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

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

It means multiply the entire fraction by 8. Think of it as making the fraction 8 times bigger while keeping its value the same by creating an equivalent fraction.

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

Simplify your answer back to lowest terms. $ \frac{64}{72} $ divided by their GCD of 8 gives $ \frac{8}{9} $ - the original fraction! If you get the same fraction, you're correct.

Q: Is there a difference between multiplying by 8 and increasing by factor 8?

No difference! Both mean the same thing. Increasing by a factor of 8 is just another way to say multiply by 8. The key is creating equivalent fractions.

Q: Can I simplify the answer further?

You should check! $ \frac{64}{72} $ can be simplified by dividing both by 8 to get $ \frac{8}{9} $, but the question asks for the result in this specific form, so $ \frac{64}{72} $ is the correct answer.

Fraction Multiplication with Scaling Factor

Increase the following fraction by a factor of 8:

$\frac{8}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's start by expanding the fraction by eight.

00:09 Next, we multiply the fraction with the factor given to us.

00:14 Make sure to multiply both the top and the bottom numbers.

00:18 Now, let's calculate these multiplications.

00:21 And that gives us the solution to our problem!

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:

$\frac{8}{9}=$

Step-by-step solution

Let's multiply both the numerator and denominator by 8 as follows:

$\frac{8\times8}{9\times8}=\frac{64}{72}$

Final Answer

$\frac{64}{72}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerator and denominator by the same factor
Technique: $\frac{8}{9} \times 8 = \frac{8 \times 8}{9 \times 8} = \frac{64}{72}$
Check: Simplified form should equal original: $\frac{64}{72} = \frac{8}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Only multiplying the numerator by the factor
Don't just multiply 8 × 8 = 64 and keep denominator as 9 = $\frac{64}{9}$ ! This changes the fraction's value completely. Always multiply both numerator AND denominator by the same factor to create an equivalent fraction.

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?

It means multiply the entire fraction by 8. Think of it as making the fraction 8 times bigger while keeping its value the same by creating an equivalent fraction.

Why do I multiply both top and bottom by 8?

Multiplying both numerator and denominator by the same number creates an equivalent fraction. It's like having $\frac{8}{9} \times \frac{8}{8} = \frac{64}{72}$ , and since $\frac{8}{8} = 1$ , the value stays the same!

How can I check if my answer is correct?

Simplify your answer back to lowest terms. $\frac{64}{72}$ divided by their GCD of 8 gives $\frac{8}{9}$ - the original fraction! If you get the same fraction, you're correct.

Is there a difference between multiplying by 8 and increasing by factor 8?

No difference! Both mean the same thing. Increasing by a factor of 8 is just another way to say multiply by 8. The key is creating equivalent fractions.

Can I simplify the answer further?

You should check! $\frac{64}{72}$ can be simplified by dividing both by 8 to get $\frac{8}{9}$ , but the question asks for the result in this specific form, so $\frac{64}{72}$ is the correct answer.

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