What is Dividing Both Sides?

S1-SA5-0141

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

Dividing both sides means performing the exact same division operation on both the left side and the right side of an equation. This keeps the equation balanced and true, helping us find the value of an unknown number.

Simple Example

Quick Example

Imagine you have 10 ladoos equally divided between 2 plates. If you want to know how many ladoos are on one plate, you divide the total ladoos (10) by the number of plates (2). If you write this as '2 x (ladoos on one plate) = 10', dividing both sides by 2 helps you find the answer.

Worked Example

Step-by-Step

Let's say 3 friends collected 24 stickers equally. How many stickers did each friend get?

Step 1: Write down the problem as an equation. Let 's' be the number of stickers each friend got.
3 x s = 24

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Step 2: To find 's', we need to get rid of the '3' that is multiplying 's'. We do the opposite operation, which is division.

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Step 3: Divide both sides of the equation by 3.
(3 x s) / 3 = 24 / 3

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Step 4: Simplify both sides.
(3/3) x s = 8
1 x s = 8

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Step 5: So, s = 8.

Answer: Each friend got 8 stickers.

Why It Matters

Dividing both sides is a fundamental skill used in almost all STEM fields. Scientists use it to solve formulas, engineers use it to design structures, and even economists use it to understand market trends. Mastering this helps you think logically and solve complex problems in many careers like data analysis, software development, and research.

Common Mistakes

MISTAKE: Dividing only one side of the equation. For example, in 2x = 10, only dividing 10 by 2 to get x = 5, but forgetting to show (2x)/2. | CORRECTION: Always apply the division to both the left and the right sides of the equals sign to keep the equation balanced.

MISTAKE: Dividing by the wrong number. For example, in 4x = 12, dividing by 12 instead of 4. | CORRECTION: Divide by the number that is multiplying the unknown variable (the coefficient) to isolate the variable.

MISTAKE: Making calculation errors during division. For example, 30 / 5 = 7 instead of 6. | CORRECTION: Double-check your division calculations, especially when dealing with larger numbers or decimals.

Practice Questions

Try It Yourself

QUESTION: If 5 pens cost Rs 45, what is the cost of one pen? (Let 'p' be the cost of one pen) | ANSWER: p = Rs 9

QUESTION: A car travels 120 km in 3 hours. What is its average speed per hour? (Let 's' be the speed) | ANSWER: s = 40 km/hour

QUESTION: The total weight of 7 identical bags of rice is 63 kg. If 2 such bags are sold, how much rice is left? (First find weight of one bag) | ANSWER: 45 kg

MCQ

Quick Quiz

If 6 multiplied by a number 'y' is equal to 42, what is the value of 'y'?

The Correct Answer Is:

To solve 6y = 42, you divide both sides by 6. So, y = 42 / 6, which equals 7. Options A, C, and D are incorrect calculations.

Real World Connection

In the Real World

When you buy groceries online from apps like Zepto or Blinkit and want to know the per-item cost after a discount, you use this. For example, if a pack of 4 yogurts costs Rs 100, you divide 100 by 4 to find that each yogurt costs Rs 25. This helps you compare prices and budget your expenses.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an equals sign (=) | VARIABLE: A symbol (like x or y) that represents an unknown number | COEFFICIENT: The number multiplying a variable (e.g., 3 in 3x) | BALANCE: Keeping both sides of an equation equal by performing the same operation on both sides | ISOLATE: To get a variable by itself on one side of the equation

What's Next

What to Learn Next

Great job understanding how to divide both sides! Next, you can learn about 'Multiplying Both Sides'. It's another important technique to solve equations and works similarly, using the opposite operation of division.