Algebra: An Introduction for Class 6 Maths

What is Algebra? From Arithmetic to Variables

In Arithmetic, you have worked with numbers like 2, 7, 105, etc. You know how to add, subtract, multiply, and divide them. For example, 3 + 5 = 8. All these numbers have a fixed value.

Algebra introduces a new idea: a number that can change or a number that we don't know yet. We call this a variable. We use letters from the alphabet (like a, b, c, x, y, z) to represent these variables.

Imagine you are making squares with matchsticks. To make 1 square, you need 4 matchsticks. To make 2 squares, you need 8 matchsticks. How many matchsticks do you need to make 'n' squares? The answer is 4 × n. Here, 'n' is a variable. It can be 1, 2, 10, or any other number of squares you want to make. The expression '4 × n' (which we write as 4n) is an algebraic expression. It gives us a general rule, which is much more powerful than just calculating for one specific case. Algebra is the tool that lets us create and use these general rules.

Key Terms in Algebra

Variable

A symbol, usually a letter, that represents an unknown number or a quantity that can change. For example, in the expression x + 5, 'x' is the variable.

Constant

A number that has a fixed value and does not change. For example, in the expression x + 5, '5' is a constant.

Algebraic Expression

A combination of constants, variables, and arithmetic operations (+, -, ×, ÷). For example, 2y - 3, 4x, and z/2 + 7 are all algebraic expressions.

Equation

A statement that two algebraic expressions are equal. It always contains an equal sign (=). For example, x + 5 = 12 is an equation.

Forming Algebraic Expressions: Worked Examples

• Situation: Sarita has 10 more marbles than Ameena. Let Ameena have 'x' marbles. Thinking: 'More than' means we need to add. Sarita has Ameena's marbles PLUS 10. Expression: The number of marbles Sarita has is x + 10.
• Situation: A number 'y' is multiplied by 5 and then 3 is subtracted from the result. Thinking: First, multiply y by 5, which gives 5y. Then, subtract 3 from this result. Expression: The final expression is 5y - 3.
• Situation: Raju's father's age is 2 years more than 3 times Raju's age. Let Raju's age be 'z' years. Thinking: First, find '3 times Raju's age', which is 3 × z or 3z. Then, add 2 years to this ('2 years more'). Expression: Raju's father's age is 3z + 2.
• Situation: The cost of one pen is ₹8. What is the cost of 'p' pens? Thinking: To find the total cost, we multiply the cost of one item by the number of items. Expression: The total cost is 8 × p, which is written as 8p.

Remember These Rules!

• Multiplication in algebra is often hidden. '4x' means '4 multiplied by x'. We don't need to write the '×' sign.
• The number comes first. We write '5y', not 'y5'.
• A variable by itself has a '1' in front of it. 'x' is the same as '1x'. This is important for later when you add and subtract expressions.
• Order matters for subtraction and division. '5 less than y' is y - 5, not 5 - y.
• An expression does not have an equals sign. If you see an '=', you are looking at an equation, not just an expression.

Practice Questions with Solutions

• Q: The side of a regular hexagon is denoted by 'l'. Express the perimeter of the hexagon using 'l'. A: Step 1: A regular hexagon is a polygon with 6 equal sides. Step 2: The perimeter of a polygon is the sum of the lengths of all its sides. Step 3: Since each side has length 'l', the perimeter is l + l + l + l + l + l, which is equal to 6 times l. Final answer: The perimeter of the hexagon is 6l.
• Q: Write an algebraic expression for the statement: '7 subtracted from the product of x and y'. A: Step 1: First, find the 'product of x and y'. Product means multiplication. So, the product is x × y, which is written as xy. Step 2: Next, '7 subtracted from' this product means we take the product (xy) and subtract 7 from it. Final answer: The expression is xy - 7.
• Q: Leela is Radha's younger sister. Leela is 4 years younger than Radha. Write Leela's age in terms of Radha's age. Take Radha's age to be 'x' years. A: Step 1: We are given Radha's age as 'x' years. Step 2: We are told that Leela is '4 years younger'. 'Younger than' implies subtraction. Step 3: To find Leela's age, we must subtract 4 from Radha's age (x). Final answer: Leela's age is (x - 4) years.
• Q: If a = 3 and b = 5, find the value of the expression 2a + 4b - 10. A: Step 1: Write down the expression: 2a + 4b - 10. Step 2: Substitute the given values of a and b into the expression. Replace 'a' with 3 and 'b' with 5. The expression becomes (2 × 3) + (4 × 5) - 10. Step 3: Perform the multiplications first: 2 × 3 = 6 and 4 × 5 = 20. The expression is now 6 + 20 - 10. Step 4: Perform the addition and subtraction from left to right: 6 + 20 = 26, and then 26 - 10 = 16. Final answer: The value of the expression is 16.

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