What is Transposition?

S3-SA1-0075

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Transposition is a method used in algebra to move a term from one side of an equation to the other. When you transpose a term, its operation (addition, subtraction, multiplication, division) changes to its opposite. It helps us solve equations to find the value of an unknown variable.

Simple Example

Quick Example

Imagine you have 'my score + 10 = 50'. To find 'my score', you need to move '+10' to the other side. When '+10' crosses the '=' sign, it becomes '-10'. So, 'my score = 50 - 10', which means 'my score = 40'.

Worked Example

Step-by-Step

Let's solve the equation: x + 7 = 15

1. Our goal is to find the value of 'x'.
---2. We need to move the '+7' from the left side (LHS) to the right side (RHS) of the equation.
---3. When '+7' crosses the '=' sign, it changes its operation from addition to subtraction.
---4. So, the equation becomes: x = 15 - 7
---5. Now, perform the subtraction: 15 - 7 = 8
---6. Therefore, x = 8.

Answer: x = 8

Why It Matters

Transposition is a fundamental skill used in almost all areas of science and technology. Engineers use it to design bridges, data scientists use it to analyze patterns in information like cricket scores, and even doctors use it to calculate medicine dosages. Mastering this helps you solve complex problems in future studies and careers.

Common Mistakes

MISTAKE: Changing the sign of a term but not moving it across the equals sign. For example, in x + 5 = 10, writing x - 5 = 10. | CORRECTION: The sign change only happens when the term crosses the equals sign to the other side.

MISTAKE: Not changing the operation correctly. For example, moving a '+5' and changing it to 'x / 5' instead of 'x - 5'. | CORRECTION: Remember the pairs: '+' becomes '-', '-' becomes '+', '×' becomes '÷', and '÷' becomes '×'.

MISTAKE: Applying transposition to only part of a term. For example, in 2x + 3 = 11, moving just '3' and leaving '2x' as '2x - 3 = 11'. | CORRECTION: Treat each full term (like '2x' or '+3') as a single unit when transposing.

Practice Questions

Try It Yourself

QUESTION: Solve for y: y - 4 = 9 | ANSWER: y = 13

QUESTION: Find the value of p: 3p = 21 | ANSWER: p = 7

QUESTION: If 2x + 5 = 17, what is x? | ANSWER: x = 6

MCQ

Quick Quiz

When you transpose '+8' from the left side of an equation to the right side, what does it become?

-8

×8

÷8

The Correct Answer Is:

When a term is moved across the equals sign, its operation changes to the opposite. The opposite of addition ('+') is subtraction ('-'). So, '+8' becomes '-8'.

Real World Connection

In the Real World

Imagine you're checking your mobile data usage. If you know your total data pack (e.g., 2 GB) and the data you have left (e.g., 0.5 GB), you can use transposition to find out how much data you've already used. 'Data used + 0.5 GB = 2 GB' becomes 'Data used = 2 GB - 0.5 GB'. This helps you manage your data plan efficiently, just like apps do!

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | TERM: A single number, variable, or product of numbers and variables (e.g., 5, x, 3y). | VARIABLE: A letter (like x, y, a) representing an unknown value. | OPERATION: A mathematical action like addition (+), subtraction (-), multiplication (×), or division (÷).

What's Next

What to Learn Next

Great job understanding transposition! Next, you should learn about 'Solving Linear Equations in One Variable'. This will build on your transposition skills to solve more complex equations with variables on both sides, which is super useful for many real-world problems.