What is Dividing Both Sides of an Equation?

S1-SA5-1196

Grade Level:

Class 5

Maths, Computing, AI, Physics

Definition

What is it?

Dividing both sides of an equation means performing the same division operation on both the left and right sides of the '=' sign. This keeps the equation balanced, ensuring that the unknown value (like 'x') remains true. It helps us find the value of an unknown variable.

Simple Example

Quick Example

Imagine you have 6 laddoo boxes, and each box has the same number of laddoos. If you know there are a total of 24 laddoos, you can write this as 6 x (laddoos per box) = 24. To find out how many laddoos are in one box, you divide both sides of the equation by 6.

Worked Example

Step-by-Step

Let's say 4 friends share the cost of a new cricket bat. The total cost is Rs 800. We want to find out how much each friend pays.
Step 1: Write the equation. Let 'c' be the cost each friend pays. So, 4 x c = 800.
---Step 2: To find 'c', we need to get 'c' by itself. 'c' is being multiplied by 4.
---Step 3: To undo multiplication, we divide. So, divide both sides of the equation by 4.
---Step 4: (4 x c) / 4 = 800 / 4
---Step 5: On the left side, 4/4 becomes 1, leaving 'c'. On the right side, 800 divided by 4 is 200.
---Step 6: So, c = 200.
---Answer: Each friend pays Rs 200.

Why It Matters

This concept is fundamental in Maths, helping solve problems in Physics to calculate speed or force. In Computing, it's used in algorithms to distribute tasks or resources efficiently. Engineers use it to design structures and even AI systems use it for calculations.

Common Mistakes

MISTAKE: Dividing only one side of the equation. E.g., if 3x = 15, student writes x = 15 / 3 (correct) but forgets to show 3x/3. | CORRECTION: Always show the division on both sides of the '=' sign to maintain balance. (3x)/3 = 15/3.

MISTAKE: Dividing by the wrong number. E.g., if 5x = 20, student divides by 5 on the left but by 20 on the right. | CORRECTION: Divide both sides by the number that is multiplying the variable (the coefficient). Here, divide both sides by 5.

MISTAKE: Incorrectly performing the division on the number side. E.g., if 6x = 42, student divides 42 by 6 and gets 6. | CORRECTION: Double-check your division calculation. 42 divided by 6 is 7, not 6.

Practice Questions

Try It Yourself

QUESTION: If 7 packets of biscuits cost Rs 105, how much does 1 packet cost? (Let 'b' be the cost of one packet). | ANSWER: 7b = 105; b = 105/7; b = Rs 15

QUESTION: A car covers 180 km in 3 hours. What is its speed in km per hour? (Speed = Distance / Time). Let 's' be the speed. | ANSWER: 3s = 180; s = 180/3; s = 60 km/hr

QUESTION: A school needs to buy 15 new footballs. If the total bill is Rs 4500, and there is an additional delivery charge of Rs 150, what is the cost of one football? (First, subtract delivery charge from total). | ANSWER: 15f + 150 = 4500; 15f = 4500 - 150; 15f = 4350; f = 4350/15; f = Rs 290

MCQ

Quick Quiz

If 9 notebooks cost Rs 360, which operation will help find the cost of one notebook?

Add 9 to both sides of the equation

Subtract 9 from both sides of the equation

Multiply both sides of the equation by 9

Divide both sides of the equation by 9

The Correct Answer Is:

To undo multiplication (9 x cost), you must perform the inverse operation, which is division. Dividing both sides by 9 will isolate the cost of one notebook.

Real World Connection

In the Real World

When a food delivery app like Swiggy calculates the average delivery time for its riders, it uses division. If 5 riders complete 15 deliveries in total, dividing 15 by 5 helps find the average deliveries per rider. Similarly, when you calculate your average marks across different subjects, you use this concept.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, separated by an '=' sign. | VARIABLE: A symbol (usually a letter like x or y) representing an unknown value. | COEFFICIENT: The number multiplying a variable (e.g., 5 in 5x). | BALANCE: Keeping both sides of an equation equal.

What's Next

What to Learn Next

Great job understanding this! Next, you can learn about 'Multiplying Both Sides of an Equation'. It's another way to keep equations balanced and helps you solve more complex problems where variables are divided by numbers.