Multiply 3/5 by a Factor of 2: Fraction Scaling Problem

Q: What does 'increase by a factor of 2' mean for fractions?

It means creating an equivalent fraction where both the numerator and denominator are multiplied by 2. The fraction's value stays the same, but it's written in a different form.

Q: Why do I multiply both parts instead of just the numerator?

Multiplying only the numerator changes the fraction's actual value! To keep the same value but scale the fraction, you must multiply both numerator and denominator by the same number.

Q: How can I check if my scaled fraction is correct?

Convert both fractions to decimals: $ \frac{3}{5} = 0.6 $ and $ \frac{6}{10} = 0.6 $. If they're equal, your scaling is correct!

Q: Is there a difference between scaling and simplifying fractions?

Scaling makes fractions larger (multiply by numbers >1) or keeps them the same size. Simplifying makes fractions smaller by dividing by common factors. Both create equivalent fractions!

Q: Can I scale by any number I want?

Yes! You can scale by any non-zero number. Multiply both numerator and denominator by the same factor: 3, 4, 10, or even fractions like 1/2.

Fraction Scaling with Equivalent Forms

Increase the following fraction by a factor of 2:

$\frac{3}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 2

00:03 Multiply the fraction by the given factor

00:06 Make sure to multiply both numerator and denominator

00:13 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 2:

$\frac{3}{5}=$

Step-by-step solution

Let's multiply both the numerator and denominator by 2 as follows:

$\frac{3\times2}{5\times2}=\frac{6}{10}$

Final Answer

$\frac{6}{10}$

Key Points to Remember

Essential concepts to master this topic

Scaling Rule: Multiply both numerator and denominator by same factor
Technique: For factor 2: $\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$
Check: Verify equivalent value: $\frac{3}{5} = 0.6$ and $\frac{6}{10} = 0.6$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the scaling factor
Don't multiply just 3 by 2 to get $\frac{6}{5}$ = wrong fraction! This changes the value completely from 0.6 to 1.2. Always multiply both numerator AND denominator by the same factor to keep equivalent value.

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 2' mean for fractions?

It means creating an equivalent fraction where both the numerator and denominator are multiplied by 2. The fraction's value stays the same, but it's written in a different form.

Why do I multiply both parts instead of just the numerator?

Multiplying only the numerator changes the fraction's actual value! To keep the same value but scale the fraction, you must multiply both numerator and denominator by the same number.

How can I check if my scaled fraction is correct?

Convert both fractions to decimals: $\frac{3}{5} = 0.6$ and $\frac{6}{10} = 0.6$ . If they're equal, your scaling is correct!

Is there a difference between scaling and simplifying fractions?

Scaling makes fractions larger (multiply by numbers >1) or keeps them the same size. Simplifying makes fractions smaller by dividing by common factors. Both create equivalent fractions!

Can I scale by any number I want?

Yes! You can scale by any non-zero number. Multiply both numerator and denominator by the same factor: 3, 4, 10, or even fractions like 1/2.

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