To determine which multiplication expression is equal to [tex]\(\frac{3}{4} \div \frac{1}{3}\)[/tex], let's follow the steps for dividing fractions and converting it into a multiplication problem.
When we divide by a fraction, we multiply by its reciprocal. So, let's determine the reciprocal of [tex]\(\frac{1}{3}\)[/tex], which is [tex]\(\frac{3}{1}\)[/tex].
Now, rewrite the expression [tex]\(\frac{3}{4} \div \frac{1}{3}\)[/tex] as:
[tex]\[
\frac{3}{4} \times \frac{3}{1}
\][/tex]
Next, we need to compare this multiplication to the given options.
- Option A: [tex]\(\frac{4}{3} \times \frac{1}{3}\)[/tex]
\[\frac{4}{3}\) is not equal to [tex]\(\frac{3}{4}\)[/tex], so this option is incorrect.
- Option B: [tex]\(\frac{3}{4} \times \frac{3}{1}\)[/tex]
This matches our derived multiplication expression perfectly, so this option is correct.
- Option C: [tex]\(\frac{4}{3} \times \frac{3}{1}\)[/tex]
[tex]\(\frac{4}{3}\)[/tex] is not equal to [tex]\(\frac{3}{4}\)[/tex], so this option is incorrect.
- Option D: [tex]\(\frac{3}{4} \times \frac{1}{3}\)[/tex]
This does not match [tex]\(\frac{3}{4} \times \frac{3}{1}\)[/tex], so this option is incorrect.
Therefore, the correct multiplication expression that is equal to [tex]\(\frac{3}{4} \div \frac{1}{3}\)[/tex] is:
Option B: [tex]\(\frac{3}{4} \times \frac{3}{1}\)[/tex].
