Simplification: Concepts, Formulas, and Clear Examples

Simplification MCQs test BODMAS, fraction/decimal arithmetic, surds, and approximation for nearest value.

Bracket first, then orders/power, then ×÷ left to right, then +−.

Estimate to eliminate 2 options before fine calculation.

BODMAS order

• Brackets → Orders (powers/roots) → Division & Multiplication (L→R) → Addition & Subtraction (L→R).

Fraction operations

Add/subtract

$$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$$

Multiply/divide

$$\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd},\ \frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}$$

Surds and rationalize

Rationalize

$$\frac{1}{\sqrt{a}+\sqrt{b}} = \frac{\sqrt{a}-\sqrt{b}}{a-b}$$

Example — Nested root

$\sqrt{48}=\sqrt{16\cdot3}=4\sqrt{3}$.

Decimals and percentages

• Convert % to decimal for multiply.
• Align decimal points on add/sub.

Approximation

• Round to 1–2 sig figs; compare relative error to option gap.

Squares near 50/100

• $(50+x)^2=2500+100x+x^2$ mental trick.
• $(a+b)(a-b)=a^2-b^2$ for quick multiply.

Step-by-step method for exam questions

1. Scan brackets and powers first.
2. Convert mixed numbers to improper fractions if needed.
3. Do ×÷ before +−; left to right within tier.
4. Simplify surds/factor cancel early.
5. Approximate if options far apart.
6. Pick exact or nearest per question.

Formula cheat sheet

Frequently asked questions

Left to right for + only?

Yes when only addition; mixed × and + do × first.

0÷0?

Undefined—unlikely valid MCQ answer.

Which approximation?

Round to make mental product within option tolerance.

Long decimal divide?

Scale numerator/denominator to remove decimal temporarily.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.