Question

which fractions correctly describe the white part of the shape? select all that apply a \\(\frac{4}{10}\\) b \\(\frac{4}{12}\\) c \\(\frac{1}{3}\\) d \\(\frac{8}{12}\\)

Explanation:

Step1: Count total and white parts

The hexagon is divided into 12 equal - sized triangular parts (total parts \(n = 12\)). By looking at the figure, the number of white triangular parts \(w=4\).

Step2: Analyze option a

For option a, the fraction is \(\frac{4}{10}\). But we know the total number of parts is 12, not 10. So \(\frac{4}{10}\) does not represent the white part.

Step3: Analyze option b

The fraction for option b is \(\frac{4}{12}\). Since the number of white parts is 4 and total parts is 12, \(\frac{4}{12}\) can be simplified. \(\frac{4\div4}{12\div4}=\frac{1}{3}\), and \(\frac{4}{12}\) is a valid representation of the white part.

Step4: Analyze option c

Simplify \(\frac{4}{12}\) (from option b) by dividing numerator and denominator by 4, we get \(\frac{1}{3}\). So \(\frac{1}{3}\) is also a valid representation of the white part.

Step5: Analyze option d

The fraction for option d is \(\frac{8}{12}\). The number of white parts is 4, not 8, so \(\frac{8}{12}\) does not represent the white part.

Answer:

b. \(\frac{4}{12}\), c. \(\frac{1}{3}\)