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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).
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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.
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Expression
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Meaning
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Substituted
values
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Substitute into expression
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Value of
expression
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5q
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5 × q
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q = 2
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5 × 2
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10
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3ab
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3 × a × b
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a = 5 and b = 6
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3 × 5 × 6
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90
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2(e + f)
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2 × (e + f)
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e = 3 and f = 4
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2 (3 + 4)
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14
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4m2
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4 × m × m
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m = 8
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4 × 8 × 8
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256
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Remember the normal rules of BEDMAS apply to algebra too. This is the ORDER that things are worked out.
Brackets
Exponents
Division
Multiplication
Addition
Subtraction
Substitution is an important part of algebra and many problems involving formulae and equations are worked out using substitution.
Formulae
A 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
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Quantity being found
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Formula
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Variables
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| Perimeter of a rectangle |
P = 2l + 2w
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P = perimeter of rectangle
l = length of rectangle
w = width of rectangle
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| Cost of pizzas from Don's Pizzeria |
C = 9x + 4
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C = total cost of pizzas
x = number of $9 pizzas ordered
The 4 is the $4 delivery charge
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| Volume of a cube |
V = l3
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V = volume of prism
l = length of prism |
| Distance travelled |
d = st
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d = distance
s = speed
t = 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.
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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
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