Simplification

A long expression with several operations is worked in one fixed order, called VBODMAS: Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction. The whole method lives in one example: $64 \div 4 \text{ of } 2$ is $64 \div 8 = 8$, while $64 \div 4 \times 2$ is $16 \times 2 = 32$.

1. V for vinculum: a bar over an expression, like $\overline{9 - 7}$, is cleared first.
2. B for brackets: innermost first, $( )$ then $\{ \}$ then $[ ]$.
3. O for of: 'of' means multiply, but it happens before $\div$ and $\times$.
4. D and M: division and multiplication, strictly left to right.
5. A and S: addition and subtraction, again left to right.

$64 \div 4 \text{ of } 2$ means $64 \div (4 \times 2) = 8$, not $(64 \div 4) \times 2 = 32$. The examiner builds both versions into the options. The same trap appears with fractions: $\dfrac{3}{4}$ of $48 \div 2$ is $\left(\dfrac{3}{4} \times 48\right) \div 2 = 18$.

Start with the innermost bracket and move outward, one layer at a time. A minus sign in front of a bracket flips every sign inside: $25 - (10 - 6) = 25 - 10 + 6 = 21$. Never open all layers in one go; each layer must become a single number first.

When only $\div$ and $\times$ appear, walk left to right: $60 \div 5 \times 3 = 12 \times 3 = 36$. Doing $60 \div 15 = 4$ instead is the standard slip, and 4 is always among the options.

A fraction inside a fraction is simplified from the bottom up. For $1 + \dfrac{1}{1 + \dfrac{1}{2}}$: the bottom gives $1 + \dfrac{1}{2} = \dfrac{3}{2}$, then $\dfrac{1}{3/2} = \dfrac{2}{3}$, then $1 + \dfrac{2}{3} = \dfrac{5}{3}$. Keep fractions as fractions; decimals half way through breed errors.

Digit-sum check: replace each number by its digit sum and repeat the operation; the digit sum of your answer must match. $48 + 36 = 84$: digit sums $3 + 9 \to 12 \to 3$, and $84 \to 12 \to 3$. Last-digit check: for products and sums, work only with last digits. $7 \times 8 + 6 = 62$, and last digits $6 + 6 \to 2$ agree.