Simplify $\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}$

Step 1: Analyze the question We need to simplify a fraction whose numerator is a product of mixed numbers and whose denominator is a division of mixed number by a fraction. Convert the mixed numbers to improper fractions first.

Step 2: Numerator

• 1⅞ = 15/8
• 2⅖ = 12/5

Numerator = (15/8) × (12/5) = 180/40 = 9/2 = 4½

Step 3: Denominator

• 6¾ = 27/4

Denominator = (27/4) ÷ (3/4) = (27/4) × (4/3) = 9

Step 4: Divide (9/2) ÷ 9 = 9/2 × 1/9 = 1/2

Answer: ½, which is option D.

Tip: Always convert mixed numbers to improper fractions before multiplying or dividing. Also, watch out: 4½ (option B) is only the numerator, so don't stop before dividing by the denominator.