Multiply Fraction 3/7 by a Factor of 3: Step-by-Step Solution

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

It means you're making an equivalent fraction where both the numerator and denominator are 3 times larger. The fraction's value stays the same, but it looks different!

Q: Why don't I just multiply 3/7 by 3 to get 9/7?

That would change the fraction's value! When you increase by a factor, you're creating an equivalent fraction, not changing its value. Think of it like having the same pizza cut into smaller pieces.

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

Simplify both fractions to lowest terms. $ \frac{9}{21} $ divides by 3 to give $ \frac{3}{7} $ - they're the same!

Q: What if the question asked for a factor of 2 or 4?

Same process! For factor 2: $ \frac{3 \times 2}{7 \times 2} = \frac{6}{14} $. For factor 4: $ \frac{3 \times 4}{7 \times 4} = \frac{12}{28} $. Always multiply both parts by the factor.

Q: Is there a difference between 'multiply by 3' and 'factor of 3'?

Yes! 'Multiply by 3' means $ \frac{3}{7} \times 3 = \frac{9}{7} $ (changes value). 'Factor of 3' means $ \frac{3 \times 3}{7 \times 3} = \frac{9}{21} $ (equivalent fraction).

Fraction Multiplication with Factor Scaling

Increase the following fraction by a factor of 3:

$\frac{3}{7}=$

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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 three.

00:08 Next, multiply the fraction by the given factor.

00:12 Make sure you multiply both the top and bottom numbers.

00:16 Now, let's calculate these multiplications.

00:20 And that's how we find 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:

$\frac{3}{7}=$

Step-by-step solution

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

Step 1: Identify the original fraction, which is $\frac{3}{7}$ .
Step 2: Multiply both the numerator and denominator by 3 to increase the fraction by a factor of 3.
Step 3: Calculate the new fraction.

Now, let's work through each step:
Step 1: The original fraction is $\frac{3}{7}$ .
Step 2: Multiply the numerator (3) by 3 to get 9, and multiply the denominator (7) by 3 to get 21.
So, the new fraction becomes $\frac{9}{21}$ .

Therefore, the solution to the problem is $\frac{9}{21}$ .

Final Answer

$\frac{9}{21}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: Factor of 3 means $\frac{3}{7} \times \frac{3}{3} = \frac{9}{21}$
Check: Original fraction $\frac{3}{7}$ equals $\frac{9}{21}$ when simplified ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 3 by 3 to get $\frac{9}{7}$ = wrong answer! This changes the fraction's value completely. Always multiply both numerator AND denominator by the same factor to keep the fraction equivalent.

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?

It means you're making an equivalent fraction where both the numerator and denominator are 3 times larger. The fraction's value stays the same, but it looks different!

Why don't I just multiply 3/7 by 3 to get 9/7?

That would change the fraction's value! When you increase by a factor, you're creating an equivalent fraction, not changing its value. Think of it like having the same pizza cut into smaller pieces.

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

Simplify both fractions to lowest terms. $\frac{9}{21}$ divides by 3 to give $\frac{3}{7}$ - they're the same!

What if the question asked for a factor of 2 or 4?

Same process! For factor 2: $\frac{3 \times 2}{7 \times 2} = \frac{6}{14}$ . For factor 4: $\frac{3 \times 4}{7 \times 4} = \frac{12}{28}$ . Always multiply both parts by the factor.

Is there a difference between 'multiply by 3' and 'factor of 3'?

Yes! 'Multiply by 3' means $\frac{3}{7} \times 3 = \frac{9}{7}$ (changes value). 'Factor of 3' means $\frac{3 \times 3}{7 \times 3} = \frac{9}{21}$ (equivalent fraction).

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