Home MATHEMATICS TOPIC 7: ALGEBRA ~ MATHEMATICS FORM 1

# TOPIC 7: ALGEBRA ~ MATHEMATICS FORM 1

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2 ## 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