Algebra Class 6 Chapter Notes (CBSE Maths)

Key Terms in Algebra

Variable

A symbol, usually a letter (like x, y, n, p), that represents an unknown number or a quantity that can change. Its value is not fixed.

Constant

A quantity that has a fixed, unchanging value. All numbers like 5, -10, 0, and 2/3 are constants.

Algebraic Expression

A mathematical phrase made by combining variables, constants, and arithmetic operations (+, −, ×, ÷). Example: 2y + 7.

Equation

A mathematical statement that two expressions are equal. It always contains an equals sign (=). Example: 2y + 7 = 15.

Term

A single part of an expression, which could be a variable, a constant, or a product of variables and constants. In the expression 3a + 4b - 5, the terms are 3a, 4b, and -5.

Solution of an Equation

The specific value of the variable that makes the equation a true statement (i.e., makes the Left Hand Side equal to the Right Hand Side).

Understanding Variables: The Heart of Algebra

The most important new idea in algebra is the variable. Think of a variable as an empty box where you can put different numbers. In arithmetic, you work with fixed numbers like 2 + 3 = 5. The numbers 2, 3, and 5 are constants—their values never change. But what if we want to describe a situation where a number isn't known? For example, "I had some chocolates, and my friend gave me 3 more." We don't know the starting number of chocolates. We can use a variable, like 'c', to represent this unknown amount. The total number of chocolates can now be written as the expression c + 3. This shows the power and flexibility of algebra. The letter 'c' is not just a random symbol; it's a placeholder for a number we might find later. If we later find out you started with 5 chocolates, you can replace 'c' with 5 to get 5 + 3 = 8. If you started with 10, you get 10 + 3 = 13. The variable allows us to create a general rule that works for any starting amount.

Forming Algebraic Expressions

Must Remember

• {"point":"An expression like x + 4 does not have an answer until the value of x is known."}
• {"point":"An equation like x + 4 = 10 has a specific solution (here, x must be 6)."}
• {"point":"An equation always has an equals sign (=), but an expression does not."}
• {"point":"A variable can have different values in different problems. A constant's value is always fixed."}
• {"point":"Writing a number and a variable together, like 4m, implies multiplication (4 × m)."}
• {"point":"An equation has two sides: Left Hand Side (LHS) and Right Hand Side (RHS). The solution makes LHS = RHS."}
• {"point":"Be careful with subtraction order: \"5 subtracted from y\" is y - 5, not 5 - y."}
• {"point":"Matchstick patterns are a common way to introduce rules. If one square needs 4 matchsticks, 'n' squares might be represented by a rule like 3n + 1 (if they share sides)."}

How to Solve a Simple Equation by Trial and Error

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Worked Examples

• Example 1: Writing an Expression Question: Raju's father's age is 2 years more than 3 times Raju's age. If Raju's age is y years, what is his father's age? Solution: 1. Raju's age = y 2. 3 times Raju's age = 3y 3. 2 years more than that = 3y + 2 So, the father's age is 3y + 2 years.
• Example 2: Evaluating an Expression Question: Find the value of the expression 100 - 10x for x = 5. Solution: 1. Write the expression: 100 - 10x 2. Substitute the value x = 5: 100 - 10(5) 3. Calculate the product first: 100 - 50 4. Perform the subtraction: 50 So, the value of the expression is 50.
• Example 3: Checking a Solution Question: Check whether n = 4 is a solution to the equation 2n + 5 = 13. Solution: 1. Take the Left Hand Side (LHS): 2n + 5 2. Substitute n = 4: 2(4) + 5 3. Calculate: 8 + 5 = 13 4. Compare with the Right Hand Side (RHS), which is 13. Since LHS = RHS, n = 4 is a solution.

Exam Tip: Avoid Common Errors

A very common mistake is confusing an 'expression' with an 'equation'. Remember:

• An expression like 2x + 5 is a phrase and cannot be 'solved'. You can only find its value if you are given a value for x.
• An equation like 2x + 5 = 15 is a complete sentence that makes a claim of equality. It can be solved to find the specific value of x that makes the statement true.

In an exam, read the question carefully. If it says "form an expression," do not add an = 0 or any other equality. If it says "form an equation," you must include the equals sign.

Quick Revision Check

• Write an algebraic expression for "A number p multiplied by 2 and then 1 is subtracted". 2p - 1
• What is the difference between a variable and a constant? A variable (like x) can take different numerical values, while a constant (like 7) has a fixed value.
• If a = 5 and b = 2, what is the value of the expression 3a - 4b? 3(5) - 4(2) = 15 - 8 = 7.
• Is y = 10 a solution for the equation y/2 + 1 = 6? Yes. LHS = 10/2 + 1 = 5 + 1 = 6. Since LHS = RHS, it is a solution.

Frequently Asked Questions about Algebra

Frequently Asked Questions