What is Solving x / a = b?

S1-SA5-0238

Grade Level:

Class 4

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

Definition

What is it?

Solving x / a = b means finding the unknown value 'x' in an equation where 'x' is being divided by another number 'a', and the result is 'b'. It's like finding a missing piece of a puzzle to make the equation true.

Simple Example

Quick Example

Imagine you have some ladoos (x) and you divide them equally among 5 friends (a=5). Each friend gets 3 ladoos (b=3). To find out how many ladoos you started with, you need to solve x / 5 = 3.

Worked Example

Step-by-Step

Let's solve: x / 4 = 7

Step 1: Identify the unknown 'x'. Here, 'x' is being divided by 4.
---Step 2: To find 'x', we need to do the opposite operation of division. The opposite of division is multiplication.
---Step 3: Multiply both sides of the equation by the number that 'x' is being divided by. In this case, multiply both sides by 4.
---Step 4: (x / 4) * 4 = 7 * 4
---Step 5: On the left side, the 'divided by 4' and 'multiplied by 4' cancel each other out, leaving just 'x'.
---Step 6: x = 28
---Step 7: Check your answer: 28 / 4 = 7. This is correct.

Answer: x = 28

Why It Matters

Understanding how to solve equations like this is crucial for problem-solving in science, finance, and even daily life. Scientists use it to calculate chemical concentrations, and engineers use it to design structures. It's a foundational skill for careers in technology, research, and business.

Common Mistakes

MISTAKE: Dividing 'b' by 'a' instead of multiplying. For x / a = b, some students might do x = b / a. | CORRECTION: To isolate 'x', you must perform the inverse operation. Since 'x' is being divided by 'a', you multiply 'a' on both sides.

MISTAKE: Only multiplying one side of the equation. For x / a = b, some might do x = b * a but forget to multiply the left side. | CORRECTION: Remember the 'balance' of an equation. Whatever you do to one side, you MUST do to the other side to keep it equal.

MISTAKE: Getting confused by the order of operations if there are other numbers. | CORRECTION: Always focus on isolating 'x' first. For x / a = b, the first step is always to multiply both sides by 'a'.

Practice Questions

Try It Yourself

QUESTION: Solve for x: x / 6 = 5 | ANSWER: x = 30

QUESTION: If you share some pakoras (x) equally among 8 friends, and each friend gets 4 pakoras, how many pakoras did you start with? (Solve x / 8 = 4) | ANSWER: x = 32

QUESTION: A farmer divides his land (x acres) into 10 equal plots. Each plot is 7 acres. What is the total area of his land? (Solve x / 10 = 7) | ANSWER: x = 70 acres

MCQ

Quick Quiz

What is the first step to solve x / 3 = 9?

Divide 9 by 3

Multiply both sides by 3

Subtract 3 from both sides

Add 3 to both sides

The Correct Answer Is:

To undo the division by 3 on the left side, you must perform the inverse operation, which is multiplication by 3. You must do this to both sides of the equation.

Real World Connection

In the Real World

When you buy groceries, if the total bill for 5 packets of biscuits (a=5) is Rs 100 (b=100), and you want to find the price of one packet (x), you solve x * 5 = 100, which is similar to x = 100 / 5. This concept helps shopkeepers calculate unit prices or when you're splitting a bill with friends using apps like UPI.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign | UNKNOWN: A value represented by a letter (like 'x') that we need to find | INVERSE OPERATION: The operation that undoes another operation (e.g., multiplication is the inverse of division) | ISOLATE: To get the unknown variable (like 'x') by itself on one side of the equation

What's Next

What to Learn Next

Now that you can solve for 'x' when it's divided, you're ready to learn about solving equations where 'x' is multiplied, added, or subtracted. These skills build on each other and will make you a master problem-solver!