What is Cross-Multiplication? | Simple Explanation for Class 6

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What is the Cross-Multiplication Method?

Grade Level:

Class 6

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

Definition

What is it?

The Cross-Multiplication Method is a simple technique used to solve equations involving two fractions that are equal to each other. It helps us find an unknown value by multiplying the numerator of one fraction with the denominator of the other fraction across the equals sign.

Simple Example

Quick Example

Imagine you're buying ladoos. If 2 ladoos cost ₹40, how much would 5 ladoos cost? We can write this as a fraction problem: 2/40 = 5/x. Cross-multiplication helps us quickly find the value of 'x'.

Worked Example

Step-by-Step

Let's solve: x/3 = 4/6

Step 1: Identify the two fractions and the equals sign between them.

Step 2: Multiply the numerator of the first fraction (x) by the denominator of the second fraction (6). So, x * 6.

Step 3: Multiply the numerator of the second fraction (4) by the denominator of the first fraction (3). So, 4 * 3.

Step 4: Set the two products equal to each other: x * 6 = 4 * 3.

Step 5: Simplify both sides: 6x = 12.

Step 6: To find 'x', divide both sides by 6: x = 12 / 6.

Step 7: Calculate the final answer: x = 2.

Answer: x = 2

Why It Matters

This method is super useful in many fields! Engineers use it to scale designs, data scientists use it to compare ratios, and even economists use it for financial calculations. Learning this helps you build a strong base for problem-solving in careers like AI/ML and Physics.

Common Mistakes

MISTAKE: Multiplying numerator by numerator and denominator by denominator. | CORRECTION: Always multiply the numerator of one fraction by the denominator of the *other* fraction, across the equals sign.

MISTAKE: Forgetting to put the products equal to each other. | CORRECTION: After cross-multiplying, remember to set the two resulting products equal to each other to form an equation.

MISTAKE: Not isolating the variable correctly after cross-multiplication. | CORRECTION: Once you have the equation (e.g., 6x = 12), perform the necessary division or multiplication to find the value of the unknown variable.

Practice Questions

Try It Yourself

QUESTION: Solve for y: y/5 = 6/10 | ANSWER: y = 3

QUESTION: If 3 packets of biscuits cost ₹60, how much will 7 packets cost? Use cross-multiplication. | ANSWER: ₹140

QUESTION: Find the value of 'a' if (a+1)/4 = 9/12. | ANSWER: a = 2

MCQ

Quick Quiz

Which of these is the correct first step to solve for 'x' in 2/x = 4/8 using cross-multiplication?

2 * 4 = x * 8

2 * 8 = x * 4

2 + 8 = x + 4

2 / 4 = x / 8

The Correct Answer Is:

Cross-multiplication means multiplying the numerator of the first fraction (2) by the denominator of the second (8), and the denominator of the first (x) by the numerator of the second (4), then setting them equal. So, 2 * 8 = x * 4.

Real World Connection

In the Real World

When you see 'percent off' sales at a local shop, like '20% off on a ₹500 item,' you're often mentally using ratios similar to cross-multiplication to figure out the final price. Also, chefs use it to scale recipes up or down, making sure the taste is just right for a bigger party or a smaller family meal.

Key Vocabulary

Key Terms

FRACTION: A part of a whole, written as numerator/denominator | NUMERATOR: The top number in a fraction | DENOMINATOR: The bottom number in a fraction | EQUATION: A statement that two mathematical expressions are equal | VARIABLE: A symbol (like x or y) that represents an unknown value

What's Next

What to Learn Next

Great job understanding cross-multiplication! Next, you can explore solving more complex linear equations with variables on both sides. This method will be a handy tool in your problem-solving kit.