Specific Learning Outcomes
You are required to:
- Form algebraic expressions from real-life situations
- Form algebraic expressions from simple algebraic statements in real-life situations
- Simplify algebraic expressions in real-life situations
- Appreciate the use of algebraic expressions in real life
Content to Be Covered
- Meaning and importance of algebra
- Algebraic expressions and their parts
- Formation of algebraic expressions
- Simplifying algebraic expressions
- Real-life applications of algebra
- Interactive practice and exercises
2.0 Algebra
Algebra is a branch of mathematics that uses letters and symbols to represent numbers in expressions and equations.
Why Algebra is Important
- Used in mathematics and science formulas
- Helps solve business problems like profit and loss
- Used in computer programming and technology
2.1 Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operations.
Example: 5x + 7
Parts of an Algebraic Expression
- Coefficient: 5
- Variable: x
- Constant: 7
- Terms: 5x and 7
2.1.1 Formation of Algebraic Expressions
Example 2.1
A jar has n sweets. Two sweets are picked. How many remain?
Answer: n − 2
Example 2.2
Wilson has x apples. Charles has twice as many. Albert has 5 more than Charles.
Total apples: 5x + 5
2.1.2 Simplifying Algebraic Expressions
Example 2.3
Simplify: 2x + 4y − x + y + 6
Answer: x + 5y + 6
Example 2.4
Simplify: 2(x − y) + 3(2x − 3)
Answer: 8x − 2y − 9
🎮 Algebra Builder: Real-Life Expressions
🎯 Combine Like Terms Challenge
Score: 0/10
Exercise 2.1: Algebraic Expressions
1. A mango costs x shillings and an apple costs y shillings. Write an expression for the cost of 5 mangoes and 8 apples.
Cost of 5 mangoes = 5 × x = 5x
Cost of 8 apples = 8 × y = 8y
Total cost = 5x + 8y
2. John is x years old. Jane is 3 years younger than John. Write an expression for Jane’s age.
John’s age = x
Jane is 3 years younger
Jane’s age = x − 3
3. The diagram below shows a rectangle of length (y + 3) and width y. Write an expression for the perimeter of the rectangle.
Length = y + 3
Width = y
Perimeter = 2(length + width)
= 2((y + 3) + y)
= 2(2y + 3)
= 4y + 6
4. Simplify the expression: 4x + 2(x − y)
Start with: 4x + 2(x − y)
Open the brackets: 2(x − y) = 2x − 2y
Combine like terms:
4x + 2x − 2y = 6x − 2y