Enlarge the Fraction 7/9 by a Factor of 9: Step-by-Step Solution

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

Enlarging by a factor means creating an equivalent fraction with bigger numbers. The fraction $ \frac{7}{9} $ and $ \frac{63}{81} $ have the same value, just different-sized parts!

Q: Why do I multiply both top and bottom numbers?

To keep the fraction's value the same! Think of it like pizza slices - if you cut 7 out of 9 slices into smaller pieces, you need to cut all 9 slices the same way to keep the same amount of pizza.

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

Divide both fractions to decimals: $ \frac{7}{9} = 0.777... $ and $ \frac{63}{81} = 0.777... $. If they're equal, you did it right!

Q: Can I simplify the enlarged fraction back?

Yes! $ \frac{63}{81} $ simplifies back to $ \frac{7}{9} $ by dividing both parts by 9. This proves your enlargement worked correctly.

Fraction Enlargement with Integer Scaling

Enlarge the following fraction by the factor 9:

$\frac{7}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 9

00:03 Multiply the fraction by the given factor

00:07 Make sure to multiply both numerator and denominator

00:11 Calculate the multiplications

00:16 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 the factor 9:

$\frac{7}{9}=$

Step-by-step solution

To solve this problem, we need to enlarge the fraction $\frac{7}{9}$ by a factor of 9.

First, let's restate the initial fraction:

The given fraction is $\frac{7}{9}$ .
The factor to enlarge by is 9.

Now, we'll apply the enlargement:

Multiply the numerator (7) by the factor 9:
$7 \times 9 = 63$ .
Multiply the denominator (9) by the factor 9:
$9 \times 9 = 81$ .

Thus, the enlarged fraction is $\frac{63}{81}$ .

Comparing this result with the given multiple choice options confirms that our answer is option 3, $\frac{63}{81}$ .

Therefore, the enlarged fraction is $\frac{63}{81}$ .

Final Answer

$\frac{63}{81}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the factor
Technique: For factor 9: 7 × 9 = 63, 9 × 9 = 81
Check: Original value equals enlarged value: 7/9 = 63/81 ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 7 by 9 to get 63/9 = wrong fraction value! This changes the actual value of the fraction instead of just enlarging it. Always multiply BOTH the 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' actually mean?

Enlarging by a factor means creating an equivalent fraction with bigger numbers. The fraction $\frac{7}{9}$ and $\frac{63}{81}$ have the same value, just different-sized parts!

Why do I multiply both top and bottom numbers?

To keep the fraction's value the same! Think of it like pizza slices - if you cut 7 out of 9 slices into smaller pieces, you need to cut all 9 slices the same way to keep the same amount of pizza.

How can I check if my enlarged fraction is correct?

Divide both fractions to decimals: $\frac{7}{9} = 0.777...$ and $\frac{63}{81} = 0.777...$ . If they're equal, you did it right!

Can I simplify the enlarged fraction back?

Yes! $\frac{63}{81}$ simplifies back to $\frac{7}{9}$ by dividing both parts by 9. This proves your enlargement worked correctly.

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

Same rule applies! Multiply both numerator and denominator by that fraction. For example, enlarging by $\frac{1}{2}$ would give you a smaller equivalent fraction.

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