Simplify: (3.2 − 1 3⁄5) + (2 1⁄4 ÷ 0.5)

Correct — B. Clear each bracket on its own, then add.

First bracket, convert the mixed number: 1 3⁄5 = 1 + 0.6 = 1.6
Subtract: 3.2 − 1.6 = 1.6

Second bracket, convert: 2 1⁄4 = 2.25
Divide by 0.5, which doubles: 2.25 × 2 = 4.5

Add the two brackets: 1.6 + 4.5 = 6.1 → option (b)

Why the others are wrong

• (a)
  8.2 — 8.2 overshoots even the no-subtraction total. Leave 1 3⁄5 out entirely and 3.2 + 4.5 is still only 7.7, so 8.2 cannot come from these two brackets.
• (c)
  7.7 — 7.7 is 3.2 + 4.5, the total you get if the first bracket stays at 3.2 and 1 3⁄5 is never subtracted. Taking away 1.6 brings it to 6.1.
• (d)
  10.5 — 10.5 would need the second bracket to be 8.9, since 10.5 − 1.6 = 8.9. But 2 1⁄4 ÷ 0.5 = 2.25 × 2 = 4.5.

Put every number in one form before combining. Decimals are easiest here: 1 3⁄5 = 1.6 and 2 1⁄4 = 2.25.

Dividing by 0.5 is multiplying by 2, because 0.5 = 1⁄2 and dividing by a fraction means multiplying by its reciprocal. So 2.25 ÷ 0.5 = 4.5.

Each bracket is cleared first, and only then are the two results added.

Key facts

• A mixed number a b⁄c means a + b⁄c, so 1 3⁄5 = 1 + 3⁄5 = 1.6.
• Dividing by 0.5 doubles a number, and dividing by 0.25 multiplies it by 4.
• Fifths and quarters convert exactly: 1⁄5 = 0.2 and 1⁄4 = 0.25.

Common traps

• Reading 1 3⁄5 as 1.35. The 3⁄5 is three-fifths, 0.6, so the number is 1.6.
• Halving instead of doubling when dividing by 0.5: 2.25 ÷ 0.5 is 4.5, not 1.125.

No directly related past PYQ was found.