Multiply Fraction 8/9 by Factor of 11: Step-by-Step Solution

Q: What does 'enlarge by a factor of 11' actually mean?

It means to scale up the fraction while keeping its value the same. You multiply both the numerator and denominator by 11, creating an equivalent fraction with larger numbers.

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

Multiplying only the numerator would change the fraction's value! For example, $ \frac{88}{9} $ is much larger than $ \frac{8}{9} $. You need to multiply both parts to keep the same value.

Q: Is 88/99 the same value as 8/9?

Yes! They're equivalent fractions. You can verify this by dividing: $ 88 ÷ 11 = 8 $ and $ 99 ÷ 11 = 9 $, which gives you back $ \frac{8}{9} $.

Q: How is this different from just multiplying 8/9 × 11?

Very different results! Multiplying $ \frac{8}{9} \times 11 = \frac{88}{9} $ gives a much larger value. Enlarging by a factor creates an equivalent fraction with the same value.

Q: Can I simplify 88/99 further?

Yes! Both 88 and 99 are divisible by 11, so $ \frac{88}{99} = \frac{8}{9} $. But the question asks for the enlarged form, so $ \frac{88}{99} $ is the correct answer.

Fraction Scaling with Integer Multipliers

Enlarge the following fraction by a factor of 11:

$\frac{8}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 11

00:04 Multiply the fraction by the given factor

00:07 Make sure to multiply both numerator and denominator

00:12 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

Enlarge the following fraction by a factor of 11:

$\frac{8}{9}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Multiply the numerator of the fraction by the enlargement factor.
Step 2: Multiply the denominator of the fraction by the enlargement factor.
Step 3: Write the new fraction formed after multiplication.

Now, let's work through each step:

Step 1: The numerator of $\frac{8}{9}$ is 8. Multiply 8 by 11:
$8 \times 11 = 88$ .

Step 2: The denominator of $\frac{8}{9}$ is 9. Multiply 9 by 11:
$9 \times 11 = 99$ .

Step 3: The enlarged fraction is given by the new numerator and denominator:
$\frac{88}{99}$ .

Therefore, the solution to the problem is $\frac{88}{99}$ .

Final Answer

$\frac{88}{99}$

Key Points to Remember

Essential concepts to master this topic

Scaling Rule: Multiply both numerator and denominator by the same factor
Technique: Calculate $8 \times 11 = 88$ and $9 \times 11 = 99$
Check: Verify that $\frac{88}{99}$ equals $\frac{8}{9} \times 11$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 8 by 11 to get 88/9 = wrong answer! This changes the fraction's value 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 'enlarge by a factor of 11' actually mean?

It means to scale up the fraction while keeping its value the same. You multiply both the numerator and denominator by 11, creating an equivalent fraction with larger numbers.

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

Multiplying only the numerator would change the fraction's value! For example, $\frac{88}{9}$ is much larger than $\frac{8}{9}$ . You need to multiply both parts to keep the same value.

Is 88/99 the same value as 8/9?

Yes! They're equivalent fractions. You can verify this by dividing: $88 ÷ 11 = 8$ and $99 ÷ 11 = 9$ , which gives you back $\frac{8}{9}$ .

How is this different from just multiplying 8/9 × 11?

Very different results! Multiplying $\frac{8}{9} \times 11 = \frac{88}{9}$ gives a much larger value. Enlarging by a factor creates an equivalent fraction with the same value.

Can I simplify 88/99 further?

Yes! Both 88 and 99 are divisible by 11, so $\frac{88}{99} = \frac{8}{9}$ . But the question asks for the enlarged form, so $\frac{88}{99}$ is the correct answer.

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