Algebra - Substitution into Formulas

Substitution is the algebraic process of replacing a variable (a letter) with a specific numerical value. Imagine the variable as an empty placeholder box that you fill with a number to calculate a result.

Always use parentheses when substituting values, especially negative numbers. For example, if $x = -2$, then $x^2$ should be written as $(-2)^2 = 4$ rather than $-2^2 = -4$. This prevents common sign errors in calculations.

The Order of Operations (BIDMAS/BODMAS) must be followed after substitution. Think of this as a sequence: first solve Brackets, then Indices (powers/roots), then Division and Multiplication from left to right, and finally Addition and Subtraction.

When a variable is written directly next to a number or another variable, such as $3x$ or $ab$, it implies multiplication ($3 \times x$ or $a \times b$). Visualize these terms as being 'glued' together until they are evaluated.

Fractional formulas require you to treat the numerator and denominator as separate groups. In a formula like $\frac{a + b}{c}$, visualize a horizontal bar acting as a divider; you must calculate the entire top value ($a + b$) before dividing by $c$.

Real-world formulas describe physical relationships. For example, in the perimeter formula $P = 2l + 2w$, you can visualize a rectangle where you add two lengths ($l$) and two widths ($w$) to find the total boundary length.

Powers and Roots: If a variable is raised to a power, such as $y^3$, substitute the number first and then multiply it by itself the required number of times. If $y = 2$, then $y^3$ becomes $2 \times 2 \times 2 = 8$.