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Solve Fraction and Pie Chart Central Angle Problems for Student Subject Preference Data
Mathematics
Grade 6 of Primary School
Question Content
The table shows the favourite subjects of the students in a class: Favourite subject - Science (Frequency 2), Maths (Frequency 7), English (Frequency 6). a) What fraction of the students said maths? Give your answer in its simplest form. b) A pie chart is drawn showing this information. Work out the central angle of the maths section.
Correct Answer
a) 7/15; b) 168°
Detailed Solution Steps
1
Step 1: Calculate the total number of students by adding all frequencies: 2 + 7 + 6 = 15 students.
2
Step 2 (for part a): To find the fraction of students who chose maths, divide the frequency of maths by the total number of students: 7/15. This fraction is already in simplest form as 7 and 15 share no common factors other than 1.
3
Step 3 (for part b): Recall that the total central angle of a pie chart is 360°. Calculate the central angle for maths by multiplying the fraction of students who chose maths by 360°: (7/15) × 360° = 7 × 24° = 168°.
Knowledge Points Involved
1
Fractions in Simplest Form
A fraction is in simplest form when the numerator and denominator have no common positive integer factor other than 1. To simplify, divide both the numerator and denominator by their greatest common divisor. This is used to represent proportions clearly, like the share of students preferring a subject.
2
Frequency and Total Count Calculation
Frequency is the number of times a category appears. To find the total number of items in a data set, sum the frequencies of all categories. This is essential for calculating proportions in statistical data.
3
Pie Chart Central Angles
A pie chart uses a full circle (360°) to represent all data. The central angle for a category is calculated by multiplying the fraction of the total that the category represents by 360°. This converts proportional data into angular measurements for visual representation.
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