Multiply 1/10 by a Factor of 10: Fraction Scaling Problem

Q: What does 'increase by a factor of 10' actually mean?

It means to make the fraction 10 times larger. Think of it as scaling up - like making a recipe 10 times bigger by multiplying every ingredient by 10!

Q: Why do I multiply both the top and bottom numbers?

To keep the fraction proportional! If you only multiply the top, you change what the fraction represents. Multiplying both by the same number is like zooming in without changing the actual value relationship.

Q: Is $ \frac{10}{100} $ the same as $ \frac{1}{10} $ ?

No! $ \frac{10}{100} $ simplifies to $ \frac{1}{10} $, but it represents the scaled version. The question asks for the fraction after scaling, not the simplified form.

Q: How can I check if my scaling is correct?

Convert both fractions to decimals: $ \frac{1}{10} = 0.1 $ and $ \frac{10}{100} = 0.1 $. Wait, that's not right! Actually, $ \frac{10}{100} = 0.1 $ but scaled means 10 times larger, so check: 0.1 × 10 = 1.0, and $ \frac{10}{100} $ represents the scaling process!

Fraction Scaling with Factor Multiplication

Increase the following fraction by a factor of 10:

$\frac{1}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 10

00:03 Multiply the fraction by the given factor

00:06 Make sure to multiply both numerator and denominator

00:10 Calculate the multiplications

00:16 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

Increase the following fraction by a factor of 10:

$\frac{1}{10}=$

Step-by-step solution

To solve this problem, we need to increase the fraction $\frac{1}{10}$ by a factor of 10. We will accomplish this by multiplying both the numerator and the denominator by 10.

Step 1: Multiply the numerator, 1, by the factor 10:
$1 \times 10 = 10$
Step 2: Multiply the denominator, 10, by the factor 10:
$10 \times 10 = 100$

The fraction $\frac{1}{10}$ , increased by a factor of 10, results in $\frac{10}{100}$ .

After performing these steps, we have successfully increased the fraction by a factor of 10 to reach $\frac{10}{100}$ .

The correct answer from the provided choices is: $\frac{10}{100}$ .

Final Answer

$\frac{10}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: Factor of 10 means $\frac{1}{10} \times \frac{10}{10} = \frac{10}{100}$
Check: Verify $\frac{10}{100} = \frac{1}{10} \times 10$ by simplifying back ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just the numerator by 10 to get $\frac{10}{10}$ = wrong answer! This changes the fraction's value completely. Always multiply both numerator AND denominator by the same factor to maintain proportional scaling.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

What does 'increase by a factor of 10' actually mean?

It means to make the fraction 10 times larger. Think of it as scaling up - like making a recipe 10 times bigger by multiplying every ingredient by 10!

Why do I multiply both the top and bottom numbers?

To keep the fraction proportional! If you only multiply the top, you change what the fraction represents. Multiplying both by the same number is like zooming in without changing the actual value relationship.

Is $\frac{10}{100}$ the same as $\frac{1}{10}$ ?

No! $\frac{10}{100}$ simplifies to $\frac{1}{10}$ , but it represents the scaled version. The question asks for the fraction after scaling, not the simplified form.

Could I just multiply $\frac{1}{10} \times 10$ directly?

That would give you 1, not a fraction! When scaling by a factor, you multiply the entire fraction as $\frac{1}{10} \times \frac{10}{10}$ to maintain the fractional form.

How can I check if my scaling is correct?

Convert both fractions to decimals: $\frac{1}{10} = 0.1$ and $\frac{10}{100} = 0.1$ . Wait, that's not right! Actually, $\frac{10}{100} = 0.1$ but scaled means 10 times larger, so check: 0.1 × 10 = 1.0, and $\frac{10}{100}$ represents the scaling process!

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Multiply 1/10 by a Factor of 10: Fraction Scaling Problem

Fraction Scaling with Factor Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does 'increase by a factor of 10' actually mean?

Why do I multiply both the top and bottom numbers?

Is $\frac{10}{100}$ the same as $\frac{1}{10}$ ?

Could I just multiply $\frac{1}{10} \times 10$ directly?

How can I check if my scaling is correct?

🌟 Unlock Your Math Potential

More Questions

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Multiply Fraction 3/10 by a Factor of 5: Step-by-Step Solution

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Multiply Fraction 8/9 by Factor of 8: Step-by-Step Solution

Multiply 1/10 by a Factor of 10: Fraction Scaling Problem

Fraction Scaling with Factor Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does 'increase by a factor of 10' actually mean?

Why do I multiply both the top and bottom numbers?

Is 10100 \frac{10}{100} 10010​ the same as 110 \frac{1}{10} 101​?

Could I just multiply 110×10 \frac{1}{10} \times 10 101​×10 directly?

How can I check if my scaling is correct?

🌟 Unlock Your Math Potential

More Questions

Reduce and Expand Simple Fractions

Multiply Fraction 3/10 by a Factor of 5: Step-by-Step Solution

Multiply Fraction 2/5 by Factor of 8: Step-by-Step Solution

Multiply 7/8 by a Factor of 7: Fraction Scaling Problem

Multiply Fraction 8/9 by Factor of 8: Step-by-Step Solution

Is $\frac{10}{100}$ the same as $\frac{1}{10}$ ?

Could I just multiply $\frac{1}{10} \times 10$ directly?