Halves and quarters are the portions of a whole, and whole means the entire thing. An entire pizza, the complete birthday cake, an entire chocolate bar, etc., are examples of the whole. In mathematics, we represent halves and quarters using the concept of fractions. This topic deals with defining and finding the relationship between the halves and the quarters and their whole.

This article will elaborate on using models to divide a whole into half parts and quarter parts. It will also help solve some questions that will help practise the concepts and learn how to deal with quarters and halves in real life.

Halves and Quarters

Before we learn about halves and quarters, we need to know about the whole. Whole means something which is complete and which is not divided into parts. We can consider an entire pizza, a whole birthday cake, a whole watermelon, a whole orange etc. are examples of the whole.
The parts are the portions of a whole. When we divide a whole into two equal parts, we will get halves.
For example, if we divide a certain quantity of sugar into two equal portions, each portion obtained is half of the whole amount of the sugar.

Similarly, if we divide one orange into four equal parts, each part is one-fourth of the orange. Now, one-fourth of a whole is called a quarter.
Now, half and a quarter represent a part of the whole quantity, which are called fractions.

Fractions

A fraction is a quantity that expresses a part of the whole. Let us further learn what fractions exactly are.

The term fraction expresses a numerical quantity that is part of a whole thing. Suppose we have a large piece of pie, and we divide it into \(6\) equal portions and colour five parts in light pink and one part in dark pink. Then each part of the paper is only \(\frac{1}{6}^{\text {th }}\) of the total pie. Here, \(\frac{1}{6}\) is a fraction.

We call the above upper part of the fraction the numerator and the below part the denominator. In the above example \(\frac{1}{6}, 1\) is known as the numerator, and \(6\) is known as the denominator. We don’t always deal with whole objects in our regular life. We deal with parts or portions of whole things very often. To quantify them, we need fractions.

Representing Half as a Fraction

We can represent half as a fraction as half is also part of a whole quantity. We already discussed how we could define a part of a whole in a fraction form. Similarly, suppose we divide a whole quantity into two equal parts. In that case, the upper part of the fraction expresses what we have, that is \(1\) and, the lower part of the fraction represents the number into which the whole object is divided, that is \(2\).

So, the numerator will be \(1\), and the denominator will be \(2\) if we represent a half into fraction form.

Representing Quarter as a Fraction

We can represent quarter as a fraction as it is also a part of a whole quantity. If we divide a whole quantity into four equal parts, then the upper part of the fraction expresses what we have, i.e., \(1\) and, the lower part of the fraction says the number into which the whole object is divided, i.e., \(4\).

So, the numerator will be \(1\) and, the denominator will be \(4\) if we represent a quarter into fraction form.

Examples of Halves and Quarters

If we divide a whole into exactly two equal parts, then these parts are called halves of the whole. Each part is called half of the whole.
For example, half of an orange, half of a circular piece of paper, half glass of water, half of a watermelon.

Let us take some geometrical figures and see their half parts. We can divide a triangle, a square, a circle into two halves.

Let us take an example of a number and explain. Number \(8\) is a whole number, and we can divide it into two equal parts that are \(4\) and \(4\). So, number \(8\) is a whole, and \(4\) and \(4\) are the parts of number \(8\). In other words, we can say if we add two numbers \(4\) and \(4\), we will get the whole as \(8\). That means two \(4 \mathrm{~s}\) which we got after breaking \(8\) into two equal parts, are the halves of \(8\).

If we divide a whole into four equal parts, these parts are called quarters of the whole. Each part is known as a quarter of the whole. For example, a quarter of an orange.

Let us take some geometrical figures and see their quarter part. We can divide a square, a circle, into four quarters.

In the above figure, the blue shaded part is a quarter of the whole circle.

In the above figure, the orange shaded part is a quarter of a rectangle.

Let us take number \(8\) and explain its quarters. Number \(8\) is a whole number, and we can divide it into four equal parts are \(2, 2, 2\) and \(2\). So, number \(8\) is a whole, and four \(\text {2s}\) are the parts of number \(8\).

In other words, we can say if we add these four numbers, we will get the whole as \(8\). That means four \(\text {2s}\) which we got after breaking \(8\) into four equal parts, are the quarters of \(8\).

Relationship Between Halves and Quarters

We can divide a whole into halves as well as into quarters. There must be a relation between halves and quarters. Let us use some real-life examples and try to relate halves and quarters with each other.

From the above image, it is visible that if we cut one whole tomato into two equal pieces, we get \(\frac{1}{2}\) of the tomato and, if we again cut the half part into two identical pieces, we get \(\frac{1}{4}\) of tomato. So, \(\frac{1}{4}\) of a tomato is equal to half of \(\frac{1}{2}\) of a tomato. In other words, we can say two quarters make one half.

Solved Examples

Q.1. Express half as a fraction.
Ans: We can represent half as a fraction. Suppose we are dividing a whole quantity into two equal parts. In that case, the upper part of the fraction expresses what we have, i.e., \(1\) and, the lower part of the fraction represents the number into which the whole object is divided, i.e., \(2\).
Therefore, the fraction form of half is \(\frac{1}{2}\).

Q.2. Express a quarter as a fraction.
Ans: We can represent a quarter as we can divide an entire amount into four equal parts. In this case, the numerator will be \(1\) and, the denominator will be \(4\). Therefore, the fraction form of a quarter is \(\frac{1}{4}\).

Q.3. How many pieces will we get from the halves of a lemon?
Ans: If we divide a whole into exactly two equal parts, then these parts are called halves of the whole. Each part is known as half of the whole.
So, if we divide a lemon into halves, we will get two pieces of lemon.

Q.4. Find the quarter of \(20\).
Ans: We know that a quarter of a whole means one-fourth of a whole.
Therefore, \(\frac{1}{4} \times 20=5\)
Hence, a quarter of \(20\) is \(5\).

Q.5. Find half of \(12\).
Ans: We know that a half of a whole means \(\frac{1}{2}\) of a whole.
Therefore, \(\frac{1}{2} \times 12=6\)
Hence, half of \(12\) is \(6\).

Summary

In this article, we have learned about halves and quarters, the relation between halves and quarters. We have seen some examples of halves and quarters. We learned that we could represent half and a quarter using fractions. We have also solved some problems related to the topic.

FAQs

Q.1. What are quarters and halves?
Ans: When we divide a whole into two equal parts, we call these parts halves, and when we divide a whole into four equal parts, we call these parts quarters.

Q.2. Do halves have to be equal?
Ans: Yes, halves have to be equal. If we divide a whole into two unequal parts then, these parts can not be called halves.

Q.3. What is the difference between halves and quarters?
Ans: When we divide a whole into two equal parts, we call these parts halves, and when we divide a whole into four equal parts, we call these parts quarters.
So, the halves mean each part is \(\frac{1}{2}\) of a whole and the quarters means each piece is \(\frac{1}{4}\) of a whole.

Q.4. What is the relation between a half and a quarter?
Ans: A quarter means one-fourth that we can represent as \(\frac{1}{4}\) and two quarters means \(2 \times \frac{1}{4}=\frac{1}{2}\). So, two quarters mean one half.
Now, if we divide \(\frac{1}{2}\) into two parts, we will get \(\frac{1}{2} \div 2=\frac{1}{4}\).
So, half of one half is one quarter.

Q.5. What do you mean by three quarters?
Ans: A quarter means one-fourth that we can represent as \(\frac{1}{4}\) and three quarters means \(3 \times \frac{1}{4}=\frac{3}{4}\).

Now you are provided with all the necessary information on halves and quarters and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.