Halves and Quarters: CBSE Class 4 Maths NCERT Guide

Hello, future math wizards! Have you ever shared a chocolate bar with a friend by breaking it in the middle? Or eaten a few slices of a pizza? If you have, you already know something about fractions! This chapter, 'Halves and Quarters', is all about understanding these 'parts of a whole'. A 'half' is what you get when you share something equally between two people. A 'quarter' is what you get when you share it among four people. Learning about halves and quarters is super useful for sharing things fairly, cooking from a recipe, or even telling the time! By the end of this chapter, you will be a pro at identifying, writing, and using halves and quarters in everyday situations. Let's start this fun journey of dividing and sharing!

Understanding the 'Whole'

Before we can learn to divide, we must first understand what we are dividing. In maths, the entire thing we start with is called the 'whole'. A whole can be one single object, like one big chapati, one apple, or one sheet of paper. But a 'whole' can also be a collection or a group of things. For example, a packet of 12 crayons is a 'whole' packet. A bunch of 20 grapes is a 'whole' bunch. It's very important to first identify what the 'whole' is. If the whole is one cake, a half means cutting the cake into two equal pieces. If the whole is a group of 10 toy cars, a half means dividing the cars into two equal groups of 5 cars each. Always ask yourself, 'What is the total? What is the whole thing?' before you start finding its parts.

Key Fraction Terms: Halves, Quarters, and More!

Whole: The complete object or the entire collection of items. We can represent it with the number 1.
Half (1/2): When a whole is divided into TWO equal parts, each part is called a half. It is written as 1/2.
Quarter (1/4): When a whole is divided into FOUR equal parts, each part is called a quarter. It is written as 1/4.
Three-Quarters (3/4): This means taking three out of the four equal parts of a whole. It is written as 3/4.

Worked Examples: Finding Halves and Quarters

Example 1: Find half of 18 balls.
Step 1: 'Half' means dividing the total number into 2 equal groups.
Step 2: The total number of balls is 18.
Step 3: We calculate 18 ÷ 2.
Step 4: 18 divided by 2 is 9.
Answer: Half of 18 balls is 9 balls.
Example 2: Find a quarter of 20 flowers.
Step 1: 'A quarter' means dividing the total number into 4 equal groups.
Step 2: The total number of flowers is 20.
Step 3: We calculate 20 ÷ 4.
Step 4: 20 divided by 4 is 5.
Answer: A quarter of 20 flowers is 5 flowers.
Example 3: Find three-quarters (3/4) of a 12-slice pizza.
Step 1: First, we need to find one quarter (1/4) of the pizza. A quarter means dividing the total into 4 equal parts.
Step 2: Total slices = 12. So, 12 ÷ 4 = 3 slices. One quarter is 3 slices.
Step 3: 'Three-quarters' means we need 3 of these parts. So, we multiply the value of one quarter by 3.
Step 4: 3 slices × 3 = 9 slices.
Answer: Three-quarters of a 12-slice pizza is 9 slices.

Important Points to Remember

Equal Parts are Key! A half or a quarter must be one of two or four equal parts. If you break a chocolate bar into two unequal pieces, the pieces are not called halves.
A Quarter is Smaller than a Half. Since you are dividing the whole into more pieces (4 instead of 2), each quarter piece will be smaller than each half piece.
Two Quarters make a Half. Think of a square paper. If you fold it into 4 equal squares (quarters), taking 2 of those squares is the same as taking half of the paper. So, 1/4 + 1/4 = 1/2.
Four Quarters make a Whole. If you have all four quarters of a pizza, you have the whole pizza! So, 4/4 = 1 (the whole).

Practice Questions with Solutions

Q: There are 14 stars shown below. Colour half of them.
★★★★★★★
★★★★★★★
A: Step 1: Count the total number of stars. There are 14 stars.
Step 2: To find half, we must divide the total by 2.
Step 3: Calculate 14 ÷ 2 = 7.
Final answer: You need to colour 7 stars.
Q: A bottle contains 1 litre of juice. 1 litre is equal to 1000 millilitres (ml). If you drink a quarter of the juice, how many ml did you drink?
A: Step 1: The whole is 1 litre, which is 1000 ml.
Step 2: To find a quarter, we need to divide the whole by 4.
Step 3: Calculate 1000 ÷ 4 = 250.
Final answer: You drank 250 ml of juice.
Q: Meena has a ribbon that is 20 metres long. She uses three-quarters (3/4) of it for a project. How much ribbon did she use?
A: Step 1: The whole ribbon is 20 metres long. First, we find one-quarter (1/4) of the ribbon.
Step 2: Divide the total length by 4: 20 ÷ 4 = 5 metres. So, one-quarter is 5 metres.
Step 3: To find three-quarters, we multiply the length of one-quarter by 3.
Step 4: 5 metres × 3 = 15 metres.
Final answer: Meena used 15 metres of ribbon.
Q: There are 24 students in a class. A quarter of them like to play cricket, and half of them like to play football. How many students are left?
A: Step 1: Find the number of students who like cricket (a quarter of 24). 24 ÷ 4 = 6 students.
Step 2: Find the number of students who like football (half of 24). 24 ÷ 2 = 12 students.
Step 3: Find the total number of students who play either cricket or football. 6 + 12 = 18 students.
Step 4: Subtract this from the total number of students to find how many are left. 24 - 18 = 6 students.
Final answer: There are 6 students left.

Frequently Asked Questions

What is the difference between a half and a quarter?

A half is one of two equal parts of a whole, written as 1/2. A quarter is one of four equal parts, written as 1/4. A half is always bigger than a quarter of the same whole.

How do we write a half and a quarter using numbers?

We write a half as a fraction: 1/2. The bottom number (denominator) '2' tells us the whole is divided into two equal parts. We write a quarter as 1/4, where '4' means the whole is divided into four equal parts.

Can a group of objects be a 'whole'?

Absolutely! A 'whole' can be a single item like a pizza, or it can be a collection of items like a bunch of 12 bananas or a class of 32 students. Half of 12 bananas would be 6 bananas.