Solve the Decimal Equation: Finding the Missing Value in 5.2:?=0.52

Q: Why do I rewrite the division as multiplication?

Rewriting $ 5.2 \div ? = 0.52 $ as $ 5.2 = 0.52 \times ? $ makes it easier to isolate the unknown! Division and multiplication are inverse operations, so this transformation is always valid.

Q: How do I remember which number goes where when solving?

Think of it this way: "What number divided into 5.2 gives 0.52?" Since 5.2 is being divided, it goes on top of the fraction: $ ? = \frac{5.2}{0.52} $

Q: Can I solve this without fractions?

Yes! You can think: "0.52 times what equals 5.2?" Since $ 0.52 \times 10 = 5.2 $, the answer is 10. Both methods give the same result!

Q: What if I get confused by the decimal points?

Try this trick: Move decimal points to make whole numbers! $ \frac{5.2}{0.52} = \frac{52}{5.2} = \frac{520}{52} = 10 $. The answer stays the same when you move decimals equally.

Q: How do I check if 10 is really correct?

Substitute back into the original: $ 5.2 \div 10 = 0.52 $ ✓. Since both sides equal 0.52, your answer is definitely correct!

Division Properties with Decimal Ratios

$5.2:?=0.52$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 According to the amount of point shifts we can find the appropriate factor

00:08 As the amount of shifts, multiply this amount by 10 and that's the factor

00:15 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

$5.2:?=0.52$

Step-by-step solution

To find the value of '?', we'll set up the equation based on the division of numbers:

Given that $5.2 \div ? = 0.52$ , we can rewrite this equation as:

$5.2 = 0.52 \times ?$

To isolate the '?', we divide both sides of the equation by 0.52:

$? = \frac{5.2}{0.52}$

Calculating this division gives us:

$? = 10$

This means when 5.2 is divided by 10, the result is 0.52, confirming that '? = 10' is correct.

Therefore, the solution to the problem is $10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: In division $a \div b = c$ , we can rewrite as $a = b \times c$
Technique: Isolate unknown by dividing: $? = \frac{5.2}{0.52} = 10$
Check: Verify by substitution: $5.2 \div 10 = 0.52$ ✓

Common Mistakes

Avoid these frequent errors

Confusing the division order
Don't solve as $? = \frac{0.52}{5.2} = 0.1$ ! This reverses the dividend and divisor, giving a completely wrong result. Always remember that in $5.2 \div ? = 0.52$ , the 5.2 goes in the numerator when solving.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I rewrite the division as multiplication?

Rewriting $5.2 \div ? = 0.52$ as $5.2 = 0.52 \times ?$ makes it easier to isolate the unknown! Division and multiplication are inverse operations, so this transformation is always valid.

How do I remember which number goes where when solving?

Think of it this way: "What number divided into 5.2 gives 0.52?" Since 5.2 is being divided, it goes on top of the fraction: $? = \frac{5.2}{0.52}$

Can I solve this without fractions?

Yes! You can think: "0.52 times what equals 5.2?" Since $0.52 \times 10 = 5.2$ , the answer is 10. Both methods give the same result!

What if I get confused by the decimal points?

Try this trick: Move decimal points to make whole numbers! $\frac{5.2}{0.52} = \frac{52}{5.2} = \frac{520}{52} = 10$ . The answer stays the same when you move decimals equally.

How do I check if 10 is really correct?

Substitute back into the original: $5.2 \div 10 = 0.52$ ✓. Since both sides equal 0.52, your answer is definitely correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime