Simplify: (2 1⁄2 + 3.6) − 1.9
- (a)4.2
- (b)5.2
- (c)6.2
- (d)7.2
Answer
Why
Correct — A. Clear the bracket first, then subtract.
Mixed number to decimal: 2 1⁄2 = 2 + 0.5 = 2.5
Add inside the bracket: 2.5 + 3.6 = 6.1
Subtract: 6.1 − 1.9 = 4.2
Check by adding back: 4.2 + 1.9 = 6.1, the bracket's value → option (a)
Why the others are wrong
- (b)5.2 — 5.2 is the borrowing slip. In 6.1 − 1.9 you borrow from the 6 to make 11 − 9 = 2 tenths, then forget the 6 is now 5. Adding back gives 7.1, not 6.1.
- (c)6.2 — 6.2 is larger than the bracket's 6.1, and taking away a positive 1.9 can only make the result smaller. It fails before you finish the subtraction.
- (d)7.2 — 7.2 also exceeds the bracket's 6.1. Add back to see the gap: 7.2 + 1.9 = 9.1, three more than the 6.1 the bracket gives.
Concept
A mixed number is a sum: 2 1⁄2 means 2 + 1⁄2, not 2 × 1⁄2. Halves, quarters and fifths turn into short decimals, so convert once and work in decimals throughout.
By BODMAS the bracket is cleared first. After that the question is one subtraction, and borrowing across the decimal point is where marks go: 6.1 − 1.9 needs 11 − 9 in the tenths and 5 − 1 in the units.
All four options end in .2 and sit exactly 1 apart, so the whole-number part decides, and that is the digit a borrowing slip changes.
Key facts
- A mixed number a b⁄c equals a + b⁄c, so 2 1⁄2 = 2.5.
- 1⁄2 = 0.5, 1⁄4 = 0.25 and 1⁄5 = 0.2, all terminating decimals.
- Subtracting a positive number always leaves less than you started with.
- A subtraction is checked by adding back: 4.2 + 1.9 = 6.1.
Study next
Common traps
- Reading 2 1⁄2 as 2 × 1⁄2 = 1, which leads to 1 + 3.6 − 1.9 = 2.7.
- Borrowing in 6.1 − 1.9 without reducing the units digit, which gives 5.2.
This item puts one mixed number among decimals inside a single bracket. Decimal simplification is also asked 9 Sep 2024, 12:30, Quant Q.24 (21− 4.9 ÷ 7 + 3.9 × 0.4 + 0.9), where division and multiplication come before the addition and subtraction.
Related PYQs
No directly related past PYQ was found.