Mathematical Operations
🔒 Log in to trackSign substitution
🔒 Log in to trackThe question gives the signs new meanings: '+' means '×', '−' means '÷', and so on. First rewrite the whole expression with the new signs. Only then calculate with BODMAS. Rewriting and calculating at the same time is where every slip happens.
What sign substitution means
Picture a calculator with relabelled keys. The key printed "+" now multiplies. The key printed "×" now adds.
The question gives such a list and an expression. You must first convert the line into normal maths, then calculate. In SSC, Railway and Banking papers this is one of the most frequent reasoning questions. Done carefully, it is pure marks.
The three-step method
- Write the mapping in rough space, e.g. + → ×, − → ÷, × → +, ÷ → −.
- Rewrite the whole line with the new signs. Keep every number and bracket in place.
- 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. Then 12 + 4 − 1 = 15.
Change each sign once
"+ means × and × means +" is a swap: both changes happen at the same time.
Look only at the original line. Convert each symbol one time. Never convert a sign you have already changed. Writing the new line directly under the old one, symbol by symbol, keeps you honest.
Partial substitution
Sometimes only two signs change: "+ means × and × means +". The other signs keep their normal meaning.
9 + 4 × 7 becomes 9 × 4 + 7 = 36 + 7 = 43. The − or ÷ in the line, if any, stays as it is.
Letters standing for signs
Signs may arrive as 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 does not change: rewrite first, calculate second.
Signs inside brackets
Brackets never move and are always solved first. But the signs inside them are also coded.
If + means ÷ and − means ×, then (24 + 8) − 2 becomes (24 ÷ 8) × 2 = 3 × 2 = 6. Forgetting the sign inside the bracket is a very common loss.
Watch: After substitution, a ÷ may sit where a + used to be. The BODMAS order changes with the signs.
Pick the correct equation after substitution
A harder form gives a mapping and four full equations. Convert each left side, evaluate, and compare with its right side. Exactly one balances.
If × means + and + means ×, test 9 × 4 + 2 = 17. Substituted: 9 + 4 × 2 = 9 + 8 = 17. It balances.
Tip: Work one option per line, in writing. The right sides are plain numbers; only the left sides are coded.
Know the planted wrong answers
| Slip | What the student did |
|---|---|
| Mapping ignored | calculated the original expression |
| BODMAS skipped | rewrote correctly, then went left to right |
| Half substitution | converted some signs and missed others |
Tip: Compute the original expression once as a cross-check. If your answer equals that value, you forgot to substitute.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Full four-sign substitution
'If + means ×, − means ÷, × means + and ÷ means −, then … = ?' All four signs are reassigned.
Write the four-row mapping table.
Rewrite the whole line, converting each sign once.
Evaluate with BODMAS.
Compare with the options.
Separating 'rewrite' from 'calculate' removes every sign slip.
If + means ×, − means ÷, × means + and ÷ means −, find 6 + 2 × 4 ÷ 2 − 2.
Show solutionHide solution
Rewrite: 6 × 2 + 4 − 2 ÷ 2.
6 × 2 = 12 and 2 ÷ 2 = 1.
12 + 4 − 1 = 15.
15
Partial (two-sign) substitution
Only two signs are given new meanings; the others stay normal.
Change only the listed signs.
Keep the other signs as they are.
Evaluate with BODMAS.
An unlisted sign keeps its usual job.
If + means × and × means +, find 9 + 4 × 7.
Show solutionHide solution
Rewrite: 9 × 4 + 7.
36 + 7 = 43.
43
Substitution with brackets
The expression under substitution contains brackets.
Convert the signs inside and outside the brackets.
Solve the bracket first.
Finish with BODMAS.
Brackets fix the order, but their inner signs are still coded.
If + means ÷ and − means ×, find (24 + 8) − 2.
Show solutionHide solution
Rewrite: (24 ÷ 8) × 2.
24 ÷ 8 = 3.
3 × 2 = 6.
6
Letter-coded operators
Letters like A, B, C, D stand for the four signs.
Write the letter-to-sign table.
Replace each letter by its sign.
Evaluate with BODMAS.
A letter is just another name for a sign.
A means +, B means −, C means × and D means ÷. Find 18 C 4 D 6 A 9 B 5.
Show solutionHide solution
Rewrite: 18 × 4 ÷ 6 + 9 − 5.
18 × 4 = 72, then 72 ÷ 6 = 12.
12 + 9 − 5 = 16.
16
Substitute, then pick the correct equation
A mapping is given, and the options are four complete equations. One becomes true after substitution.
Convert the left side of the first option.
Evaluate it and compare with its right side.
Repeat for every option in writing.
Mark the one that balances.
The right side is already a plain number; only the left side is coded.
If × means + and + means ×, which equation is correct: 9 × 4 + 2 = 17, 9 + 4 × 2 = 17, 8 × 5 + 1 = 14 or 6 × 3 + 1 = 20?
Show solutionHide solution
First: 9 + 4 × 2 = 9 + 8 = 17 ✓.
Second: 9 × 4 + 2 = 38 ✗.
Third: 8 + 5 × 1 = 13 ✗. Fourth: 6 + 3 × 1 = 9 ✗.
9 × 4 + 2 = 17
Shortcuts that save time
After the correct value, evaluate the original expression once. If that number sits among the options, the examiner planted it. Seeing it confirms your substitution is the different one.
If '+' means '÷' and '×' means '+', evaluate 8 + 4 × 2.
Show solutionHide solution
Substituted: .
Original: — the 'mapping ignored' trap.
4
Mistakes to avoid
Where most students lose marks on this subtopic.
Substituting and calculating at the same time.
Rewrite the full line first, then calculate.
Converting a sign twice while handling a swap.
Read only the original line. Convert each symbol once.
Changing signs that the question did not list.
Unlisted signs keep their normal meaning.
Leaving the signs inside brackets as they were.
Convert them too. Brackets fix the order, not the meanings.
Marking the value of the original expression.
Cross-check: if your answer equals the original value, redo the substitution.
Quick revision
Read this the night before the exam.
Mapping table, then rewrite the full line, then BODMAS. Never mix the steps.
A swap like '+ means × and × means +' works both ways at once.
Signs not in the list keep their normal meaning.
Letters for signs are handled exactly the same way.
Convert signs inside brackets; solve brackets first.
Wrong options: original value, left-to-right value, half-substituted value.
Practice: 19 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 10 questions
Suggested time 7 min · wrong answers go to your mistake notebook automatically.