Halves in Math – Definition, Fractions, Facts, Examples, FAQs

What Are Halves? What Is Half in Math?

Halves are two equal parts of a whole. Splitting a whole into two equal parts gives us two halves. Each equal part is called a half.

Definition of Half (Halves)

When we split or divide a whole thing into two equal parts, we get two halves. Each individual part is known as a half.

In other words, two halves make a whole. Let’s understand the meaning of halves with the help of everyday objects.

Halves of Various Geometric Shapes

The two-dimensional shapes that are symmetric can be divided into halves. That is, we will split them into two equal parts, the two parts are exactly identical. If we fold the shape, the two parts fit or align perfectly on top of each other, or will overlap each other. So, each part is one half of the shape.

We can represent half mathematically in different ways. Let’s understand how to write half in numbers, such as a fraction, a decimal, and a percentage? Let’s find out.

Half as a Fraction

A fraction is a part of the whole. In a fraction $\frac{a}{b}$, the number  “a” on the top is the numerator that represents the number of parts taken, and the number “b” on the bottom is the denominator that represents the total number of equal parts. 

Since a half represents one part out of 2 equal parts of the whole, the numerator is 1 and the denominator is 2. Thus, we can write half in fraction form as $\frac{1}{2}$. 

$\frac{1}{2}$ is a proper fraction since the numerator (1) < denominator (2).

$\frac{1}{2}$ is also a unit fraction since the numerator is 1.

Suppose we cut a cake into 2 halves (2 equal parts), then each slice represents a fraction $\frac{1}{2}$. 

Equivalent Fractions of a Half ($\frac{1}{2}$)

Equivalent fractions are the fractions whose numerators and denominators are different but still represent the same value. 

The equivalent fractions of $\frac{1}{2}$ are $\frac{2}{4}, \frac{3}{6}, \frac{4}{8}$, and so on. 

Let’s see the visual representation of these fractions. 

Representing Half on a Number Line

Let’s represent the fraction $\frac{1}{2}$ on a number line. Divide the distance between 0 and 1 into two equal parts. It gives us two halves. So, the midpoint between 0 and 1 will represent half. 

Half as a Decimal

Decimals are the numbers that consist of a whole number part and a fractional part separated by a decimal point. 

To represent half as a decimal, divide the numerator 1 by the denominator. The decimal equivalent of a half is 0.5. 

You can notice that $\frac{5}{10} = 0.5$ is an equivalent fraction of $\frac{1}{2}$.

Half as a Percentage

A percentage is a number of a ratio that is expressed as a fraction of 100. In order to find half as a percentage, we will make the denominator 100 by multiplying both the numerator and denominator of $\frac{1}{2}$ by 50. 

$\frac{1 \times 50}{2 \times 50} = \frac{50}{100} = 50\%$ 

$\frac{1}{2} = 50\%$

Finding Half of a Number

Let’s understand how to find half of a number, a fraction, and a decimal.

Half of a Whole Number

To find half of a whole number, divide it by 2 (or multiply it by $\frac{1}{2}$ or 0.5).  

Example 1: Half of $6 = 6 \times \frac{1}{2} = 3$

Example 2: We can also find half of a whole number by dividing the number by 2. 

Half of $8 = 8 \div 2 = 4$.

Example 3: Half of an odd number 

Finding half of an odd number will give us the answer in the form of fractions. 

Half of a Fraction

We can get half of a fraction by either multiplying the fraction by $\frac{1}{2}$ or by dividing the fraction by 2. 

Example: Half of $\frac{3}{4} = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$ 

Half of a Decimal Number

For finding half of a decimal number, we either multiply the decimal number by $\frac{1}{2}$, or we divide the decimal number by 2. 

Example: Daniel has $\$17.50$. He spent half of the money purchasing a packet of candy. Find the amount spent by him.

The amount spent by him $= \$17.50 2 = \$8.75$

Facts about Halves

Conclusion

In this article, we learned about halves. Halves represent one part out of two equal parts. Let’s solve a few examples and practice problems to understand the concept better.

Solved Examples on Halves

1. How many parts should be shaded in the following figure to represent half a circle?

Solution: 

Total number of equal parts = 8

Number of parts to be shaded = half of 8

Half of $8 = \frac{1}{2} \times 8 = 4$

On shading 4 parts, we get 

2. 50% of the class participated in a debate. If there are 20 students in the class, how many students like to play soccer? 

Solution: 

Number of students in the class = 20

Number of students who play soccer = 50% of 20

50% of 20 means half of 20.

50% of 20 $= \frac{50}{100} \times 20 = \frac{1}{2} \times 20 = 20 \div 2 = 10$

3. What is half of 59?

Solution:

To find half of a fraction, we multiply it by $\frac{1}{2}$.

Half of $\frac{5}{9} = \frac{5}{9} \times \frac{1}{2} = \frac{5}{18}$

5. What is half of a half?

Solution: 

Half $= \frac{1}{2}$

Half of half $= \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$   

Half of a half is a quarter.

Practice Problems on Halves

Frequently Asked Questions about Halves