Simplification

What each letter means, the order of opening brackets and the left-to-right rule.

• Order of brackets: first the small ( ), then the curly { }, then the big [ ] — from the inside out.
• D and M have equal priority, and so do A and S — when operations of the same rank meet, go left to right. $48÷6\times 2=8\times 2=16$, not $48÷12=4$.
• “Of” always comes before division and multiplication: $\frac{2}{5}$ of $50+10$ gives 20 first, then 30.
• The part under a bar (V) is done first like a bracket: $20-\overline{7+3}=20-10=10$.

What $|x|$ means and how to simplify with it.

$|x|$ says how far $x$ is from zero. $|5|=5$ and $|-5|=5$. So $|3-9|=|-6|=6$, and $-|3-9|=-6$ (the outer minus sign stays). Do the working inside the modulus first, then make it non-negative.

When an expression has $x^2$, $\sqrt{x}$ or fractions, turn them into values first.

Powers and roots are “single units” just like brackets: in $3+2^3\times 2$ first $2^3=8$, then $8\times 2=16$, then $3+16=19$. With fractions, convert to decimals or keep proper fractions, and simplify only at the end.

The list of formulas and big-number calculations done in seconds.

When $x+y$ and $xy$ are given, find $x^2+y^2$ or $x^3+y^3$ without finding $x$ and $y$.

Multiplying by 5, 25, 125, 99, 101, 11 and fractions “of” a number.

Sums of natural numbers, squares, cubes and odd numbers.

The fill-in-the-blank questions of bank exams: undo each operation with its opposite.

The slips that cost marks.

Ways to discard wrong options without solving fully.

One-rule questions.

Exam-level questions.

Questions at the hard end of competitive exams.