Simplify the following expression using the BODMAS rule: 3/4 + (5/6 × 9/10) - 2/3

Question

Simplify the following expression using the BODMAS rule:

3/4 + (5/6 × 9/10) - 2/3

1. A. 3/5
2. B. 6/5
3. C. 13/5
4. D. 5/6 (Correct answer)

Correct Answer

Option D — 5/6

Detailed Solution & Explanation

The correct answer is $\dfrac{5}{6}$.

Shortcut Trick

• Under BODMAS the bracket goes first, and the multiplication inside it simplifies neatly:
  • $\dfrac{5}{6} \times \dfrac{9}{10} = \dfrac{45}{60} = \dfrac{3}{4}$
• The expression becomes $\dfrac{3}{4} + \dfrac{3}{4} - \dfrac{2}{3} = \dfrac{3}{2} - \dfrac{2}{3}$.
• $\dfrac{9 - 4}{6} = \dfrac{\textbf{5}}{\textbf{6}}$

Alternate Method

• Take an LCM of 60 throughout:
  • $\dfrac{3}{4} = \dfrac{45}{60}$, $\;\dfrac{5}{6} \times \dfrac{9}{10} = \dfrac{45}{60}$, $\;\dfrac{2}{3} = \dfrac{40}{60}$
• $\dfrac{45 + 45 - 40}{60} = \dfrac{50}{60} = \dfrac{5}{6}$

Additional Information

• BODMAS order: Brackets → Orders (powers and roots) → Division and Multiplication (left to right) → Addition and Subtraction (left to right). Division and multiplication rank equally, as do addition and subtraction — they are worked left to right, not division before multiplication.
• Cancelling before multiplying ($\frac{5}{6} \times \frac{9}{10}$: cancel 5 with 10 and 3 with 9 to get $\frac{3}{4}$ directly) avoids large numerators entirely.
• Distractor $\frac{13}{5}$ is what you get by ignoring the bracket and working strictly left to right — the error the question is designed to catch.