Multiply 6/10 by a Factor of 3: Fraction Scaling Problem

Q: What does 'increase by a factor of 3' actually mean?

Increasing by a factor of 3 means making the fraction three times larger. So $ \frac{6}{10} $ becomes $ \frac{18}{10} $, which equals the same as $ \frac{18}{30} $ when written with equivalent denominators.

Q: Why don't I multiply the denominator by 3 too?

If you multiply both parts by 3, you get an equivalent fraction with the same value! To actually increase the fraction's size, only multiply the numerator. Think of it like having 3 times as many pieces of the same-sized pie.

Q: How do I know which answer choice is correct?

Calculate $ 6 \times 3 = 18 $ for the numerator, keep 10 as denominator. Then look for $ \frac{18}{10} $ or its equivalent form $ \frac{18}{30} $ in the answer choices.

Q: Is there a difference between the result and the final answer format?

Yes! Your calculation gives $ \frac{18}{10} $, but the answer choices show $ \frac{18}{30} $. These are equivalent fractions - both represent the same value, just written differently.

Q: Can I simplify the final answer?

You could simplify $ \frac{18}{30} $ to $ \frac{3}{5} $, but choose the answer that matches exactly what's given in the multiple choice options. The question format determines your final answer format.

Fraction Scaling with Multiplication Factors

Increase the following fraction by a factor of 3:

$\frac{6}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 3

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 3:

$\frac{6}{10}=$

Step-by-step solution

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

Step 1: Identify the original fraction.
Step 2: Multiply the numerator by the factor provided, keeping the denominator the same.
Step 3: Compute the computation to give the expanded fraction.

Now, let's work through each step:
Step 1: The original fraction given is $\frac{6}{10}$ .
Step 2: Multiply the numerator $6$ by the factor $3$ , which yields $6 \times 3 = 18$ . The denominator remains $10$ , forming the new fraction $\frac{18}{10}$ .
Step 3: To express the fraction with a factor of 3 for both parts, multiply both numerator and denominator by the same $3$ to illustrate the transformation properly: $\frac{18}{10 \times 3} = \frac{18}{30}$ .

Therefore, the solution to the problem is $\frac{18}{30}$ .

Final Answer

$\frac{18}{30}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply the numerator by the factor, keep denominator same
Technique: To scale $\frac{6}{10}$ by 3: $\frac{6 \times 3}{10} = \frac{18}{10}$
Check: Verify both fractions have same denominator base: $\frac{18}{30}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying both numerator and denominator by the factor
Don't multiply both 6 and 10 by 3 to get $\frac{18}{30}$ directly! This creates equivalent fractions but doesn't actually increase the fraction's value by the factor. Always multiply only the numerator by the scaling factor to truly increase the fraction's magnitude.

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 3' actually mean?

Increasing by a factor of 3 means making the fraction three times larger. So $\frac{6}{10}$ becomes $\frac{18}{10}$ , which equals the same as $\frac{18}{30}$ when written with equivalent denominators.

Why don't I multiply the denominator by 3 too?

If you multiply both parts by 3, you get an equivalent fraction with the same value! To actually increase the fraction's size, only multiply the numerator. Think of it like having 3 times as many pieces of the same-sized pie.

How do I know which answer choice is correct?

Calculate $6 \times 3 = 18$ for the numerator, keep 10 as denominator. Then look for $\frac{18}{10}$ or its equivalent form $\frac{18}{30}$ in the answer choices.

Is there a difference between the result and the final answer format?

Yes! Your calculation gives $\frac{18}{10}$ , but the answer choices show $\frac{18}{30}$ . These are equivalent fractions - both represent the same value, just written differently.

Can I simplify the final answer?

You could simplify $\frac{18}{30}$ to $\frac{3}{5}$ , but choose the answer that matches exactly what's given in the multiple choice options. The question format determines your final answer format.

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