**TOPIC 7: ALGEBRA**

An algebraic expression – 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 called terms

**Example**

> x + 2x – are called like terms because they have the same variables

> 5x +9y – 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 = 3

**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 = length× widith

A = 5w cm2

Simplifying Algebraic Expressions

Simplify algebraic expressions

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

Addition and subtraction of algebraic expression is done by adding or subtracting the coefficients of the like terms or letters

Coefficient of the letter – is the number multiplying the letter

<!–[endif]–>Multiplication and division 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 – is a statement that two expressions are equal

An Equation with One Unknown

Solve an equation with one unknown

An equation can have one variable (unknown) 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 positive

**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

Mariana is 19 years

**Equations with Two Unknowns**

**Simultaneous Equations**

Solve simultaneous equations

Simultaneous equations – are groups of equations containing multiple variables

Example 7

Examples of simultaneous equation