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Smart Charts - Pie Charts

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A Pie Chart, also known as a Chapati Chart, is a circular graph used to compare parts of a whole. Each 'slice' of the pie represents a category, and the size of the slice shows its proportion relative to the total.

A pie chart divided into three sections: two quarters and one half.
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The entire circle represents the 'Whole' or the total value. For example, if we are charting a class of 6060 students, the full circle equals 6060 students.

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The size of each slice is proportional to the fraction it represents. A slice that takes up half the circle represents 12\frac{1}{2} of the total, while a quarter-slice represents 14\frac{1}{4}.

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To find the actual number represented by a slice, multiply the fraction of the slice by the total number. For example, 14\frac{1}{4} of 100100 is 14×100=25\frac{1}{4} \times 100 = 25.

📐Formulae

Value of a slice=Fraction of the slice×Total Value\text{Value of a slice} = \text{Fraction of the slice} \times \text{Total Value}

Fraction of a slice=Value of the sliceTotal Value\text{Fraction of a slice} = \frac{\text{Value of the slice}}{\text{Total Value}}

Total Value=Sum of all slice values\text{Total Value} = \text{Sum of all slice values}

Sum of all fractions in a pie chart=1\text{Sum of all fractions in a pie chart} = 1

💡Examples

Problem 1:

A class of 4040 students was asked about their favorite fruit. The Pie Chart shows that 12\frac{1}{2} of the students like Mangoes, 14\frac{1}{4} like Apples, and 14\frac{1}{4} like Bananas. Calculate the number of students for each fruit.

Solution:

  1. Total students = 4040.
  2. Students who like Mangoes = 12×40=20\frac{1}{2} \times 40 = 20 students.
  3. Students who like Apples = 14×40=10\frac{1}{4} \times 40 = 10 students.
  4. Students who like Bananas = 14×40=10\frac{1}{4} \times 40 = 10 students. \nCheck: 20+10+10=4020 + 10 + 10 = 40.

Explanation:

To find the number of students, multiply the total count by the fraction represented by each slice of the pie chart.

Problem 2:

In a library of 200200 books, a Pie Chart shows that Science books occupy 15\frac{1}{5} of the chart. How many Science books are there in the library?

Solution:

  1. Total number of books = 200200.
  2. Fraction of Science books = 15\frac{1}{5}.
  3. Number of Science books = 15×200\frac{1}{5} \times 200.
  4. Calculation: 200÷5=40200 \div 5 = 40. \nSo, there are 4040 Science books.

Explanation:

Divide the total value by the denominator of the fraction to find the value represented by that specific part of the pie chart.

Problem 3:

A survey was conducted among 8080 children about their favorite season. The pie chart shows that 12\frac{1}{2} of the children like Summer, 14\frac{1}{4} like Winter, and the remaining 14\frac{1}{4} like Rainy season. Find the number of children who like the Rainy season.

Pie chart showing Summer as half, Winter as one quarter, and Rainy as one quarter.

Solution:

Total children=80\text{Total children} = 80 Fraction who like Rainy season=14\text{Fraction who like Rainy season} = \frac{1}{4} Number of children=14×80=20\text{Number of children} = \frac{1}{4} \times 80 = 20

Explanation:

Since the Rainy season slice is exactly one-quarter of the total circle, we divide the total number of children (8080) by 44 to find the value for that specific slice.

Problem 4:

A farmer uses his 120120 acres of land to grow different crops. Based on the chart, 13\frac{1}{3} of the land is used for Wheat, and the rest is used for Rice. How many acres are used for Rice?

Pie chart divided into two segments representing 1/3 Wheat and 2/3 Rice.

Solution:

Total land=120 acres\text{Total land} = 120 \text{ acres} Fraction for Wheat=13\text{Fraction for Wheat} = \frac{1}{3} Fraction for Rice=1−13=23\text{Fraction for Rice} = 1 - \frac{1}{3} = \frac{2}{3} Acres for Rice=23×120=2×40=80 acres\text{Acres for Rice} = \frac{2}{3} \times 120 = 2 \times 40 = 80 \text{ acres}

Explanation:

If 13\frac{1}{3} of the circle is Wheat, then the remaining 23\frac{2}{3} must be Rice because the sum of all parts equals 11. We then calculate 23\frac{2}{3} of the total 120120 acres.