Reading pie charts: fractions, percents and degrees
Discover Mathematics P5: Term 2, Unit 12, Lessons 1–3
GoalLink the fraction, the percent and the angle of a sector, and read data from a pie chart.
New words
percent · a fraction with denominator 100: 25% = 25/100 = 1/4degree · a unit for measuring angles; a full circle is 360°angle of a sector · the angle at the centre of the circle between the two radii
Explanation
The whole circle is 1 whole, 100%, and 360°. So a sector that is half of the circle is 1/2 = 50% = 180°. A quarter is 1/4 = 25% = 90°. One fifth is 1/5 = 20% = 72°, and one tenth is 1/10 = 10% = 36°. To change a fraction into degrees, take that fraction of 360: 1/5 of 360 = 72°. To change a percent into a count, take that percent of the total: 30% of 200 children = 30/100 × 200 = 60 children. To change the angle of a sector into a fraction, divide by 360: 90° is 90/360 = 1/4. All the percents of a pie chart add up to 100%, and all the angles add up to 360°.
Fraction
Percent
Angle
1/2
50%
180°
1/4
25%
90°
3/4
75%
270°
1/5
20%
72°
1/10
10%
36°
1/20
5%
18°
Worked examples
20 students come to school by walking (10), bus (5), bicycle (4) or car (1). Walking: 10/20 = 1/2 = 50% = 180°. Bus: 5/20 = 1/4 = 25% = 90°. Bicycle: 4/20 = 1/5 = 20% = 72°. Car: 1/20 = 5% = 18°. The percents add up to 50 + 25 + 20 + 5 = 100 and the angles to 180 + 90 + 72 + 18 = 360.
200 children were asked. 30% chose reading. 30% of 200 = 30/100 × 200 = 60 children.
A sector has an angle of 90° in a survey of 80 people. 90/360 = 1/4 = 25%. So 1/4 of 80 = 20 people.
Class activity
Percent partners. Make cards with fractions (1/2, 1/4, 1/5, 1/10, 3/4), percents (50%, 25%, 20%, 10%, 75%) and angles (180°, 90°, 72°, 36°, 270°). Mix them and match each fraction with its percent and angle. Then take a paper circle, fold it into halves and quarters, and check the angles 180° and 90° with a protractor.
Practice
1
A sector has an angle of 54°. What fraction and what percent of the circle is it?
54/360 = 3/20 = 15/100 = 15%.
2
A sector has an angle of 36° in a survey of 200 people. How many people does it show?
36/360 = 1/10 = 10%. 10% of 200 = 20 people.
3
What angle is a sector of 25%?
25% = 1/4 and 1/4 of 360° = 90°.
4
40 children chose a favourite subject: maths 50%, science 25%, art 25%. How many chose each?
Maths: 1/2 of 40 = 20. Science: 1/4 of 40 = 10. Art: 1/4 of 40 = 10. 20 + 10 + 10 = 40.
5
50 people were asked about their favourite season. The chart shows the percents. How many people chose the 30% sector?
