Multiply Fraction 3/10 by a Factor of 5: Step-by-Step Solution

Q: What does 'increase by a factor of 5' mean for fractions?

It means to scale the entire fraction by multiplying both the numerator and denominator by 5. This creates an equivalent fraction that looks different but has the same value as the original.

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

To keep the fraction equivalent! If you only multiply the numerator, you're actually making the fraction 5 times larger, not creating an equivalent form. Both parts must change proportionally.

Q: How can I tell if my answer is equivalent to the original?

Use cross-multiplication: $ \frac{3}{10} = \frac{15}{50} $ if 3×50 = 15×10. Both equal 150, so they're equivalent!

Q: Could I simplify the answer instead?

Yes! $ \frac{15}{50} $ can be simplified to $ \frac{3}{10} $ by dividing both parts by 5. But the question asks for the scaled version, so $ \frac{15}{50} $ is correct.

Q: Is there a pattern when scaling fractions?

Absolutely! When you scale by factor n, the fraction $ \frac{a}{b} $ becomes $ \frac{n×a}{n×b} $. The numerator and denominator both get multiplied by the same number.

Fraction Scaling with Multiplicative Factors

Increase the following fraction by a factor of 5:

$\frac{3}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 5

00:04 Multiply the fraction by the given factor

00:07 Make sure to multiply both numerator and denominator

00:11 Calculate the multiplications

00:14 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 5:

$\frac{3}{10}=$

Step-by-step solution

To solve the problem of increasing the fraction $\frac{3}{10}$ by a factor of 5, follow these steps:

Step 1: Multiply the numerator by 5.
The original numerator is 3, so $3 \times 5 = 15$ .
Step 2: Multiply the denominator by 5.
The original denominator is 10, so $10 \times 5 = 50$ .
Step 3: Write the new fraction.
The resulting fraction after applying the factor is $\frac{15}{50}$ .

Thus, when we increase the fraction $\frac{3}{10}$ by a factor of 5, we get $\frac{15}{50}$ .

Therefore, the correct answer is $\frac{15}{50}$ .

Final Answer

$\frac{15}{50}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: For factor 5: $\frac{3}{10}$ becomes $\frac{3×5}{10×5} = \frac{15}{50}$
Check: Verify equivalent fractions: $\frac{3}{10} = \frac{15}{50}$ by cross-multiplying 3×50 = 15×10 ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 3 by 5 to get $\frac{15}{10}$ ! This changes the fraction's value completely. Always multiply both numerator AND denominator by the same factor to maintain equivalent fractions.

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 5' mean for fractions?

It means to scale the entire fraction by multiplying both the numerator and denominator by 5. This creates an equivalent fraction that looks different but has the same value as the original.

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

To keep the fraction equivalent! If you only multiply the numerator, you're actually making the fraction 5 times larger, not creating an equivalent form. Both parts must change proportionally.

How can I tell if my answer is equivalent to the original?

Use cross-multiplication: $\frac{3}{10} = \frac{15}{50}$ if 3×50 = 15×10. Both equal 150, so they're equivalent!

Could I simplify the answer instead?

Yes! $\frac{15}{50}$ can be simplified to $\frac{3}{10}$ by dividing both parts by 5. But the question asks for the scaled version, so $\frac{15}{50}$ is correct.

Is there a pattern when scaling fractions?

Absolutely! When you scale by factor n, the fraction $\frac{a}{b}$ becomes $\frac{n×a}{n×b}$ . The numerator and denominator both get multiplied by the same number.

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