51

Step 14: Multiply numerators: 3×3=9

Step 15: Multiply denominators: 4×4=16

Step 16: Result: 9/16

Step 17: Flip second fraction: 5/4

Step 18: Multiply: 4×5/5×4 = 20/20

Step 19: Find common denominator: 6×6=36

Step 20: 5/6 = 30/36

Step 21: 5/6 = 30/36

Step 22: Add: 30/36 + 30/36 = 60/36

Step 23: Common denominator: 49

Step 24: 42/49 - 42/49 = 0/49

Step 25: Multiply numerators: 7×1=7

Step 26: Multiply denominators: 8×8=64

Step 27: Result: 7/64

Step 28: Flip second fraction: 9/2

Step 29: Multiply: 8×9/2×2 = 72/4

Step 30: Find common denominator: 3×2=6

Step 31: 9/3 = 18/6

Step 32: 3/2 = 9/6

Step 33: Add: 18/6 + 9/6 = 27/6

Step 34: Common denominator: 12

Step 35: 3/12 - 16/12 = -13/12

Step 36: Multiply numerators: 2×5=10

Step 37: Multiply denominators: 5×4=20

Step 38: Result: 10/20

Step 39: Flip second fraction: 5/6

Step 40: Multiply: 3×5/6×6 = 15/36

Step 41: Find common denominator: 7×6=42

Step 42: 4/7 = 24/42

Step 43: 1/6 = 7/42

Step 44: Add: 24/42 + 7/42 = 31/42

Step 45: Common denominator: 56

Step 46: 35/56 - 16/56 = 19/56

Step 47: Multiply numerators: 6×3=18

Step 48: Multiply denominators: 2×8=16

Step 49: Result: 18/16

Step 50: Flip second fraction: 9/4

Step 51: Multiply: 7×9/3×4 = 63/12

Why This Works

This problem uses fractions. The key idea is to perform the same operation on both sides to keep the equation balanced. Each step brings you closer to isolating the unknown variable.

Common Mistakes to Avoid

❌ Mistake 1: Forgetting to apply the same operation to both sides of the equation.

❌ Mistake 2: Making sign errors when moving terms across the equals sign.

❌ Mistake 3: Not simplifying the final answer completely.

Practice Similar Problems

• Solve: x² - 12x + 35 = 0
• Solve: x² + 9x - 36 = 0
• Solve: x² + 0x - 49 = 0
• Solve: x² - x - 30 = 0
• Solve: x² + 20x + 96 = 0

Frequently Asked Questions