Simplify; 2$\frac{1}{4} \times 3\frac{1}{2} \div  4 \frac{3}{8}$

Step 1: Convert the mixed numbers to improper fractions

• 2¼ = 9/4
• 3½ = 7/2
• 4⅜ = 35/8

Step 2: Rewrite the expression

(9/4) × (7/2) ÷ (35/8)

Step 3: Multiply the first two fractions

(9/4) × (7/2) = 63/8

Step 4: Divide by 35/8, which means multiplying by its reciprocal

(63/8) × (8/35) = 63/35

The 8s cancel, leaving 63/35.

Step 5: Simplify

Both 63 and 35 are divisible by 7:

63/35 = 9/5 = 1⁴⁄₅

Concept: Operations of the same rank (× and ÷) are done from left to right. To divide by a fraction, flip it and multiply. Always convert mixed numbers to improper fractions first.

Answer: 1⁴⁄₅, which is option D.

Exam tip: Cancel common factors before multiplying, since it keeps the numbers small. Here, (9/4) × (7/2) × (8/35): the 8 cancels with the 4 and 2, and the 7 cancels with the 35. This leaves 9/5 straight away.