The table shows the favourite subjects of students in a class. The frequencies for Science, Maths, and English are 2, 7, and 6 respectively. a) We need to find the fraction of students who said maths, in its simplest form. b) We need to work out the central angle of the maths section in a pie chart.

1. Problem Description

The table shows the favourite subjects of students in a class. The frequencies for Science, Maths, and English are 2, 7, and 6 respectively.

a) We need to find the fraction of students who said maths, in its simplest form.

b) We need to work out the central angle of the maths section in a pie chart.

2. Solution Steps

a) Fraction of students who said Maths:

First, we need to find the total number of students.

Total students = Frequency of Science + Frequency of Maths + Frequency of English

Total students = $2 + 7 + 6 = 15$

The number of students who said Maths is

7. So, the fraction of students who said Maths is $\frac{7}{15}$.

The fraction $\frac{7}{15}$ is already in its simplest form because 7 and 15 have no common factors other than

1.

b) Central angle of the maths section:

A pie chart has a total angle of $360^{\circ}$.

The fraction of students who said Maths is $\frac{7}{15}$.

The central angle for Maths is the fraction of students who said Maths multiplied by the total angle of the pie chart.

Central angle = $\frac{7}{15} \times 360^{\circ}$

Central angle = $\frac{7 \times 360}{15}$ degrees

Central angle = $\frac{2520}{15}$ degrees

Central angle = $168^{\circ}$

3. Final Answer

a) $\frac{7}{15}$

b) $168^{\circ}$