Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Algebra → Expressions ↓


Algebraic Expressions


Algebraic expressions are a way of using letters and numbers to represent a mathematical idea. They form a fundamental part of algebra, a branch of mathematics that uses symbols to describe various elements of numbers and number theory. An algebraic expression is a combination of numbers, variables (letters) and arithmetic operations such as addition, subtraction, multiplication and division. These components combine to form meaningful quantities or relationships.

Basic elements of algebraic expressions

Let's break down algebraic expressions into their components:

  • Constants: These are fixed numbers. For example, in 3x + 5, the number 5 is a constant.
  • Variables: These are symbols, often letters, used to represent unknown values. In the expression 3x + 5, x is a variable.
  • Coefficient: A coefficient is a number that is multiplied by a variable. In 3x + 5, 3 is the coefficient of x.
  • Operators: These are symbols that indicate operations between numbers or variables, such as addition (+), subtraction (-), multiplication (×), and division (÷).
3x + 5
3 5

Writing algebraic expressions

Creating algebraic expressions involves translating phrases into mathematical language. How we can do this is explained below:

Add

Let's take a look at the phrase: "four more than a number." If the number is x, then we write the expression as follows:

x + 4

Subtraction

Consider the phrase: "Seven less than twice a number." If the number is y, then the expression will be like this:

2y - 7

Multiplication

If we have the phrase: “the product of a number and nine,” and the number is z, then the expression becomes:

9z

Division

For "a number divided by five", where the number is a, the expression is written like this:

a / 5

Types of algebraic expressions

There are different types of algebraic expressions depending on the number of terms they contain:

Monomial

A monomial is an algebraic expression that contains only one term. It can contain constants, variables, or a combination of both.

7, x, 3xy

Binomial

A binomial has two terms. These terms are usually separated by a plus (+) or minus (-) sign.

x + 5, 3x – 2

Trinomial

A trinomial is an expression with three terms.

y^2 + 2x + 1, 3x - y + 2

Evaluating algebraic expressions

Evaluating an algebraic expression involves replacing variables with real numbers and performing operations. Here's how you do it step by step:

Suppose we have the expression: 2x + 3. Let's evaluate it when x = 4.

2x + 3
  1. Replace the variable x with 4, which gives: 2(4) + 3.
  2. Multiply: 2 × 4 = 8.
  3. Add the result to 3: 8 + 3 = 11.

So, the expression 2x + 3 will have the value 11 when x = 4.

Simplification of algebraic expressions

Simplifying an expression means combining like terms and changing the expression into its simplest form.

Example

Let's simplify 3x + 2x + 4 - 5.

3x + 2x + 4 - 5
  1. Combine like terms: 3x + 2x = 5x.
  2. Subtract the constant: 4 - 5 becomes -1.
  3. So the simplified expression is: 5x - 1.

Practical uses of algebraic expressions

Algebraic expressions have many practical applications. They are used to model and solve real-world problems.

Example: Area of a rectangle

The formula for the area (A) of a rectangle is given as:

A = l × w

where l is the length, and w is the width. If you know that:

  • The length is twice the width, so l = 2w.
  • Width w = 5.

To find the area, substitute the following values:

A = 2w × w = 2 × (5) × 5 = 50

Therefore, the area of the rectangle is 50 square units.

Conclusion

Understanding algebraic expressions is a fundamental skill in mathematics. It forms the basis for solving equations, drawing lines, and much more. By learning how to write, evaluate, and simplify these expressions, you gain the tools you need to explore more complex mathematical concepts.

Mastering these fundamentals will set you up for success in algebra and beyond. Practice by rewriting word problems into algebraic expressions, and soon it will become a natural process for you. Remember, algebra is just another way of representing the numbers and operations we are already familiar with, but in a form that allows us to unlock new levels of analysis and understanding.


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Algebraic Expressions

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