Table of Contents

**TOPIC 7: ALGEBRA**

An algebraic expression â€“ is a collection of numbers, variables, operators and grouping symbols.Variables – are letters used to represent one or more numbers

**Algebraic Operations**

Symbols to form Algebraic Expressions

Use symbols to form algebraic expressions

The parts of an expression collected together are calledâ€‹â€‹Â terms

**Example**

> x + 2x â€“ are called like terms because they have the same variables

> 5x +9y â€“ are called unlike terms because they have different variables

An algebraic expression can be evaluated by replacing or substituting the numbers in the variables

**Example 1**

Evaluate the expressions below, given that x = 2 and y = 3â€‹â€‹

**Example 2**

Evaluate the expressions below, given that m = 1 and n = – 2

An expression can also be made from word problems by using letters and numbers

**Example 3**

A rectangle is 5 cm long and w cm wide. What is its area?

Solution

Let the area be A.

Then

A = lengthÃ— widith

A = 5w cm2

Simplifying Algebraic Expressions

Simplify algebraic expressions

Algebraic expressions can be simplified by addition, subtraction, multiplication and division

Additionâ€‹â€‹Â andâ€‹â€‹Â subtractionâ€‹â€‹Â of algebraic expression is done by adding or subtracting the coefficients of the like terms or letters

Coefficient of the letterâ€‹â€‹Â â€“ is the number multiplying the letter

<!–[endif]–>Multiplicationâ€‹â€‹Â andâ€‹â€‹Â divisionâ€‹â€‹Â of algebraic expression is done on the coefficients of both like and unlike terms or letters

**Example 4**

Simplify the expressions below

Solution

**Equations with One Unknown**

An equation â€“ is a statement that two expressions are equal

An Equation with One Unknown

Solve an equation with one unknown

An equation can have one variableâ€‹â€‹Â (unknown)â€‹â€‹Â on one side or two variables on both sides.

When you shift a number or term from one side of equation to another, its sign changes

If it is positive, it becomes negative

If it is negative, it becomes positiveâ€‹â€‹

**Example 5**

Solve the following equations

Solution

**An Equation from Word Problems**

Form and solve an equation from word problems

Some word problems can be solved by using equations as shown in the below examples

**Example 6**

Naomi is 5 years young than Mariana. The total of their ages 33 years. How old is Mariana?

Solution