What is the Rule for Transposition? | Simple Explanation for Class 10

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What is the Rule for Transposition in Equations?

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Transposition in equations is a rule that allows you to move a term from one side of an equation to the other. When you move a term, its sign (plus or minus) changes to its opposite. This rule helps us isolate variables to find their values.

Simple Example

Quick Example

Imagine you have 5 cricket balls, and your friend gives you 'x' more, making a total of 12 balls. The equation is 5 + x = 12. To find 'x', we need to move the 5 to the other side. When 5 moves, its sign changes from plus to minus, so it becomes x = 12 - 5, which means x = 7. You got 7 more balls!

Worked Example

Step-by-Step

Let's solve for 'y' in the equation: 3y - 7 = 14.

Step 1: Identify the term you want to move first. We want to isolate '3y', so we move '-7' to the right side.
---Step 2: Change the sign of '-7' when moving it. It becomes '+7'.
---Step 3: The equation now is: 3y = 14 + 7.
---Step 4: Perform the addition on the right side: 3y = 21.
---Step 5: Now, '3' is multiplying 'y'. To move '3' to the right side, we perform the opposite operation, which is division.
---Step 6: The equation becomes: y = 21 / 3.
---Step 7: Perform the division: y = 7.

Answer: y = 7

Why It Matters

Transposition is a fundamental skill used in almost all scientific and engineering fields. Scientists in AI/ML use it to manipulate complex formulas, engineers apply it to design circuits, and doctors use it to calculate medicine dosages. Mastering this helps you build a strong foundation for a career in technology, medicine, or research.

Common Mistakes

MISTAKE: Not changing the sign of the term when moving it to the other side. E.g., moving '+5' and keeping it '+5' on the other side. | CORRECTION: Always change the sign. If it's '+' it becomes '-', if it's '-' it becomes '+'.

MISTAKE: Confusing multiplication/division with addition/subtraction. E.g., moving '3x' by subtracting '3' instead of dividing. | CORRECTION: If a number is multiplying (like '3x'), move it by dividing. If it's dividing (like 'x/3'), move it by multiplying.

MISTAKE: Applying transposition incorrectly to terms within brackets. E.g., in 2(x+3) = 10, trying to move '+3' directly. | CORRECTION: First, either distribute the number outside the bracket (2x + 6 = 10) or move the multiplier (x+3 = 10/2) before transposing terms inside the original bracket.

Practice Questions

Try It Yourself

QUESTION: Solve for 'a': a + 10 = 25 | ANSWER: a = 15

QUESTION: Find the value of 'x': 4x - 8 = 20 | ANSWER: x = 7

QUESTION: If the cost of 5 samosas is Rs 75, and you also pay Rs 10 for chai, what is the cost of one samosa? (Let 's' be the cost of one samosa). | ANSWER: 5s + 10 = 75 => 5s = 65 => s = 13. One samosa costs Rs 13.

MCQ

Quick Quiz

What happens to the sign of a term when it is moved from one side of an equation to the other?

It remains the same.

It changes to its opposite.

It always becomes positive.

It always becomes negative.

The Correct Answer Is:

The core rule of transposition states that when you move a term across the equals sign, its sign must change. A plus becomes a minus, and a minus becomes a plus.

Real World Connection

In the Real World

When a delivery app like Swiggy or Zomato calculates the total bill, it adds the food price, delivery fee, and taxes. If you want to know just the food price, you use transposition! You'd take the total bill, subtract the known delivery fee and taxes to find the food cost. This is also how scientists at ISRO adjust rocket trajectories by solving equations for unknown variables.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | TERM: A single number, variable, or product/quotient of numbers and variables. | VARIABLE: A letter (like x, y, a) representing an unknown value. | ISOLATE: To get a variable by itself on one side of the equation.

What's Next

What to Learn Next

Now that you've mastered transposition, you're ready to tackle more complex linear equations and even equations with variables on both sides. This skill is crucial for understanding algebraic expressions and solving problems in physics and chemistry.