🔢 Fraction Operations Challenge

Work out the following operations and select the correct response from the choices provided.

(2²⁄₃ - ⅚) ÷ 2¹⁄₅ × ¾ + 1³⁄₇ = ?
Work it out step by step...
7
8
9
÷
4
5
6
×
1
2
3
-
0
/
=
+
🤔
Let me calculate...

📝 Step-by-Step Solution

1
Convert mixed numbers to improper fractions:
2²⁄₃ = ⁸⁄₃     2¹⁄₅ = ¹¹⁄₅     1³⁄₇ = ¹⁰⁄₇
2
Solve the bracket first (subtraction):
⁸⁄₃ - ⅚ = ¹⁶⁄₆ - ⅚ = ¹¹⁄₆
3
Division (multiply by reciprocal):
¹¹⁄₆ ÷ ¹¹⁄₅ = ¹¹⁄₆ × ⅕⁄₁₁ = ⁵⁄₆
4
Multiplication:
⅚ × ¾ = ¹⁵⁄₂₄ = ⅝
5
Final addition:
⅝ + ¹⁰⁄₇ = Find common denominator (56)
³⁵⁄₅₆ + ⁸⁰⁄₅₆ = ¹¹⁵⁄₅₆
6
Simplify (if needed) or convert to mixed number:
¹¹⁵⁄₅₆ = 2³⁄₅₆ or simplified: 2¹⁄₁₁ = ²¹⁄₁₁

🎯 Operation Flow

2²⁄₃ - ⅚
→
¹¹⁄₆
→
÷ 2¹⁄₅
→
⅚
→
× ¾
→
⅝
→
+ 1³⁄₇
→
²¹⁄₁₁

Select the correct answer:

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📚 Order of Operations (BODMAS/PEMDAS)

Remember: Brackets, Orders, Division/ Multiplication, Addition/ Subtraction

Complete Calculation:

  1. Convert mixed numbers: 2²⁄₃ = ⁸⁄₃, 2¹⁄₅ = ¹¹⁄₅, 1³⁄₇ = ¹⁰⁄₇
  2. Brackets: ⁸⁄₃ - ⅚ = ¹¹⁄₆
  3. Division: ¹¹⁄₆ ÷ ¹¹⁄₅ = ¹¹⁄₆ × ⅕⁄₁₁ = ⅚
  4. Multiplication: ⅚ × ¾ = ⅝
  5. Addition: ⅝ + ¹⁰⁄₇ = ³⁵⁄₅₆ + ⁸⁰⁄₅₆ = ¹¹⁵⁄₅₆ = ²¹⁄₁₁

Final Answer: ²¹⁄₁₁ (or 1¹⁰⁄₁₁ as a mixed number)