What is Solving a / x = b?

S1-SA5-0239

Grade Level:

Class 4

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

Definition

What is it?

Solving a / x = b means finding the unknown value of 'x' when you know 'a' and 'b'. It's like figuring out how many parts 'x' you need to divide 'a' into to get 'b'.

Simple Example

Quick Example

Imagine you have 20 ladoos (a). You want to share them equally among some friends (x), so each friend gets 5 ladoos (b). The equation would be 20 / x = 5. Solving this means finding how many friends you can share with.

Worked Example

Step-by-Step

Let's solve the equation 30 / x = 6.

Step 1: We want to get 'x' by itself. Right now, 'x' is dividing 30.
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Step 2: To move 'x' to the other side and multiply, we can multiply both sides of the equation by 'x'.
30 / x * x = 6 * x
30 = 6x
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Step 3: Now we have 30 = 6x. This means 6 multiplied by 'x' equals 30.
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Step 4: To find 'x', we need to divide both sides by 6.
30 / 6 = 6x / 6
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Step 5: Calculate the division.
5 = x
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So, the value of x is 5.

Why It Matters

Understanding how to solve equations like this is super important! Engineers use it to design bridges, scientists use it to understand chemical reactions, and even app developers use it to create games. It's a basic skill for problem-solving in many cool careers like a Data Scientist or a Financial Analyst.

Common Mistakes

MISTAKE: Thinking 'x' is always the number being divided. | CORRECTION: 'x' is the divisor here, meaning it's the number that 'a' is divided BY.

MISTAKE: Dividing 'b' by 'a' instead of 'a' by 'b' to find 'x'. For example, for 30 / x = 6, some might do 6 / 30. | CORRECTION: To isolate 'x', you rearrange the equation to x = a / b. So, for 30 / x = 6, it becomes x = 30 / 6.

MISTAKE: Not moving 'x' correctly when rearranging the equation. | CORRECTION: When 'x' is in the denominator (dividing), multiply both sides by 'x' first to bring it to the numerator, then divide by 'b'.

Practice Questions

Try It Yourself

QUESTION: Solve for x: 45 / x = 9 | ANSWER: x = 5

QUESTION: If 72 pencils are to be divided equally among 'x' students, and each student gets 8 pencils, what is 'x'? | ANSWER: x = 9

QUESTION: A car travels 150 km. If it covers 'x' km per hour and takes 3 hours to complete the journey, what is 'x'? (Hint: Total distance / speed = time) | ANSWER: x = 50

MCQ

Quick Quiz

Which step is correct to solve 24 / x = 4?

x = 4 / 24

x = 24 * 4

x = 24 / 4

x = 24 - 4

The Correct Answer Is:

To solve for 'x' in 24 / x = 4, you first multiply both sides by 'x' to get 24 = 4x. Then, you divide both sides by 4 to get x = 24 / 4. Options A, B, and D perform incorrect operations.

Real World Connection

In the Real World

When you buy things in bulk, like a big packet of biscuits for ₹90 and you know each biscuit costs ₹5, you might want to know how many biscuits ('x') are in the packet. The equation would be 90 / x = 5. Or, if a delivery rider from Zepto has 120 orders to deliver in 6 hours, they might use this to figure out how many orders ('x') they need to deliver per hour: 120 / x = 6.

Key Vocabulary

Key Terms

EQUATION: A statement that two mathematical expressions are equal | UNKNOWN: A quantity whose value is not known, usually represented by a letter like 'x' | DIVISOR: The number by which another number is divided | QUOTIENT: The result of dividing one number by another

What's Next

What to Learn Next

Great job understanding this! Next, you can learn about 'Solving ax = b'. This will teach you how to find an unknown when it's being multiplied, building on what you've learned about division.