Simplify the following: 21− 4.9 ÷ 7 + 3.9 × 0.4 + 0.9

Correct — C. BODMAS: clear division and multiplication first as one tier, then addition and subtraction as the next, each tier left to right.

4.9 ÷ 7 = 0.7
3.9 × 0.4 = 1.56 (39 × 4 = 156, and there are two decimal places between the factors)

The line becomes 21 − 0.7 + 1.56 + 0.9. Now work left to right:
21 − 0.7 = 20.3
20.3 + 1.56 = 21.86
21.86 + 0.9 = 22.76 → option (c)

Why the others are wrong

• (a)
  26.32 — 26.32 overshoots 22.76 by 3.56 — more than either computed term is worth, so an operator step has gone wrong rather than the running addition.
• (b)
  18.23 — Killed by a range check before any arithmetic: 18.23 is below 21, and the only subtraction in the line takes 0.7 off 21 before two additions put more back.
• (d)
  24.12 — 24.12 is 1.36 above 22.76. Every term is exact to two decimal places, so this is a slip in the running total, not an ordering error.

BODMAS ranks operations: brackets, then orders (powers and roots), then division and multiplication as one shared tier, then addition and subtraction as a second shared tier.

Within a tier you work left to right. The two persistent myths are that division always precedes multiplication and that addition always precedes subtraction; both are false, because each pair shares a rank.

In a bracket-free line like this one the only real hazard is remembering that the minus sign attaches to the quotient 4.9 ÷ 7 — that is, to 0.7 — and not to 4.9 alone.

Key facts

• Division and multiplication share one precedence level and are performed left to right.
• Addition and subtraction share the next level down, also left to right.
• 4.9 ÷ 7 = 0.7 and 3.9 × 0.4 = 1.56, so the line reduces to 21 − 0.7 + 1.56 + 0.9 = 22.76.
• A minus sign in front of a division applies to the whole quotient, not to the numerator.

Common traps

• Working strictly left to right and computing 21 − 4.9 first.
• Misplacing the decimal point in 3.9 × 0.4 — it is 1.56, not 0.156 or 15.6.
• Treating the minus sign as a bracket that outranks the division.

No directly related past PYQ was found.