Simplification & Approximation — IBPS Clerk / SBI Clerk

Simplification & Approximation is the single heaviest topic in clerk-level Numerical Ability, and it actually contains two distinct question types that demand opposite disciplines. A simplification question asks for an EXACT answer and must be evaluated precisely via BODMAS; an approximation question explicitly allows rounding and rewards deliberately estimating rather than computing exactly — confusing the two, by rounding a simplification question or over-computing an approximation question, wastes time in both directions.

1. Simplification: exact BODMAS evaluation

A simplification question gives a multi-step numeric expression — often mixing fractions, decimals, brackets and basic operations — and requires the exact value, following Brackets, Of, Division, Multiplication, Addition, Subtraction strictly in that order. Division and multiplication are resolved left to right as they appear, not division-always-first; the same left-to-right rule applies once only addition and subtraction remain.

$\frac{15\times 8}{4+2}-6=14$

The bracket resolves first ($4+2=6$), then the multiplication and division proceed left to right ($15\times 8=120$, then $120÷6=20$), and finally the subtraction finishes the expression ($20-6=14$).

2. Simplification with fractions

When a simplification expression contains fractions being added or multiplied together with other terms, converting every fraction to a common form before combining is what prevents a sign or order error. $\left(\frac{3}{4}+\frac{2}{3}\right)\times 12$ resolves the bracket first using the LCM of 4 and 3 (which is 12): $\frac{9}{12}+\frac{8}{12}=\frac{17}{12}$, then $\frac{17}{12}\times 12=17$.

3. Approximation: deliberate, fast rounding

An approximation question explicitly permits rounding to the nearest convenient number, and the skill is choosing a rounding that stays close enough to the true value while making the arithmetic fast — usually rounding percentages to the nearest 5 or 10, and numbers to the nearest 10 or 100. $39.98\%$ of $250.1$ approximates cleanly to $40\%$ of $250=100$; the actual value is close enough that the rounding introduces negligible error relative to the multiple-choice options' spacing.

4. Choosing what to round

Not every number in an approximation expression needs rounding — round only the values that are awkward to compute exactly, and leave already-clean numbers as they are. $11.02\times 19.97$ rounds cleanly to $11\times 20=220$, since both factors are already close to round numbers; rounding a number that is already convenient (like exactly 20) adds unnecessary imprecision for no speed benefit.

5. Square roots, cubes and powers in approximation

Approximation questions frequently include a square root, cube or power term, and recognising a NEARBY perfect square/cube is faster than computing the root directly. $\sqrt{80.9}$ is close to $\sqrt{81}=9$, and using 9 as the estimate is accurate enough for a multiple-choice approximation question, since the actual root ($\approx 8.99$) rounds to the same nearby integer.

Worked Examples

Example 1. Simplify exactly: $\frac{15\times 8}{4+2}-6$.

Bracket first: $4+2=6$. Then $15\times 8=120$, $120÷6=20$. Finally $20-6=14$.

Answer: 14.

Example 2. Simplify exactly: $\left(\frac{3}{4}+\frac{2}{3}\right)\times 12$.

LCM of 4 and 3 is 12: $\frac{9}{12}+\frac{8}{12}=\frac{17}{12}$. Then $\frac{17}{12}\times 12=17$.

Answer: 17.

Example 3. Simplify exactly: $\sqrt{144}+\sqrt[3]{125}$.

$\sqrt{144}=12$ and $\sqrt[3]{125}=5$. Sum $=17$.

Answer: 17.

Example 4. Approximate: $39.98\%$ of $250.1$ + $\sqrt{80.9}$.

Round $39.98\%$ to $40\%$ and $250.1$ to $250$: $40\%$ of $250=100$. Round $\sqrt{80.9}$ to the nearby $\sqrt{81}=9$. Sum $\approx 100+9=109$.

Answer: approximately 109.

Example 5. Approximate: $11.02\times 19.97$.

Round to the nearest clean numbers already close by: $11\times 20=220$.

Answer: approximately 220.

Example 6. Approximate: $24.9\%$ of $601$.

Round $24.9\%$ to $25\%$ and $601$ to $600$: $25\%$ of $600=150$.

Answer: approximately 150.

Example 7. Simplify exactly: $12.5\%$ of $640$ + $\frac{3}{8}$ of $96$.

$12.5\%$ of $640=\frac{1}{8}\times 640=80$. $\frac{3}{8}$ of $96=36$. Sum $=80+36=116$.

Answer: 116.

Summary

Simplification demands an EXACT answer via strict BODMAS — brackets first, then division/multiplication left to right, then addition/subtraction left to right — never rounded.

Approximation explicitly allows rounding, and the skill is choosing which numbers to round (usually percentages to the nearest 5 or 10, numbers to the nearest 10 or 100) while leaving already-clean numbers untouched, since rounding a convenient number wastes the time it was meant to save.

For roots, cubes and powers inside an approximation question, recognising a nearby perfect square or cube gives a fast, sufficiently accurate estimate without computing the exact root — the small resulting error is negligible relative to the spacing between multiple-choice options.

Confusing the two question types — rounding a simplification question, or computing an approximation question to full precision — costs time in both directions; reading which type a question actually is comes before any calculation.