CBSE Class 4 Mathematics NCERT Solutions: Unit 9 Halves and Quarters

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NCERT Solutions PDF Class 4 PDF

CBSE Class 4 Mathematics Unit-9 Halves and Quarters introduces students to the foundational concepts of fractions. This unit explores how to divide whole objects and shapes into equal parts, specifically focusing on halves (two equal parts) and quarters (four equal parts). Through practical examples like dividing chapatis, chocolates, and paper, students will visually understand the meaning of these fractions. The NCERT Solutions offer clear, step-by-step guidance to help children identify, create, and represent halves and quarters. These exercises encourage critical thinking about spatial reasoning and build a solid base for more complex fraction concepts in the future. The aim is to make learning about halves and quarters engaging and accessible, ensuring students grasp these essential mathematical ideas effectively.

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Quick info

BoardCBSE
ClassClass 4
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterUnit-9 Halves And Quarters

Chapter summary

Unit 9, 'Halves and Quarters,' for Class 4 Mathematics NCERT Solutions, introduces students to the basic principles of dividing whole objects into two or four equal parts. It covers practical examples like dividing food items and paper shapes. The solutions explain how to visually represent and create halves and quarters, and explore various methods for dividing rectangles into equal portions, reinforcing the understanding of fractions through hands-on activities and clear illustrations.

Learning outcomes

  • Understand the concept of dividing a whole into two equal halves.
  • Learn to divide a whole into four equal quarters.
  • Visually identify and represent halves and quarters of different shapes.
  • Explore multiple ways to divide a rectangle into halves and quarters.
  • Apply the concept of equal division to practical scenarios.

Topics covered

Paper topics

  • Understanding Halves
  • Understanding Quarters
  • Dividing Objects Equally
  • Fractions as Equal Parts
  • Shapes and Division
  • Rectangles into Halves
  • Rectangles into Quarters
  • Visualizing Fractions

Important topics

  • Concept of Halves
  • Concept of Quarters
  • Equal Division of Objects
  • Dividing Rectangles
  • Visual Representation of Fractions

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Questions and Solutions

Half-Half

1. If the cats ask you to divide the chapati equally, how will you divide it?
Solution: To divide the chapati equally for the cats, I would first imagine the chapati as a circle. Then, I would carefully fold it exactly in the middle, bringing one edge to meet the other. This fold creates a crease line down the center. By tearing the chapati along this crease line, I will get two perfectly equal halves.

Half of Half

2. If two more cats come for food, how will you divide one chapati equally for four cats?
Solution: To divide one chapati equally among four cats, I will first divide it into two equal halves, just like before. Then, I will take each of these halves and fold it again exactly in the middle. This second fold will divide each half into two smaller equal parts. When I tear the chapati along all the crease lines, I will have four equal pieces, which are called quarters.

Half of Many Pieces

1. Circle the portion that Reena got.
Solution: Rani divided her chocolate bar equally and gave half to her friend Reena. If the chocolate bar is shown divided into 6 equal pieces, then half of the chocolate bar would be 3 pieces (since 6 divided by 2 equals 3). Therefore, you should circle 3 of the 6 pieces to show the portion Reena received.
2. How many pieces of chocolate are there?
Solution: By observing the chocolate bar in the image, we can count the total number of small, equal pieces it is divided into. There are six distinct pieces of chocolate shown.
3. How many pieces were left with Rani?
Solution: Rani started with a chocolate bar that had 6 pieces. She gave half of it to her friend Reena. Half of 6 pieces is 3 pieces (6 ÷ 2 = 3). So, Rani gave 3 pieces to Reena. The number of pieces left with Rani is the total pieces minus the pieces given away: 6 - 3 = 3 pieces.

