Fractions of Shapes
Fractions of shapes is one of the first ways students learn to understand fractions. By dividing shapes into equal parts and shading some of them, you can see what a fraction looks like.
In Class 3, you learn to identify fractions by looking at pictures of circles, rectangles, squares, and triangles that have been divided into equal parts. The shaded part tells you the fraction.
This visual approach makes fractions easier to understand before working with numbers alone.
What is Fractions of Shapes - Class 3 Maths (Fractions (Grade 3))?
A fraction of a shape shows a part of a whole shape that has been divided into equal parts.
Fraction = Shaded Parts ÷ Total Equal Parts
The numerator (top number) = number of shaded parts.
The denominator (bottom number) = total number of equal parts.
Important: The parts MUST be equal in size. If a shape is divided into unequal parts, you cannot write a simple fraction.
Types and Properties
Common Shapes Used for Fractions
1. Circles
A circle can be divided into 2, 3, 4, 6, or 8 equal parts. Each part is called a sector.
- Circle divided into 2 parts → each part = 1/2
- Circle divided into 4 parts → each part = 1/4
2. Rectangles
Rectangles can be divided using vertical lines, horizontal lines, or both.
- Rectangle divided into 3 equal columns → each column = 1/3
3. Squares
Squares can be divided by lines through the middle or diagonals.
- Square divided into 4 equal parts by two lines → each part = 1/4
4. Triangles
Triangles can be divided into smaller equal triangles or into equal strips.
Solved Examples
Example 1: Example 1: Reading a Fraction from a Circle
Question: A circle is divided into 4 equal parts. 1 part is shaded. What fraction is shaded?
Think:
- Total equal parts = 4
- Shaded parts = 1
- Fraction = 1/4
Answer: 1/4 (one-quarter) is shaded.
Example 2: Example 2: Shading a Rectangle
Question: A rectangle is divided into 6 equal parts. 2 parts are shaded. What fraction is shaded?
Think:
- Total equal parts = 6
- Shaded parts = 2
- Fraction = 2/6
Answer: 2/6 of the rectangle is shaded.
Example 3: Example 3: Unshaded Fraction
Question: A square is divided into 8 equal parts. 5 parts are shaded. What fraction is NOT shaded?
Think:
- Total parts = 8
- Shaded = 5, so not shaded = 8 − 5 = 3
- Fraction not shaded = 3/8
Answer: 3/8 of the square is not shaded.
Example 4: Example 4: Half of a Shape
Question: Aditi folds a piece of paper in half and colours one side. What fraction is coloured?
Think:
- Folding in half creates 2 equal parts
- She colours 1 part
- Fraction = 1/2
Answer: 1/2 (one-half) of the paper is coloured.
Example 5: Example 5: Identifying Equal Parts
Question: A rectangle is divided into 4 parts, but 2 parts are big and 2 parts are small. Can we write a fraction for one small part?
Think:
- The parts are NOT equal in size
- Fractions need equal parts
- We cannot write a simple fraction
Answer: No, we cannot write a fraction because the parts are not equal.
Example 6: Example 6: Fraction of a Triangle
Question: A triangle is divided into 3 equal parts. 2 parts are coloured. What fraction is coloured?
Think:
- Total equal parts = 3
- Coloured parts = 2
- Fraction = 2/3
Answer: 2/3 of the triangle is coloured.
Example 7: Example 7: Word Problem – Pizza Slices
Question: Dev cuts a pizza into 8 equal slices. He eats 3 slices. What fraction of the pizza did he eat?
Think:
- Total slices = 8
- Slices eaten = 3
- Fraction = 3/8
Answer: Dev ate 3/8 of the pizza.
Example 8: Example 8: Shade to Match a Fraction
Question: A circle is divided into 6 equal parts. Shade 4/6 of the circle. How many parts do you shade?
Think:
- The fraction says 4/6
- The numerator is 4
- Shade 4 out of 6 parts
Answer: Shade 4 parts out of 6.
Example 9: Example 9: Whole as a Fraction
Question: A square is divided into 5 equal parts. All 5 parts are shaded. What fraction is shaded?
