Simplify the following.

Correct — D. The expression is (5 − 15⁄16) × 1 12⁄13. Clear the bracket first.

5 − 15⁄16 = 80⁄16 − 15⁄16 = 65⁄16

Turn the mixed number into an improper fraction:
1 12⁄13 = (13 + 12)⁄13 = 25⁄13

Multiply, cancelling 65 against 13:
(65⁄16) × (25⁄13) = (5 × 25)⁄16 = 125⁄16

125 ÷ 16 = 7 remainder 13, so the value is 7 13⁄16 — option (d).

Why the others are wrong

• (a)
  Option (a) reads 7 11⁄16, that is 123⁄16. The whole part is right, but 65 cancels against 13 to give 5, and 5 × 25 is 125, not 123.
• (b)
  Option (b) reads 5 13⁄16. The bracket alone is already 65⁄16 = 4 1⁄16, and multiplying by 25⁄13 ≈ 1.92 nearly doubles it, so the answer must land near 7.8.
• (c)
  Option (c) reads 5 11⁄16, wrong in both halves. It carries neither the 125 numerator nor the near-doubling that 25⁄13 forces.

Two conversions, then one cancellation.

A whole number minus a proper fraction becomes a single fraction over the same denominator: 5 = 80⁄16, so 5 − 15⁄16 = 65⁄16.

A mixed number a b⁄c becomes (ac + b)⁄c, so 1 12⁄13 = 25⁄13. A mixed number can never be multiplied with its whole part left outside.

Then hunt for a common factor across the multiplication sign before multiplying out. Here 65 and 13 share 13, which turns a four-digit product into 5 × 25.

Key facts

• A mixed number a b⁄c equals (a × c + b)⁄c, so 1 12⁄13 = 25⁄13.
• 5 − 15⁄16 = 80⁄16 − 15⁄16 = 65⁄16, which is 4 1⁄16.
• (65⁄16) × (25⁄13) = 125⁄16, because 65 and 13 cancel to 5.
• 125⁄16 = 7 13⁄16, since 16 × 7 = 112 and 125 − 112 = 13.

Common traps

• Multiplying 65⁄16 by 12⁄13 and dropping the whole 1 in 1 12⁄13
• Writing 5 − 15⁄16 as 4 15⁄16 instead of 4 1⁄16
• Multiplying out 65 × 25 and 16 × 13 before cancelling, then wrestling with 1625⁄208

No directly related past PYQ was found.