Mathematical Operations

What sign substitution means

Imagine a calculator whose keys have been relabelled: the key marked "+" now multiplies and the key marked "×" now adds. The question gives you such a list of new meanings and an expression. You must first convert the expression into normal maths and only then calculate. In SSC, Railway and Banking papers this is one of the most frequent reasoning questions, and it is almost pure marks if you are careful.

The three-step method

1. Write the mapping in a small table in your rough space, e.g. + → ×, − → ÷, × → +, ÷ → −.
2. Rewrite the whole line with the new signs. Keep every number and every bracket exactly where it is.
3. Calculate with BODMAS on the rewritten line.

Example: If + means ×, − means ÷, × means + and ÷ means −, find 6 + 2 × 4 ÷ 2 − 2. Rewrite: 6 × 2 + 4 − 2 ÷ 2. Now BODMAS: 6 × 2 = 12 and 2 ÷ 2 = 1, so 12 + 4 − 1 = 15.

Convert each sign only once

When the list says "+ means × and × means +", both changes happen at the same time. Look at the original line, and convert each symbol one time. Do not convert a sign that you have already changed. A good habit is to write the new line below the old one, symbol by symbol, looking only at the old line.

Partial substitution

Sometimes only two signs are changed ("+ means ×, × means +"). The other signs keep their normal meaning. Example: 9 + 4 × 7 becomes 9 × 4 + 7 = 36 + 7 = 43.

Letter-coded signs

The signs may be replaced by letters: "A means +, B means −, C means ×, D means ÷". Then 18 C 4 D 6 A 9 B 5 means 18 × 4 ÷ 6 + 9 − 5. Left to right for × and ÷: 72 ÷ 6 = 12. Then 12 + 9 − 5 = 16. The method is the same: rewrite first, then calculate.

Substitution with brackets

Brackets never move and are always solved first, but the signs inside the brackets are also converted. Example: if + means ÷ and − means ×, then (24 + 8) − 2 becomes (24 ÷ 8) × 2 = 3 × 2 = 6. Forgetting to convert the sign inside the bracket is a very common loss.

Choose the correct equation after substitution

A harder form gives a mapping and four equations. Convert each left side, evaluate it, and compare with the right side. Exactly one option balances. Work in writing, one option per line.

Know the planted wrong answers

Most options are made from these slips:

Slip	What the student did
Mapping ignored	calculated the original expression
BODMAS skipped	rewrote correctly but went left to right
Half substitution	converted some signs and missed others

If your answer equals the original expression's value, you forgot to substitute. That quick check saves many marks.

Quick revision

• Mapping table → rewrite the full line → BODMAS. Never substitute and calculate together.
• All changes are simultaneous: convert each symbol once, reading the ORIGINAL line.
• Signs not in the list keep their normal meaning.
• Letters for signs (A, B, P, Q...) are handled the same way.
• Convert signs inside brackets too; brackets are still solved first.
• Wrong options = original value, left-to-right value, half-substituted value.