Think:
- Total parts = 5, Shaded = 5
- Fraction = 5/5 = 1 whole
Answer: 5/5 = 1 (the whole square is shaded).
Example 10: Example 10: Comparing Fractions Using Shapes
Question: Two identical circles are divided into 4 equal parts each. Circle A has 1 part shaded. Circle B has 3 parts shaded. Which has more shaded area?
Think:
- Circle A = 1/4 shaded
- Circle B = 3/4 shaded
- 3/4 > 1/4
Answer: Circle B has more shaded area.
Real-World Applications
Where Do We Use Fractions of Shapes?
- Sharing food: Cutting a cake, pizza, or chapati into equal slices.
- Colouring and art: Colouring a fraction of a design or pattern.
- Maps and diagrams: Showing what fraction of an area is covered.
- Building understanding: Seeing fractions as shapes helps before working with fraction numbers.
Key Points to Remember
- A fraction of a shape = shaded parts / total equal parts.
- The parts MUST be equal in size to write a fraction.
- The numerator = shaded parts; the denominator = total parts.
- If all parts are shaded, the fraction equals 1 (one whole).
- If no parts are shaded, the fraction equals 0.
- The unshaded fraction = 1 − shaded fraction (e.g., if 3/8 is shaded, 5/8 is not shaded).
- Circles, rectangles, squares, and triangles can all be used to show fractions.
Practice Problems
- A circle is divided into 3 equal parts. 2 parts are shaded. What fraction is shaded?
- A rectangle has 8 equal parts. 5 parts are coloured. What fraction is coloured?
- A square is divided into 4 equal parts. 1 part is shaded. What fraction is NOT shaded?
- Ria cuts a ribbon into 5 equal pieces. She uses 2 pieces. What fraction did she use?
- Draw a rectangle divided into 6 equal parts and shade 3/6.
- A triangle has 4 equal parts. All 4 are shaded. Write the fraction.
- Arjun colours 7 out of 10 equal strips. What fraction is coloured? What fraction is not coloured?
Frequently Asked Questions
Q1. What is a fraction of a shape?
A fraction of a shape shows a part of a whole shape that has been divided into equal parts. The shaded (or coloured) parts over the total equal parts gives the fraction.
Q2. Why must the parts be equal?
Fractions represent fair or equal division. If the parts are unequal, each part represents a different amount, and you cannot write a simple fraction like 1/4 or 2/3.
Q3. How do I find the fraction of a shaded shape?
Count the total number of equal parts (this is the denominator). Count the shaded parts (this is the numerator). Write the fraction as numerator/denominator.
Q4. What if no parts are shaded?
If no parts are shaded, the fraction is 0. For example, 0 out of 4 equal parts = 0/4 = 0.
Q5. What if all parts are shaded?
If all parts are shaded, the fraction equals 1 (one whole). For example, 6 out of 6 parts = 6/6 = 1.
Q6. Can different shapes show the same fraction?
Yes. A circle divided into 4 parts with 1 shaded, and a rectangle divided into 4 parts with 1 shaded, both show 1/4. The shape does not matter — the fraction is the same.
Q7. How do I find the fraction that is NOT shaded?
Subtract the shaded parts from the total parts. If 3 out of 8 parts are shaded, the unshaded fraction is (8 − 3)/8 = 5/8.
Q8. What shapes are best for showing fractions?
Circles and rectangles are most common because they are easy to divide into equal parts. Squares and triangles are also used.
Q9. Is 2/4 the same as 1/2 when shown on shapes?
Yes. If a shape has 4 equal parts and 2 are shaded, it shows 2/4 which equals 1/2. Both fractions cover the same amount of area.
Related Topics
- Introduction to Fractions
- Numerator and Denominator
- Fractions of a Collection
- Comparing Fractions (Grade 3)
- Equivalent Fractions (Grade 3)
- Unit Fractions
- Fractions on a Number Line
- Half, Quarter and Three-Quarter
- Adding Like Fractions (Grade 3)
- Subtracting Like Fractions (Grade 3)
- Fraction Word Problems (Grade 3)
