Multiply Fraction 10/12 by a Factor of 2: Step-by-Step Solution

Q: What does 'increase by a factor of 2' actually mean?

It means to scale the fraction by multiplying both the numerator and denominator by 2. This creates an equivalent fraction with the same value but larger numbers.

Q: Why do I multiply both top AND bottom by 2?

Because $ \frac{2}{2} = 1 $, so you're really multiplying by 1! This keeps the fraction's value the same: $ \frac{10}{12} \times \frac{2}{2} = \frac{10}{12} \times 1 = \frac{10}{12} $

Q: How is this different from just multiplying the fraction by 2?

Very different! Multiplying $ \frac{10}{12} \times 2 = \frac{20}{12} $ actually doubles the value. Scaling by factor 2 means $ \frac{10 \times 2}{12 \times 2} = \frac{20}{24} $ keeps the same value.

Q: Can I simplify the answer further?

Yes! $ \frac{20}{24} $ can be simplified by dividing both by 4 to get $ \frac{5}{6} $. However, the question asks for the scaled version, so $ \frac{20}{24} $ is correct.

Q: How do I check if my scaling is correct?

Convert both fractions to decimals! $ \frac{10}{12} = 0.833... $ and $ \frac{20}{24} = 0.833... $ If they match, your scaling is perfect!

Fraction Scaling with Factor Multiplication

Increase the following fraction by a factor of 2:

$\frac{10}{12}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's begin by expanding the fraction by multiplying it by 2.

00:10 Next, we'll multiply both the top and bottom of the fraction by this number.

00:16 Remember, every part of the fraction gets multiplied, even the denominator.

00:21 Now, calculate the result of these multiplications.

00:25 And there you have it! That's how we solve this problem.

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 2:

$\frac{10}{12}=$

Step-by-step solution

To solve this problem, we need to increase the fraction $\frac{10}{12}$ by a factor of 2. This can be accomplished by multiplying both the numerator and the denominator by 2, to maintain the value relationship while doubling the fraction.

Let's go through the solution step-by-step:

Step 1: Identify the original fraction, which is $\frac{10}{12}$ .
Step 2: Multiply the numerator by 2. This results in $10 \times 2 = 20$ .
Step 3: Multiply the denominator by 2. This results in $12 \times 2 = 24$ .
Step 4: Construct the new fraction $\frac{20}{24}$ .

The fraction $\frac{20}{24}$ is the result of increasing the original fraction by a factor of 2. In this case, this number is confirmed to be the correct answer.

Therefore, the solution to the problem is $\frac{20}{24}$ .

Final Answer

$\frac{20}{24}$

Key Points to Remember

Essential concepts to master this topic

Factor Rule: Multiply both numerator and denominator by same factor
Technique: For factor 2: $\frac{10}{12} \times \frac{2}{2} = \frac{20}{24}$
Check: Verify both fractions have same decimal value: 10/12 = 20/24 ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 10 by 2 to get 20/12 = wrong fraction! This changes the fraction's actual value instead of just scaling it. 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 'increase by a factor of 2' actually mean?

It means to scale the fraction by multiplying both the numerator and denominator by 2. This creates an equivalent fraction with the same value but larger numbers.

Why do I multiply both top AND bottom by 2?

Because $\frac{2}{2} = 1$ , so you're really multiplying by 1! This keeps the fraction's value the same: $\frac{10}{12} \times \frac{2}{2} = \frac{10}{12} \times 1 = \frac{10}{12}$

How is this different from just multiplying the fraction by 2?

Very different! Multiplying $\frac{10}{12} \times 2 = \frac{20}{12}$ actually doubles the value. Scaling by factor 2 means $\frac{10 \times 2}{12 \times 2} = \frac{20}{24}$ keeps the same value.

Can I simplify the answer further?

Yes! $\frac{20}{24}$ can be simplified by dividing both by 4 to get $\frac{5}{6}$ . However, the question asks for the scaled version, so $\frac{20}{24}$ is correct.

How do I check if my scaling is correct?

Convert both fractions to decimals! $\frac{10}{12} = 0.833...$ and $\frac{20}{24} = 0.833...$ If they match, your scaling is perfect!

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