What is an Equation With One Unknown?

S1-SA5-1188

Grade Level:

Class 5

Maths, Computing, AI, Physics, Logic

Definition

What is it?

An equation with one unknown is like a math puzzle where you need to find a secret number. It has an equals sign (=) and only one letter (like 'x' or 'y') representing the number you need to find. The goal is to figure out what that secret number is.

Simple Example

Quick Example

Imagine you bought a packet of biscuits for Rs 10 and a chai for some unknown amount. The total bill was Rs 25. If we let 'x' be the price of the chai, the equation would be: 10 + x = 25. Here, 'x' is the one unknown we need to find.

Worked Example

Step-by-Step

Let's solve: x + 7 = 15

1. Our goal is to get 'x' by itself on one side of the equals sign.
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2. To remove '+ 7' from the left side, we do the opposite operation: subtract 7.
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3. Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced. So, we subtract 7 from both sides.
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4. x + 7 - 7 = 15 - 7
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5. This simplifies to: x = 8
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ANSWER: x = 8

Why It Matters

Understanding equations with one unknown is super important! It's the basic building block for advanced Maths, Physics problems, and even how computers solve puzzles. Engineers use it to design bridges, and scientists use it to understand the universe.

Common Mistakes

MISTAKE: Adding or subtracting only from one side of the equation. For example, x + 5 = 10 becomes x = 10 - 5 (correct) or x + 5 - 5 = 10 (incorrect). | CORRECTION: Always perform the same operation (add, subtract, multiply, divide) on BOTH sides of the equals sign to keep the equation balanced.

MISTAKE: Confusing the operation. For example, in 3x = 12, trying to subtract 3 instead of dividing by 3. | CORRECTION: Identify the operation connecting the number and the unknown (e.g., if it's 3x, it means 3 multiplied by x, so you need to divide to isolate x).

MISTAKE: Not showing clear steps, leading to calculation errors. For example, jumping directly to the answer without showing the intermediate step. | CORRECTION: Write down each step clearly, especially when moving numbers across the equals sign. This helps catch mistakes.

Practice Questions

Try It Yourself

QUESTION: If you have some cricket cards (let's say 'y' cards) and your friend gives you 5 more, you now have 12 cards. Write this as an equation and find 'y'. | ANSWER: y + 5 = 12; y = 7

QUESTION: A auto-rickshaw driver charges Rs 20 plus Rs 5 per kilometer. If a ride cost Rs 45, how many kilometers ('k') was the ride? Write the equation and solve. | ANSWER: 20 + 5k = 45; 5k = 25; k = 5 kilometers

QUESTION: Your mom baked a batch of ladoos. She gave half of them to your neighbours. Then, she ate 2 ladoos. If 10 ladoos are left, how many ('L') did she bake initially? | ANSWER: L/2 - 2 = 10; L/2 = 12; L = 24 ladoos

MCQ

Quick Quiz

Which of these is an equation with one unknown?

5 + 3 = 8

x + y = 10

7 - z = 4

2 < 6

The Correct Answer Is:

Option C, '7 - z = 4', has an equals sign and only one letter 'z' as the unknown. Options A and D do not have an unknown, and Option B has two unknowns (x and y).

Real World Connection

In the Real World

Equations with one unknown are used everywhere! When you check your mobile data balance, the app uses equations to calculate how much data ('x') you have left after using some. Delivery apps like Swiggy or Zomato use them to calculate the unknown delivery time based on distance and traffic.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, using an '=' sign. | UNKNOWN: A quantity whose value is not known, usually represented by a letter like x, y, or z. | VARIABLE: Another name for an unknown, as its value can 'vary'. | BALANCE: Keeping both sides of an equation equal by performing the same operation on both sides.

What's Next

What to Learn Next

Great job understanding the basics! Next, you can learn about 'Equations with Two Unknowns' or 'Linear Equations'. These build on what you've learned here and help you solve even more complex real-world puzzles.