Many Shapes from a Half Sheet

1. Draw different shapes using these triangles. One such shape is shown here.
Solution: Take a rectangular piece of paper and fold it in half to create a crease. Cut along this crease to get two identical triangles. Each triangle represents half of the original sheet. You can then arrange these two triangles in different ways to form new shapes. For example, placing them side-by-side along their longest edge will recreate the original rectangle. You can also place them with their right-angle corners touching to form a larger triangle or a diamond shape.

Many Ways to Cut into Half

1. In how many different ways can you cut a rectangle into half? Draw 5 different ways. Can you check if they are equal?
Solution: A rectangle can be cut into two equal halves in many ways. The key is that the cut must divide the rectangle into two parts of exactly the same size and shape. Five different ways include:
  1. Cutting horizontally across the middle.
  2. Cutting vertically down the middle.
  3. Cutting diagonally from one corner to the opposite corner.
  4. Cutting with a zig-zag line exactly in the middle.
  5. Cutting with a curved line that divides the rectangle symmetrically.
To check if they are equal, you can try to place one half exactly on top of the other. If they perfectly overlap, the division is equal.
2. In how many different ways can you cut a rectangle into four equal parts? Draw five different ways. Can you check if they are equal?
Solution: A rectangle can be divided into four equal parts in several ways. The crucial aspect is that all four parts must be identical in size and shape. Here are five ways:
  1. Divide the rectangle into two equal halves with a horizontal line, and then divide each half again with a vertical line.
  2. Divide the rectangle into two equal halves with a vertical line, and then divide each half again with a horizontal line.
  3. Draw two vertical lines to divide the rectangle into three equal parts, and then draw one horizontal line through the middle. (This needs careful adjustment to ensure 4 equal parts). A simpler way is to draw two parallel vertical lines and one parallel horizontal line, creating a grid of 9 smaller rectangles, and then select 4 that form an equal division. The most straightforward is dividing into 4 equal columns or 4 equal rows.
  4. Divide the rectangle into four equal columns using three vertical lines.
  5. Divide the rectangle into four equal rows using three horizontal lines.
  6. Divide the rectangle into four equal parts by drawing two lines that intersect at the center, one horizontal and one vertical.
To verify equality, you can attempt to superimpose the four parts onto each other. If they match perfectly, the division is correct.

Common mistakes

  • Confusing halves with unequal parts.
  • Difficulty in visualizing quarters of different shapes.
  • Not understanding that halves and quarters must be equal in size.
  • Struggling to draw different ways to divide a shape equally.

Revision tips

  • Practice drawing different ways to divide shapes into halves and quarters.
  • Use real-life objects like chapatis or paper to demonstrate equal division.
  • Focus on understanding that each part must be exactly the same size.
  • Review the visual examples provided in the solutions for clarity.

Practice MCQs

Q1. If a chapati is divided into two equal parts, what is each part called?

Q2. How many quarters make a whole?

Q3. If Rani had 6 pieces of chocolate and gave half to Reena, how many pieces did Reena get?

Q4. Which of these shapes can be easily cut into two equal triangles?

Q5. When dividing a rectangle into halves, what is the key condition?

Frequently asked questions

What is the main concept covered in CBSE Class 4 Maths Unit 9?

Unit 9 focuses on teaching students the fundamental concepts of dividing whole objects and shapes into two equal parts (halves) and four equal parts (quarters).

How do the NCERT Solutions help students understand halves and quarters?

The solutions provide step-by-step explanations, visual examples, and practical scenarios to help students grasp how to divide items equally and identify halves and quarters accurately.

Are there different ways to cut a shape into halves or quarters?

Yes, the unit explores various methods to cut shapes like rectangles into halves and quarters, demonstrating that multiple approaches can result in equal parts.

Why is it important to divide shapes into equal parts?

Dividing shapes into equal parts is the foundation of understanding fractions. It teaches precision and the concept that a fraction represents a part of a whole that is divided equally.

How can these solutions be used for exam revision?

Students can use these solutions to review the concepts of halves and quarters, practice identifying equal parts, and understand the methods for dividing shapes, which are common topics in exams.

Important links

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.