## Substitution

 In sport, a substitute replaces a player on a team. In this example the player wearing the number 8 shirt is being replaced by a new player, number 13. In algebra, substitution means replacing a variable, letter or pronumeral with a number. The value of the term or expression can then be worked out. (Sometimes calledevaluating). For example, the term 4b means 4 × b.

If b = 2 then
4b = 4 × 2 = 8

In the example above the value of b = 2 has been substituted into the term 4b to give a value of 8.

Sometimes an expression may have two or more variables and each one of these can be given a value.

 Expression Meaning Substituted values Substitute into expression Value ofexpression 5q 5 × q q = 2 5 × 2 10 3ab 3 × a × b a = 5 and b = 6 3 × 5 × 6 90 2(e + f) 2 × (e + f) e = 3 and f = 4 2 (3 + 4) 14 4m2 4 × m × m m = 8 4 × 8 × 8 256

Remember the normal rules of BEDMAS apply to algebra too. This is the ORDER that things are worked out.

Brackets
Exponents
Division
Multiplication
Subtraction

Substitution is an important part of algebra and many problems involving formulae and equations are worked out using substitution.

### Formulae

formula is a rule or equation used to calculate the value of a quantity. The plural of formula is formulae or formulas. There are all types of formulae for calculating various quantities in many areas of life.

Examples

 Quantity being found Formula Variables Perimeter of a rectangle P = 2l + 2w P = perimeter of rectanglel = length of rectanglew = width of rectangle Cost of pizzas from Don's Pizzeria C = 9x + 4 C = total cost of pizzasx = number of \$9 pizzas orderedThe 4 is the \$4 delivery charge Volume of a cube V = l3 V = volume of prisml = length of prism Distance travelled d = st d = distances = speedt = time

The subject of a formula is the term which is often on its own on the left hand side.

e.g. For the cost of pizzas formula above the subject of the formula is C

### Substitution into a Formula

To find the value of a quantity in a formula we substitute the given values into a formula in place of the variables.

 e.g. If we want to buy 6 pizzas from Don's Pizzeria Use the formula, C = 9x + 4 C = 9 × 6 + 4 C = \$58 The cost of the pizzas plus delivery is \$58 