Question

which expression is equivalent to \\(\frac{18}{37}\\)?
\\(\bigcirc\\) a. \\(37 \div \frac{1}{18}\\)
\\(\bigcirc\\) b. \\(37 \div 18\\)
\\(\bigcirc\\) c. \\(18 \div 37\\)
\\(\bigcirc\\) d. \\(18 \div \frac{1}{37}\\)

Explanation:

Step1: Recall fraction - division relationship

A fraction $\frac{a}{b}$ (where $b
eq0$) is equivalent to $a\div b$. This is because the fraction bar can be interpreted as a division symbol, where the numerator is the dividend and the denominator is the divisor.

Step2: Apply the relationship to $\frac{18}{37}$

For the fraction $\frac{18}{37}$, the numerator $a = 18$ and the denominator $b=37$. Using the relationship $\frac{a}{b}=a\div b$, we substitute $a = 18$ and $b = 37$. So, $\frac{18}{37}$ is equivalent to $18\div37$.

Let's also check the other options to be sure:

• Option A: $37\div\frac{1}{18}=37\times18$, which is not equal to $\frac{18}{37}$.
• Option B: $37\div18=\frac{37}{18}$, which is the reciprocal of $\frac{18}{37}$, not equal.
• Option D: $18\div\frac{1}{37}=18\times37$, which is not equal to $\frac{18}{37}$.

Answer:

C. $18\div37$