Simplify 1$\frac{3}{4} - (2 \frac{1}{3} + 4)$

Analyze the question: We need to simplify 1¾ − (2⅓ + 4). Work out the bracket first, then subtract.

Concept: Follow BODMAS (brackets first). Convert mixed numbers to improper fractions, or work with whole numbers and fractions separately, using a common denominator.

Solution:

Step 1: Bracket 2⅓ + 4 = 6⅓

Step 2: Subtract 1¾ − 6⅓

Convert to improper fractions with denominator 12:

• 1¾ = 7/4 = 21/12
• 6⅓ = 19/3 = 76/12

21/12 − 76/12 = −55/12

Step 3: Convert back to a mixed number 55 ÷ 12 = 4 remainder 7, so −55/12 = −4 7/12

Answer: −4 7/12, which is option C.

Tip: When you subtract a bigger number from a smaller one, the answer is negative. Here 6⅓ is clearly bigger than 1¾, so you should expect a negative result. That lets you eliminate options A and B straight away. Always do the bracket first, and check your sign before choosing an option.