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