Question

you be the teacher you have blue ribbon and red ribbon in the ratio $\frac{1}{2} : \frac{1}{5}$. your friend finds the value of the ratio. the value of the ratio is $\frac{1}{2} div \frac{1}{5} = \frac{1}{10}$. is your friend correct? yes no explain your reasoning.

Explanation:

Step1: Recall ratio division rule

To find the value of a ratio \( \frac{a}{b} : \frac{c}{d} \), we divide \( \frac{a}{b} \) by \( \frac{c}{d} \), which is \( \frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\times\frac{d}{c} \).

Step2: Apply the rule to the given ratio

The given ratio is \( \frac{1}{2} : \frac{1}{5} \). So we calculate \( \frac{1}{2} \div \frac{1}{5} \). Using the division of fractions rule (multiply by reciprocal), we get \( \frac{1}{2}\times\frac{5}{1}=\frac{5}{2} \), not \( \frac{1}{10} \).

Answer:

No. The correct value of \( \frac{1}{2} : \frac{1}{5} \) is \( \frac{1}{2}\div\frac{1}{5}=\frac{1}{2}\times5 = \frac{5}{2} \), so the friend is incorrect.