Multiply Fraction 9/10 by Scale Factor 8: Step-by-Step Solution

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

Enlarging means creating an equivalent fraction that's 8 times larger in both parts. Think of it like zooming in - everything gets bigger proportionally while keeping the same value.

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

To keep the fraction equivalent! If you only multiply the top, you change the fraction's value. Multiplying both by 8 keeps $ \frac{9}{10} = \frac{72}{80} $ mathematically equal.

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

Use cross-multiplication: multiply diagonally and see if you get equal results. For $ \frac{9}{10} $ and $ \frac{72}{80} $: 9×80 = 720 and 10×72 = 720 ✓

Q: Can I simplify the enlarged fraction?

You can simplify, but the problem asks for the enlarged form. $ \frac{72}{80} $ shows the scaling clearly, while $ \frac{9}{10} $ (simplified) loses that information.

Fraction Scaling with Integer Factors

Enlarge the following fraction by the factor 8:

$\frac{9}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's expand the fraction, by multiplying it by 8.

00:09 Remember, multiply both the top and bottom of the fraction by this factor.

00:14 Take your time, and multiply both the numerator, and the denominator.

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

00:23 Great job! And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Enlarge the following fraction by the factor 8:

$\frac{9}{10}=$

Step-by-step solution

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

Step 1: Multiply the numerator by the enlargement factor.
Step 2: Multiply the denominator by the enlargement factor.
Step 3: Write down the new fraction.

Now, let's work through each step:
Step 1: Multiply the numerator of $\frac{9}{10}$ , which is 9, by the factor 8:
$9 \times 8 = 72$
Step 2: Multiply the denominator of $\frac{9}{10}$ , which is 10, by the factor 8:
$10 \times 8 = 80$
Step 3: The enlarged fraction is $\frac{72}{80}$ .

Therefore, the solution to the problem is that $\frac{9}{10}$ enlarged by a factor of 8 is $\frac{72}{80}$ .

Final Answer

$\frac{72}{80}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the scale factor
Technique: Scale $\frac{9}{10}$ by 8: multiply 9×8=72 and 10×8=80
Check: Verify equivalent fractions: $\frac{9}{10} = \frac{72}{80}$ by cross-multiplying 9×80=720=10×72 ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the scale factor
Don't multiply just 9 by 8 to get $\frac{72}{10}$ = wrong enlargement! This creates a different fraction value, not an enlarged equivalent. Always multiply both numerator AND denominator by the same scale factor.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

$\frac{4}{8}=$

FAQ

Everything you need to know about this question

What does 'enlarge by a factor of 8' actually mean?

Enlarging means creating an equivalent fraction that's 8 times larger in both parts. Think of it like zooming in - everything gets bigger proportionally while keeping the same value.

Why do I multiply both top and bottom numbers?

To keep the fraction equivalent! If you only multiply the top, you change the fraction's value. Multiplying both by 8 keeps $\frac{9}{10} = \frac{72}{80}$ mathematically equal.

How can I check if my enlarged fraction is correct?

Use cross-multiplication: multiply diagonally and see if you get equal results. For $\frac{9}{10}$ and $\frac{72}{80}$ : 9×80 = 720 and 10×72 = 720 ✓

Can I simplify the enlarged fraction?

You can simplify, but the problem asks for the enlarged form. $\frac{72}{80}$ shows the scaling clearly, while $\frac{9}{10}$ (simplified) loses that information.

What if the scale factor was a fraction instead?

Same process! Multiply both numerator and denominator by the fractional scale factor. The key is always multiplying both parts by the same amount.

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