2.03 Expressions & Formule

Expression

Algebraic statement that does NOT include an equals sign, there is no stated value equal to the expression which allows us to solve it (because there is nothing to solve).

Expressions are made by arithmetically combining terms (e.g. adding, subtracting, multiplying, or dividing terms). A single term can also be an expression.

Expressions can also be simplified. E.g: x + x + x simplifies into 3x.

Formulae

Worded rule, definition, or relationship between different variables/quantities written using letters, constants, and an equals sign. Formulas on their own cannot be solved, but once substituting numbers to replace variables in formulas, then equations can be formed, which can subsequently be solved.

E.g: “Weight, w, is mass, m, multiplied by gravitational field strength, g. OR w = mg”.

if w = 50N and g = 10N/kg, find m.

w = mg → 50 = 10m → m = 5kg

What can letters represent in expressions and formulae?

Unknown numbers or a variables.

How do you change the subject of formulae?

Conduct inverse operations to isolate the variable you want to change into the subject. If powers are involved, you can use roots to inverse their effect.

Example: Rearrange the formula v^2 = u^2 + 2as so that u is the subject.

v^2 = u^2 + 2as

u^2 = v^2 - 2as

u = √(v^2 - 2as)

If the subject appears twice, rearrange all the terms containing the variable to 1 side of the equation, and all of the terms not containing that variable to the other side of the equation. Factorize out the variable, then divide the right hand side by the bracketed expression.

For example: Rearrange p = (2 - ax) / (x - b) so x is the subject.

p(x - b) = 2 - ax

px - pb = 2 - ax

px + ax = pb + 2

x (p + a) = pb + 2

x = (pb + 2) / (p + a)

Substitution

Replacing variables with their values (these values may be numbers or another algebraic expression) to either solve equations, find other values in formulae, or compute the values of expressions.

How do you evaluate expressions or solve formulae by substitution?

For expressions:

1. Write the original expression.

2. Replace the variables with the given numerical values.

   1. Remember to use brackets around negative numbers.

3. Simplify/compute any calculations where possible.

Example: Calculate 18x + 42 where x = 45.

18x + 42 =

18(45) + 42 =

810 + 42 =

852

For formulae:

1. Write the original formula.

2. Replace the variables with the given numerical values.

   1. Remember to use brackets around negative numbers.

3. Solve the equation.

Example: w = mg, find m if w is 50N and g is 10N/kg

w = mg →

50 = 10m →

m = 5kg