Enlarge Fraction 2/15 by Factor of 3: Step-by-Step Solution

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

Enlarging a fraction means creating an equivalent fraction with bigger numbers. The value stays the same, but both the numerator and denominator get multiplied by the given factor.

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

Use cross-multiplication! For $ \frac{2}{15} = \frac{6}{45} $, check if 2 × 45 = 15 × 6. Both equal 90, so they're equivalent!

Q: Is there a difference between enlarging and simplifying fractions?

Yes! Enlarging makes the numbers bigger while keeping the same value. Simplifying makes them smaller. Both create equivalent fractions but go in opposite directions.

Fraction Enlargement with Scale Factors

Enlarge the following fraction by the factor 3:

$\frac{2}{15}=$

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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

00:03 Multiply the fraction by the given factor

00:06 Make sure to multiply both numerator and denominator

00:09 Calculate the multiplications

00:13 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

Enlarge the following fraction by the factor 3:

$\frac{2}{15}=$

Step-by-step solution

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

Step 1: Identify the given fraction $\frac{2}{15}$ .
Step 2: Multiply both the numerator and the denominator by the factor 3.
Step 3: Write the new fraction.

Now, let's work through each step:

Step 1: The given fraction is $\frac{2}{15}$ .

Step 2: We need to enlarge this fraction by a factor of 3.
Multiply the numerator: $2 \times 3 = 6$ .
Multiply the denominator: $15 \times 3 = 45$ .

Step 3: The enlarged fraction is $\frac{6}{45}$ .

Therefore, the solution to the problem is $\frac{6}{45}$ .

Final Answer

$\frac{6}{45}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: For factor 3: $\frac{2}{15}$ becomes $\frac{2 \times 3}{15 \times 3} = \frac{6}{45}$
Check: Verify equivalent fractions: $\frac{2}{15} = \frac{6}{45}$ by cross-multiplication ✓

Common Mistakes

Avoid these frequent errors

Only multiplying the numerator by the scale factor
Don't multiply just 2 by 3 to get 6/15! This changes the fraction's value completely. Enlarging means the fraction stays equivalent but with bigger numbers. Always multiply both numerator AND denominator by the same 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' actually mean?

Enlarging a fraction means creating an equivalent fraction with bigger numbers. The value stays the same, but both the numerator and denominator get multiplied by the given factor.

Why multiply both parts instead of just the numerator?

If you only multiply the numerator, you change the fraction's value! For example, $\frac{6}{15}$ is NOT equal to $\frac{2}{15}$ . Multiplying both parts keeps the fractions equivalent.

How can I check if my enlarged fraction is correct?

Use cross-multiplication! For $\frac{2}{15} = \frac{6}{45}$ , check if 2 × 45 = 15 × 6. Both equal 90, so they're equivalent!

Is there a difference between enlarging and simplifying fractions?

Yes! Enlarging makes the numbers bigger while keeping the same value. Simplifying makes them smaller. Both create equivalent fractions but go in opposite directions.

What if the factor is a fraction instead of a whole number?

The same rule applies! Multiply both numerator and denominator by the fractional factor. Just remember to simplify your final answer if possible.

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