Multiply 8/11 by a Factor of 6: Fraction Scaling Problem

Q: What does 'increase by a factor of 6' actually mean?

Scaling by a factor means creating an equivalent fraction with larger numbers. You multiply both the numerator and denominator by 6, so $ \frac{8}{11} $ becomes $ \frac{48}{66} $ - same value, different form!

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

To keep the fraction's value the same! If you only multiply the numerator, you get a completely different number. Multiplying both parts by the same factor creates an equivalent fraction.

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

Simplify your answer back to lowest terms! $ \frac{48}{66} $ should reduce to the original $ \frac{8}{11} $ when you divide both parts by their greatest common factor.

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

No difference! Scaling a fraction by a factor is exactly how you create equivalent fractions. Both terms describe the same process of multiplying numerator and denominator by the same number.

Fraction Scaling with Multiplying Factors

Increase the following fraction by a factor of 6:

$\frac{8}{11}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 6

00:03 Multiply the fraction by the given factor

00:06 Make sure to multiply both numerator and denominator

00:10 Calculate the multiplications

00:15 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

Increase the following fraction by a factor of 6:

$\frac{8}{11}=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the given fraction as $\frac{8}{11}$ .
Step 2: Determine the factor to increase by, which is 6.
Step 3: Multiply the numerator by the factor: $8 \times 6 = 48$ .
Step 4: Multiply the denominator by the factor: $11 \times 6 = 66$ .

Now, let's perform the calculation to expand the fraction:

Starting with the original fraction:

$\frac{8}{11}$

We need to multiply both the numerator and the denominator by the factor of 6:

The new numerator is:

$8 \times 6 = 48$

The new denominator is:

$11 \times 6 = 66$

Thus, the fraction increased by a factor of 6 is:

$\frac{48}{66}$

Therefore, the solution to the problem is $\frac{48}{66}$ .

Final Answer

$\frac{48}{66}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: Scale $\frac{8}{11}$ by 6: numerator becomes 8×6=48, denominator becomes 11×6=66
Check: Verify $\frac{48}{66}$ equals original value when simplified ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just the numerator by 6 to get $\frac{48}{11}$ = wrong fraction value! This changes the fraction's value completely instead of creating an equivalent fraction. 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 6' actually mean?

Scaling by a factor means creating an equivalent fraction with larger numbers. You multiply both the numerator and denominator by 6, so $\frac{8}{11}$ becomes $\frac{48}{66}$ - same value, different form!

Why do I multiply both parts instead of just one?

To keep the fraction's value the same! If you only multiply the numerator, you get a completely different number. Multiplying both parts by the same factor creates an equivalent fraction.

How can I check if my scaled fraction is correct?

Simplify your answer back to lowest terms! $\frac{48}{66}$ should reduce to the original $\frac{8}{11}$ when you divide both parts by their greatest common factor.

Is there a difference between scaling and equivalent fractions?

No difference! Scaling a fraction by a factor is exactly how you create equivalent fractions. Both terms describe the same process of multiplying numerator and denominator by the same number.

What if the factor was a fraction instead of a whole number?

Same rule applies! Multiply both numerator and denominator by the fractional factor. For example, scaling by $\frac{1}{2}$ would give you $\frac{8 \times \frac{1}{2}}{11 \times \frac{1}{2}} = \frac{4}{5.5}$ .

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