What is Multiplying Both Sides? | Simple Explanation for Class 5

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What is Multiplying Both Sides of an Equation?

Grade Level:

Class 5

Maths, Computing, AI, Physics

Definition

What is it?

Multiplying both sides of an equation means performing the same multiplication operation on both the left side and the right side of the equals sign. This action keeps the equation balanced and true, just like adding or subtracting the same number on both sides. It helps us find the value of an unknown variable.

Simple Example

Quick Example

Imagine you have two bowls, each with 3 laddoos. So, Bowl 1 = 3 laddoos and Bowl 2 = 3 laddoos. If you decide to double the number of laddoos in Bowl 1, you must also double the laddoos in Bowl 2 to keep them equal. So, 3 x 2 = 6 laddoos in Bowl 1 and 3 x 2 = 6 laddoos in Bowl 2. Both sides are still equal!

Worked Example

Step-by-Step

Let's solve for 'x' in the equation: x / 4 = 5

1. Our goal is to get 'x' by itself on one side of the equation.
2. Currently, 'x' is being divided by 4.
3. To undo division by 4, we need to multiply by 4.
4. We must multiply BOTH sides of the equation by 4 to keep it balanced.
5. (x / 4) * 4 = 5 * 4
6. x = 20

Answer: x = 20

Why It Matters

This concept is fundamental for solving problems in Maths, Physics, and even in designing AI algorithms. Engineers use it to calculate forces, while computer programmers apply it in game development and data analysis. Mastering this helps you build a strong foundation for future STEM careers.

Common Mistakes

MISTAKE: Multiplying only one side of the equation. For example, in x/2 = 5, multiplying only x/2 by 2 to get x, but leaving the other side as 5. | CORRECTION: Always multiply BOTH sides of the equation by the same number to maintain balance.

MISTAKE: Multiplying by the wrong number. For example, if x is divided by 3 (x/3), trying to multiply by 2 instead of 3. | CORRECTION: Multiply by the reciprocal of the number that is dividing the variable (e.g., if dividing by 3, multiply by 3).

MISTAKE: Forgetting to multiply all terms on a side if there's more than one. For example, in (x+2)/3 = 4, only multiplying x by 3 instead of (x+2) by 3. | CORRECTION: Treat each side as a whole. If a side has multiple terms grouped, multiply the entire group.

Practice Questions

Try It Yourself

QUESTION: Solve for 'y': y / 6 = 3 | ANSWER: y = 18

QUESTION: If the cost of 5 samosas is x rupees, and each samosa costs 12 rupees, write an equation and solve for x. Then, if the cost of each samosa doubles, how would you show that in the equation? | ANSWER: Equation: x / 5 = 12. Solving for x: x = 60. If cost doubles, you would multiply both sides by 2: (x/5)*2 = 12*2, or x/5 = 24. So x would be 120.

QUESTION: A car travels 'd' kilometers in 2 hours. If its speed is 40 km/h, the equation is d / 2 = 40. How many kilometers does the car travel? If the car travels for 3 times the original duration, what would be the new equation to find the distance? | ANSWER: d = 80 km. New equation: d / (2 * 3) = 40, or d / 6 = 40. So d would be 240 km.

MCQ

Quick Quiz

Which operation keeps the equation 7 = 7 balanced?

Multiplying the left side by 2

Multiplying the right side by 3

Multiplying both sides by 5

Multiplying the left side by 4 and the right side by 40

The Correct Answer Is:

Multiplying both sides by the same number (5 in this case) ensures the equation remains balanced. Options A, B, and D perform different operations on each side, making the equation unequal.

Real World Connection

In the Real World

Imagine you're a shopkeeper calculating prices. If you know the price of 5 pens is 50 rupees, you can write this as P / 5 = 10 (where P is total price, 10 is price per pen). To find the total price, you'd multiply both sides by 5. This skill is used daily in budgeting, calculating travel distances for Ola/Uber rides, or even scaling recipes for a family dinner.

Key Vocabulary

Key Terms

EQUATION: A statement that two mathematical expressions are equal | VARIABLE: A symbol (usually a letter) representing an unknown value | BALANCE: To keep both sides of an equation equal | RECIPROCAL: One of a pair of numbers whose product is 1 (e.g., the reciprocal of 4 is 1/4)

What's Next

What to Learn Next

Now that you understand multiplying both sides, you're ready to learn about 'Dividing Both Sides of an Equation'. It's the opposite operation but uses the same principle of keeping the equation balanced, helping you solve even more complex problems!