Which of the following fractions is the largest?

Correct — A. The stem prints four fractions as images — 2⁄3, 6⁄53, 79⁄90 and 33⁄44 — and asks which is largest. Option (a) is 79⁄90.

Decimalise each one:
79⁄90 = 0.8778
33⁄44 = 3⁄4 = 0.75
2⁄3 = 0.6667

6⁄53 = 0.1132 is nowhere near the others.

Faster route — measure the gap to 1. 1 − 79⁄90 = 11⁄90 and 1 − 33⁄44 = 11⁄44. Same numerator, larger denominator, smaller gap, so 79⁄90 sits closest to 1 → option (a).

Why the others are wrong

• (b)
  Option (b) is 2⁄3 = 0.6667. It beats 6⁄53 comfortably but loses to both 33⁄44 (0.75) and 79⁄90 (0.8778).
• (c)
  Option (c) is 33⁄44, which reduces to 3⁄4 = 0.75. Larger digits do not make a larger fraction — it still falls short of 0.8778.
• (d)
  Option (d) is 6⁄53 ≈ 0.1132, the smallest here: its numerator is barely more than a ninth of its denominator, since 6 × 9 = 54.

Ranking fractions has three standard routes, and the skill is picking the cheap one.

Cross-multiplication is exact but slow across four candidates. Decimal conversion always works and is safest under time pressure.

The third route compares each fraction with a landmark such as 1. Here 79⁄90 and 33⁄44 both fall short of 1 by a numerator of 11, so the whole question reduces to comparing 11⁄90 with 11⁄44: with equal numerators the larger denominator gives the smaller value, and therefore the smaller shortfall.

Key facts

• For two fractions with the same numerator, the one with the larger denominator is the smaller fraction.
• 33⁄44 reduces to 3⁄4, which is exactly 0.75.
• 79⁄90 = 0.8778 to four decimal places, the largest of the four printed fractions.
• 6⁄53 ≈ 0.1132, a shade above 1⁄9.

Common traps

• Ranking by the size of the digits rather than the value of the ratio, which makes 33⁄44 look biggest.
• Cross-multiplying all six pairs when one glance at 6⁄53 removes it immediately.
• Failing to reduce 33⁄44 to 3⁄4 and then miscomputing 33 ÷ 44.

No directly related past PYQ was found.