Solve the Division Equation: 52.3 ÷ ? = 0.523

Q: Why do I convert the division notation to multiplication?

Converting $ 52.3 : x = 0.523 $ to $ 52.3 = 0.523 \times x $ makes it easier to isolate the unknown variable. This standard algebraic form helps you see exactly what operations to perform.

Q: How do I handle the decimal division?

When dividing $ 52.3 \div 0.523 $, notice that 52.3 is exactly 100 times larger than 0.523. This pattern recognition makes the calculation much simpler than long division!

Q: What if I get confused about which number goes where?

Remember: in $ a : b = c $, we're asking "a divided by what equals c?" So the unknown b equals $ a \div c $. The dividend stays on top, result goes on bottom.

Q: How can I check my answer quickly?

Multiply your answer by the result: $ 100 \times 0.523 = 52.3 $. If you get back to the original number, your division is correct!

Q: Why is the answer a nice round number like 100?

This happens when the original number and result have a simple relationship. Here, 52.3 is exactly 100 times 0.523, which creates this clean answer. Not all division problems will have such neat solutions!

Division Equations with Decimal Operations

$52.3:?=0.523$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Multiply by the factor to find the unknown

00:09 Move the decimal point according to the number of zeros, and find the unknown

00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$52.3:?=0.523$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recognize the given expression as a division problem: $52.3 : x = 0.523$ .
Step 2: Convert it into a multiplication equation: $52.3 = 0.523 \times x$ .
Step 3: Solve for $x$ . This means rearranging the equation: $x = \frac{52.3}{0.523}$ .
Step 4: Perform the division to find $x$ .

Now, let's work through these steps:

Step 1: We start with $52.3 : x = 0.523$ .

Step 2: By converting the division into multiplication, we have $52.3 = 0.523 \times x$ .

Step 3: Isolating $x$ , we rewrite this as $x = \frac{52.3}{0.523}$ .

Step 4: Performing the division yields $x = 100$ .

Therefore, the solution to the problem is $x = 100$ .

Final Answer

$100$

Key Points to Remember

Essential concepts to master this topic

Equation Setup: Convert division notation to multiplication form for easier solving
Technique: Rearrange 52.3 = 0.523 × x to x = 52.3 ÷ 0.523
Check: Verify by calculating 52.3 ÷ 100 = 0.523 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly setting up the division
Don't divide 0.523 by 52.3 instead of 52.3 by 0.523 = 0.01 instead of 100! This flips the relationship and gives the reciprocal answer. Always identify which number is the dividend and which is the divisor from the original equation.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why do I convert the division notation to multiplication?

Converting $52.3 : x = 0.523$ to $52.3 = 0.523 \times x$ makes it easier to isolate the unknown variable. This standard algebraic form helps you see exactly what operations to perform.

How do I handle the decimal division?

When dividing $52.3 \div 0.523$ , notice that 52.3 is exactly 100 times larger than 0.523. This pattern recognition makes the calculation much simpler than long division!

What if I get confused about which number goes where?

Remember: in $a : b = c$ , we're asking "a divided by what equals c?" So the unknown b equals $a \div c$ . The dividend stays on top, result goes on bottom.

How can I check my answer quickly?

Multiply your answer by the result: $100 \times 0.523 = 52.3$ . If you get back to the original number, your division is correct!

Why is the answer a nice round number like 100?

This happens when the original number and result have a simple relationship. Here, 52.3 is exactly 100 times 0.523, which creates this clean answer. Not all division problems will have such neat solutions!

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