What is the result of2 1⁄4 ÷ 0.5?
- (a)4.25
- (b)4.5
- (c)4.75
- (d)5.25
Answer
Why
Correct — B. Put both numbers in forms that divide cleanly.
Mixed number: 2 1⁄4 = (2 × 4 + 1)⁄4 = 9⁄4 = 2.25
Divisor: 0.5 = 1⁄2, so ÷ 0.5 means × 2
Multiply: 2.25 × 2 = 4.5 → option (b)
Check: 4.5 × 0.5 = 2.25 = 2 1⁄4
Why the others are wrong
- (a)4.25 — 4.25 doubles only the whole part (2 × 2 + 1⁄4). The quarter doubles too: 2 × 2 + 2 × 1⁄4 = 4 + 0.5 = 4.5.
- (c)4.75 — 4.75 × 0.5 = 2.375, which is 2 3⁄8, not 2 1⁄4. Multiplying back by the divisor is the quickest check on a division.
- (d)5.25 — 5.25 × 0.5 = 2.625, which is 2 5⁄8, not 2 1⁄4. Only 4.5 halves back to the number being divided.
Concept
Dividing by a decimal is easiest as multiplying by its reciprocal. 0.5 = 1⁄2, and the reciprocal of 1⁄2 is 2, so ÷ 0.5 doubles the number.
A mixed number a b⁄c means a + b⁄c, so 2 1⁄4 = 9⁄4. Then 9⁄4 × 2 = 9⁄2 = 4.5. Dividing a positive number by anything between 0 and 1 makes it larger.
The response sheet prints this stem as a picture. It reads 2 1⁄4 ÷ 0.5: two and a quarter, divided by 0.5.
Key facts
- Dividing by 0.5 is the same as multiplying by 2.
- Dividing by 0.25 multiplies by 4, and dividing by 0.2 multiplies by 5.
- 2 1⁄4 = 9⁄4 = 2.25.
Study next
Common traps
- Halving instead of doubling: 2.25 × 0.5 = 1.125 is a multiplication, not this division.
- Reading 2 1⁄4 as 2 × 1⁄4 = 0.5: the space in a mixed number means 2 + 1⁄4.
The same 2 1⁄4 ÷ 0.5 sits inside a longer simplification at 15 Sep 2025, 16:00, Quant Q.1, and (7⁄8 × 2.4) ÷ 0.6 = 3.5 is asked at 15 Sep 2025, 12:30, Quant Q.1.
Related PYQs
No directly related past PYQ was found.