Multiply Fraction 1/3 by Scale Factor 4: Fraction Enlargement

Q: What does 'enlarge by a factor' mean for fractions?

Enlarging by a factor means creating an equivalent fraction with bigger numbers. You multiply both the numerator and denominator by the same number, so $ \frac{1}{3} $ enlarged by factor 4 becomes $ \frac{4}{12} $.

Q: Why don't we just multiply the whole fraction by 4?

Multiplying the whole fraction by 4 would give you $ 4 \times \frac{1}{3} = \frac{4}{3} $, which is a different value! Enlarging means keeping the same value but using bigger equivalent numbers.

Q: Are there other ways to enlarge the same fraction?

Yes! You could multiply by any factor: $ \frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{5}{15} $. The question specifically asks for factor 4, so $ \frac{4}{12} $ is the answer.

Q: What if the enlarged fraction can be simplified?

Even if $ \frac{4}{12} $ simplifies to $ \frac{1}{3} $, keep the enlarged form as your answer since that's what the question asks for!

Fraction Scaling with Equivalent Forms

Enlarge the following fraction by the factor 4:

$\frac{1}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 4

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 4:

$\frac{1}{3}=$

Step-by-step solution

To solve the problem of enlarging the fraction $\frac{1}{3}$ by a factor of 4, we will follow these steps:

Step 1: Identify the given fraction and enlargement factor. The fraction is $\frac{1}{3}$ and the factor is 4.
Step 2: Multiply both the numerator and denominator of the fraction by the enlargement factor. This means we calculate:

$\frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Step 3: Check if the fraction can be simplified. Here, $\frac{4}{12}$ can be simplified to $\frac{1}{3}$ , but since we aim to express it in an "enlarged" form, $\frac{4}{12}$ is a correct representation when enlarged by the given factor.

Step 4: Verify against answer choices if applicable. In our list of choices, $\frac{4}{12}$ is listed as choice 3, which matches our calculated answer.

Therefore, the solution to the problem is $\frac{4}{12}$ .

Final Answer

$\frac{4}{12}$

Key Points to Remember

Essential concepts to master this topic

Scaling Rule: Multiply both numerator and denominator by same factor
Technique: $\frac{1}{3} \times \frac{4}{4} = \frac{4}{12}$ preserves fraction value
Check: Verify $\frac{4}{12} = \frac{1}{3}$ by dividing 4÷4 and 12÷4 ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the scale factor
Don't multiply just 1 by 4 to get $\frac{4}{3}$ = wrong value! This changes the fraction's actual value instead of creating an equivalent form. Always multiply both numerator AND denominator by the same scale 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 'enlarge by a factor' mean for fractions?

Enlarging by a factor means creating an equivalent fraction with bigger numbers. You multiply both the numerator and denominator by the same number, so $\frac{1}{3}$ enlarged by factor 4 becomes $\frac{4}{12}$ .

Why don't we just multiply the whole fraction by 4?

Multiplying the whole fraction by 4 would give you $4 \times \frac{1}{3} = \frac{4}{3}$ , which is a different value! Enlarging means keeping the same value but using bigger equivalent numbers.

How can I tell if my enlarged fraction is correct?

Simplify your answer back to lowest terms. If it equals the original fraction, you're correct! For example: $\frac{4}{12} \div \frac{4}{4} = \frac{1}{3}$ ✓

Are there other ways to enlarge the same fraction?

Yes! You could multiply by any factor: $\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{5}{15}$ . The question specifically asks for factor 4, so $\frac{4}{12}$ is the answer.

What if the enlarged fraction can be simplified?

Even if $\frac{4}{12}$ simplifies to $\frac{1}{3}$ , keep the enlarged form as your answer since that's what the question asks for!

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