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

Q: What does 'increase by a factor of 8' mean for fractions?

It means to scale the entire fraction by multiplying both the numerator and denominator by 8. This keeps the same proportional value but in a different form, like zooming in on a photo.

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

Multiplying only the numerator would change the value of the fraction! To keep the same value but scale it, you must multiply both parts equally.

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

Convert both fractions to decimals: $ \frac{2}{5} = 0.4 $ and $ \frac{16}{40} = 0.4 $. If they're equal, you scaled correctly!

Q: Should I simplify the final answer?

In this case, keep it as given in the answer choices. While $ \frac{16}{40} $ can simplify to $ \frac{2}{5} $, the question asks for the scaled version.

Fraction Scaling with Multiplicative Factors

Increase the following fraction by a factor of 8:

$\frac{2}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 8

00:03 Multiply the fraction by the given factor

00:07 Make sure to multiply both numerator and denominator

00:11 Calculate the multiplications

00:14 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 8:

$\frac{2}{5}=$

Step-by-step solution

To solve the problem of increasing the fraction $\frac{2}{5}$ by a factor of 8, we follow these steps:

Multiply the numerator of the fraction by the factor of 8.
Multiply the denominator of the fraction by the same factor of 8 to preserve the value relation.
Check the result against the options provided, especially since this is a multiple-choice question.

Following these steps:

Step 1: Multiply the numerator:

The numerator is 2. Multiplying 2 by 8 gives $2 \times 8 = 16$ .

Step 2: Multiply the denominator:

The denominator is 5. Multiplying 5 by 8 gives $5 \times 8 = 40$ .

Thus, the fraction becomes $\frac{16}{40}$ after being increased by a factor of 8.

The correct answer among the provided choices is:

$\frac{16}{40}$

Final Answer

$\frac{16}{40}$

Key Points to Remember

Essential concepts to master this topic

Scaling Rule: Multiply both numerator and denominator by the same factor
Technique: For $\frac{2}{5} \times 8 = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}$
Check: Verify equivalent fractions: $\frac{2}{5} = \frac{16}{40} = 0.4$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 2 by 8 to get $\frac{16}{5}$ = wrong fraction value! This changes the actual value of the fraction instead of scaling it proportionally. Always multiply both numerator AND denominator by the same factor.

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 8' mean for fractions?

It means to scale the entire fraction by multiplying both the numerator and denominator by 8. This keeps the same proportional value but in a different form, like zooming in on a photo.

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

Multiplying only the numerator would change the value of the fraction! To keep the same value but scale it, you must multiply both parts equally.

How can I check if my scaled fraction is correct?

Convert both fractions to decimals: $\frac{2}{5} = 0.4$ and $\frac{16}{40} = 0.4$ . If they're equal, you scaled correctly!

Should I simplify the final answer?

In this case, keep it as given in the answer choices. While $\frac{16}{40}$ can simplify to $\frac{2}{5}$ , the question asks for the scaled version.

What if the factor was a fraction instead of 8?

Same principle! Multiply both numerator and denominator by that fraction. For example, scaling by $\frac{1}{2}$ means: $\frac{2 \times \frac{1}{2}}{5 \times \frac{1}{2}} = \frac{1}{2.5}$

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