CBSE Class 6 Maths: Algebra Exercise 11.4 - Forming Simple Equations

Understanding Simple Equations: The Basics

In Algebra Exercise 11.4, our main goal is to understand what a simple equation is and how to construct one. An equation is like a balanced scale, where what's on one side is exactly equal to what's on the other side. It always contains an 'equals' sign (=).

For example, consider the statement: "The sum of a number and 5 is 12." Here, "a number" is something we don't know. In algebra, we use letters like x, y, a, b, etc., to represent these unknown numbers. These letters are called variables because their values can 'vary' or change. The numbers like 5 and 12 are called constants because their values stay fixed. To turn our statement into an equation, we first pick a variable, say x, for "a number". "The sum of a number and 5" becomes x + 5. "Is 12" means it's equal to 12. So, the equation is x + 5 = 12. This equation has a Left Hand Side (LHS) (x + 5) and a Right Hand Side (RHS) (12), separated by the equals sign. Learning to translate these simple English sentences into mathematical equations is the key skill this exercise builds.

Step-by-Step: How to Form an Equation from a Statement

1. Step 1: Identify the Unknown Quantity — Read the statement carefully and identify what 'number' or 'quantity' is unknown. This is what you need to find. For example, in "7 added to a number gives 15", 'a number' is unknown.
2. Step 2: Assign a Variable — Choose a letter (like x, y, a, p, m, etc.) to represent the unknown quantity. It's good practice to stick to lowercase letters. Let's say we use 'x' for 'a number'.
3. Step 3: Translate Keywords into Mathematical Operations — Look for keywords that indicate mathematical operations: 'sum', 'added to', 'more than', 'increased by' -> '+' (addition) 'difference', 'subtracted from', 'less than', 'decreased by' -> '-' (subtraction) 'product', 'times', 'multiplied by' -> '×' or '' (multiplication, often just written as '3x' for '3 times x') 'quotient', 'divided by' -> '÷' or '/' (division) 'is', 'gives', 'equals' -> '=' (equals sign).
4. Step 4: Write the Algebraic Expression for LHS — Using your variable and the mathematical operations, write the expression that represents the first part of the statement, typically before the 'is' or 'gives'.
5. Step 5: Write the Algebraic Expression for RHS — Identify the value or expression that the first part is equal to. This forms the Right Hand Side of your equation.
6. Step 6: Combine to Form the Equation — Join the LHS and RHS with an equals sign (=). For our example: "7 added to a number gives 15". Unknown: 'a number' Variable: 'x' Keywords: 'added to' -> '+', 'gives' -> '=' LHS: 'x + 7' RHS: '15' Equation: x + 7 = 15.

Worked Examples: Building Equations

• Example 1: Write the equation for: "4 times a number p is 20." Step 1: Identify Unknown and Variable. The unknown is 'a number', which is already given as 'p'. Step 2: Translate Keywords. 'times' means multiplication (×), 'is' means equals (=). Step 3: Form the Equation. "4 times p" is written as 4p. "Is 20" means = 20. Resulting Equation: 4p = 20.
• Example 2: Form an equation for: "If you subtract 5 from 6 times a number y, you get 7." Step 1: Identify Unknown and Variable. The unknown is 'a number', given as 'y'. Step 2: Translate Keywords. '6 times y' is multiplication (6y). 'subtract 5 from' means - 5. 'you get' means equals (=). Step 3: Form the Equation. "6 times a number y" is 6y. "subtract 5 from 6 times a number y" is 6y - 5. "you get 7" means = 7. Resulting Equation: 6y - 5 = 7.
• Example 3: Write the equation: "One-fourth of a number m is 3 more than 2." Step 1: Identify Unknown and Variable. The unknown is 'a number', given as 'm'. Step 2: Translate Keywords. 'One-fourth of' means division by 4, or multiplying by 1/4 (m/4). 'is' means equals (=). '3 more than 2' means 2 + 3. Step 3: Form the Equation. "One-fourth of a number m" is m/4. "is 3 more than 2" means = 2 + 3. Resulting Equation: m/4 = 2 + 3 (which simplifies to m/4 = 5).

Exam Tip: Avoiding Common Mistakes

When forming equations, students often make a few common errors. Be careful with these!

1. "Subtracted from" vs. "Subtract": If a statement says "5 subtracted from a number x", it means x - 5, not 5 - x. The number being subtracted from comes first. Similarly, "5 less than a number x" is also x - 5.
2. Order of Operations: Pay attention to how phrases are structured. "Twice a number increased by 3" (2x + 3) is different from "Twice the number increased by 3" (2(x + 3)). In Class 6, you'll mainly see the first type, but it's good to be aware.
3. Missing the 'Equals' Sign: Remember, an equation must have an equals sign. If it doesn't, it's an expression, not an equation. x + 7 is an expression; x + 7 = 10 is an equation.
4. Careful Reading: Read the entire statement at least twice before you start writing the equation. Sometimes a tiny word can change the entire meaning.

Practice Questions with Solutions

• Q: Write the equation for: "The sum of a number n and 9 is 20." A: Step 1: Identify the unknown quantity, which is 'a number', represented by 'n'. Step 2: Translate 'sum' as '+' and 'is' as '='. Step 3: Form the expression 'n + 9' for "The sum of a number n and 9". Step 4: Combine with 'is 20' to get ' = 20'. Final answer: n + 9 = 20
• Q: Form an equation for: "8 less than a number x is 15." A: Step 1: The unknown is 'a number', represented by 'x'. Step 2: '8 less than' implies subtraction, where 8 is taken from the number. 'is' means '='. Step 3: "8 less than a number x" is written as x - 8. Step 4: Combine with 'is 15' to get ' = 15'. Final answer: x - 8 = 15
• Q: Write the equation for: "If you divide a number p by 5, you get 6." A: Step 1: The unknown is 'a number', represented by 'p'. Step 2: 'divide by 5' means ÷ 5 or / 5. 'you get' means '='. Step 3: "divide a number p by 5" is written as p / 5. Step 4: Combine with 'you get 6' to get ' = 6'. Final answer: p / 5 = 6
• Q: Form an equation for: "Three-fourths of a number y is 12." A: Step 1: The unknown is 'a number', represented by 'y'. Step 2: 'Three-fourths of' means (3/4) multiplied by the number. 'is' means '='. Step 3: "Three-fourths of a number y" is written as (3/4)y or 3y/4. Step 4: Combine with 'is 12' to get ' = 12'. Final answer: 3y/4 = 12

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