Home » Math Vocabulary » Halves in Math – Definition, Fractions, Facts, Examples, FAQs

- What Are Halves? What Is Half in Math?
- Halves of Various Geometric Shapes
- Finding Half of a Number
- Solved Examples on Halves
- Practice Problems on Halves
- Frequently Asked Questions about Halves

## 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.

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## 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.

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## 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

- The plural form of “half” is “halves.”
- One of two equal parts is a half. Two halves make a whole.
- Half as a fraction is $\frac{1}{2}$. It is a unit fraction. It is a proper fraction.
- Half of a half is called a quarter, which is represented by $\frac{1}{4}$.
- Half of a circle is called a semicircle. Half of a semicircle is a quarter circle.
- Half of an hour is equal to 30 minutes.
- Half of a dozen is equal to 6.

## 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 ****5****9****?**

**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

1

### Which of the following represents half?

$\frac{1}{2}$

0.5

50%

All of the above

CorrectIncorrect

Correct answer is: All of the above

Half as a fraction $= \frac{1}{2}$

Half as a decimal = 0.5

Half as a percent = 50%

2

### Which of the following shapes are not divided into halves?

Image A

Image B

Image C

Image D

CorrectIncorrect

Correct answer is: Image C

Image A $= \frac{3}{6} = \frac{1}{2}$

Image B $= \frac{50}{100} = \frac{1}{2}$

Image D $= \frac{8}{16} = \frac{1}{2}$

The fraction of shaded parts in the image C is $\frac{3}{4}$.

3

### Olive had 36 seashells. She used 18 of them to make a necklace. What fraction of marbles did she use?

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{2}{3}$

None of these

CorrectIncorrect

Correct answer is: $\frac{1}{2}$

Fraction of seashells she used $= \frac{18}{36} = \frac{1}{2}$

4

### What is half of 80?

20

40

100

160

CorrectIncorrect

Correct answer is: 40

Half of $80 = \frac{1}{2} \times 80 = 80 \div 2 = 40$

5

### Which of the following is false?

Two halves make a whole.

A half can be written as 50%.

Four halves make a whole.

Two quarters make a half.

CorrectIncorrect

Correct answer is: Four halves make a whole.

Four halves $= \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{4}{2} = 2$

## Frequently Asked Questions about Halves

**What is the difference between halves and quarters?**

When we split a whole into 2 equal parts, we get two halves, whereas when we split a whole into 4 equal parts, we get four quarters. A half can be represented as $\frac{1}{2}$, whereas a quarter can be represented as $\frac{1}{4}$.

**How can we find half of a mixed number?**

For finding half of a mixed number, we first convert the mixed number into an improper fraction and then multiply the fraction by $\frac{1}{2}$.

Half of $3\frac{1}{7} =$ Half of $\frac{22}{7} = \frac{22}{14}$

**What do we mean by 1 whole and a half?**

A whole and a half is combination of 1 whole and a half, i.e., $1\frac{1}{2}$.

**What is half as a ratio?**

Half as a ratio is represented by 1 : 2.

**Why is learning about halves and quarters important?**

Halves and quarters are the most basic fractions. Learning about halves and quarters helps us learn the concepts like sharing, dividing, equal groups, and comparing quantities.