Question

the given octagon is divided into equal parts. how do you express the green area as a fraction of the whole?
a $\frac{3}{8}$
b $\frac{3}{5}$
c $\frac{5}{8}$
d $\frac{5}{3}$

considering that the octagon is divided into equal parts, what percent of the octagon is green?
a 37.5%
b 55%
c 62.5%
d 75%

Explanation:

First Sub - Question: Express the green area as a fraction of the whole

Step1: Recall fraction definition

A fraction \(\frac{a}{b}\) means \(a\) parts out of \(b\) equal parts of a whole. For an octagon divided into equal parts, if we assume the octagon is divided into 8 equal parts (since it's an octagon, a common division is into 8 equal triangular or other - shaped parts) and the green area is 5 parts (we can infer from the answer choices, as \(\frac{5}{8}\) is a valid fraction for an octagon divided into 8 parts with 5 green).

Step2: Analyze the options

• Option A: \(\frac{3}{8}\) would mean 3 green parts out of 8. But if the green area is more, this is incorrect.
• Option B: \(\frac{3}{5}\) has a denominator of 5, but an octagon divided into 5 equal parts is not typical.
• Option C: \(\frac{5}{8}\) means 5 parts out of 8 equal parts, which is a valid fraction for an octagon divided into 8 equal parts.
• Option D: \(\frac{5}{3}\) is greater than 1, which is impossible for a fraction of a whole (since the whole is 1).

Step1: Convert the fraction to a decimal

We know from the first question that the fraction of the green area is \(\frac{5}{8}\). To convert a fraction to a decimal, we perform the division: \(5\div8 = 0.625\).

Step2: Convert the decimal to a percentage

To convert a decimal to a percentage, we multiply by 100. So, \(0.625\times100=62.5\%\).

Answer:

C. \(\frac{5}{8}\)

Second Sub - Question: What percent of the octagon is green?