Simplify:(1 2⁄5 + 2.6) − 1 3⁄4

Correct — A. Turn each mixed number into a decimal, then finish the bracket first.

1 2⁄5 = 1 + 0.4 = 1.4
1 3⁄4 = 1 + 0.75 = 1.75
Bracket: 1.4 + 2.6 = 4
Subtract: 4 − 1.75 = 2.25 → option (a)

Why the others are wrong

• (b)
  2.1 — It needs the bracket to be 3.85, since 3.85 − 1.75 = 2.1. The bracket is exactly 4, because the decimal parts 0.4 and 0.6 make a whole.
• (c)
  2.35 — It is 4.1 − 1.75, as if 1 2⁄5 were 1.5. But 2⁄5 = 0.4, so the bracket is 1.4 + 2.6 = 4.
• (d)
  2.5 — It is 4 − 1.5, as if 1 3⁄4 were 1.5. But 3⁄4 = 0.75, so the subtraction is 4 − 1.75 = 2.25.

A mixed number such as 1 2⁄5 means 1 + 2⁄5: a whole part plus a fraction. To combine it with decimals, convert only the fraction part: 2⁄5 = 4⁄10 = 0.4 and 3⁄4 = 75⁄100 = 0.75.

Here the bracket closes to a whole number, 1.4 + 2.6 = 4, which leaves one easy subtraction.

Key facts

• 1 2⁄5 = 1.4 and 1 3⁄4 = 1.75: the whole part stays and the fraction part becomes the decimal.
• Common conversions: 1⁄4 = 0.25, 1⁄2 = 0.5, 3⁄4 = 0.75, 1⁄5 = 0.2, 2⁄5 = 0.4.
• A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factor other than 2 or 5.

Common traps

• Reading 1 3⁄4 as 1 × 3⁄4: a mixed number is a sum, 1 + 3⁄4 = 1.75, not a product.
• Converting the fraction part from its digits rather than by dividing, e.g. treating 2⁄5 as 0.25 instead of 0.4.

No directly related past PYQ was found.