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 are a fundamental part of mathematics, especially as you move into topics that require the use of variables, constants, and various operations. Understanding expressions is crucial for solving algebraic problems. In this essay, we will explore what expressions are, how they are used, and how you can use them to solve problems. We will start with the basics and gradually delve into more complex aspects, giving ample examples as well.

What is the expression?

In mathematics, an expression is a combination of numbers, variables, and operations (such as addition, subtraction, multiplication, and division) that represents a specific value. For example:

 3x + 5
Here, 3x + 5 is an expression where 3 is a coefficient, x is a variable, and 5 is a constant.

Components of expression

An algebraic expression consists of several components:

1. Constants

A constant is a fixed number that does not change. In the expression 4x + 7, the number 7 is a constant. Constants add a value to the expression independently of the variables.

2. Variables

Variables are symbols used to represent unknown values. They can take different numerical values. In the expression 4x + 7, x is the variable. Variables allow expressions to be flexible and applicable to different situations.

3. Coefficient

A coefficient is a number that multiplies a variable. In the expression 4x + 7, 4 is the coefficient of the variable x. It tells you how many times to multiply the variable by itself.

4. Operator

Operators are symbols that indicate operations that can be performed between numbers and variables. Common operators include:

  • Addition (+)
  • Subtraction (-)
  • Multiplication (*)
  • Division (/)
In the expression 4x + 7, + is the operator that denotes addition.

Types of expression

Algebraic expressions can be classified into different types depending on their structure. Here are some common types:

1. Monomial

A monomial is an expression that has only one term. It can be a constant, a variable, or the product of constants and variables.

 5
 3x
 -7xy

2. Binomial

A binomial is an expression with two terms separated by a plus or minus sign.

 x + 2
 3y - 7

3. Trinomial

A trinomial is an expression with three terms.

 a + b + c
 2x - 4y + 6

4. Polynomials

A polynomial is an expression with one or more terms. Monomials, binomials, and trinomials are all types of polynomials.

 x^3 + 2x^2 - 5x + 7

Combining like terms

One of the basic skills in algebra is combining like terms to simplify expressions. Like terms are terms in an expression that have the same variable raised to the same power. You can only combine like terms.

For example:

 3x + 4x
These are like terms, and you can combine them by adding their coefficients:
 (3 + 4)x = 7x

Distributive property

The distributive property is an important principle in algebra that is used to simplify expressions. It states that for any numbers a, b, and c:

 a(b + c) = ab + ac

Let us apply this rule:

 2(x + 3)
Applying the distributive property:
 2 * x + 2 * 3 = 2x + 6

It works the same way for subtraction:

 a(b - c) = ab - ac

Simplification of expressions

Simplifying means writing expressions in the most compact or efficient form without changing their value. This includes combining like terms, using the distributive property, and performing arithmetic operations.

Example:

Simplify the expression:

 3x + 5 + 2x - 7
Combine like terms:
 (3x + 2x) + (5 - 7) = 5x - 2

Evaluating the expression

Evaluating an expression means finding the value of the expression when variables are replaced with specific numbers.

Example:

Evaluate the expression 2x + 3 for x = 4.

 2 * 4 + 3 = 8 + 3 = 11

Practising with expressions

Practicing with different expressions helps to strengthen understanding. Below are some sample exercises:

Exercise 1:

Simplify the expression

 4y + 2 - 3y + 7

Solution:

 (4y - 3y) + (2 + 7) = y + 9

Exercise 2:

Evaluate the expression 3a + 4 when a = 5.

 3 * 5 + 4 = 15 + 4 = 19

Use of expressions in real-life problems

Expressions are not just abstract concepts; they can be applied to solve real-world problems. Consider a situation where you are buying several items from a store and you need to calculate the total cost.

Example problem:

If the price of an apple is $a and you buy three apples and two bananas, each of which costs $b, then the total cost is represented by the following expression:

 3a + 2b
If a = 2 and b = 1.5, then the total cost is:
 3 * 2 + 2 * 1.5 = 6 + 3 = 9

Conclusion

Expressions are an important part of algebra, providing the foundation for further study in mathematics. By understanding how to create, simplify, and evaluate expressions, students can solve more complex problems with confidence. Practicing with expressions not only helps with mathematical calculations but also improves problem-solving skills in everyday situations.


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