Fraction Definition

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word “fractio,” which means “to break,” is the source of the English term “fraction.” The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilised fractions to solve because they were the first civilisation to understand fractions.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions were 1st written in India with one number above the other, but without a line. The line used to divide the numerator and also the denominator was only added by Arabs.

Fraction Definition

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. 

Types of Fractions

Proper fractions

Fractions that have a smaller numerator than their denominator are said to be proper fractions. Proper fractions include, for instance, 4/7, 3/11, 2/7, and more.

Improper Fraction

When the numerator of a fraction is more than or equal to the denominator, the fraction is said to be improper. It consistently equals or exceeds the whole. as in 7/4, 5/3, 8/3, and so more.

Unit fraction

Unit fractions are those where the numerator is 1. Such as in 1/4, 1/5, 1/8, and more.

Equivalent Fraction

After being simplified, equivalent fractions are those that express the same value. To determine equivalent fractions of a particular fraction:

The given fraction’s numerator and denominator can both be multiplied by the same number.

The numerator and denominator of given fraction can both be divided by the same number.

Mixed Fraction

An improper fraction and a whole number combine to form a mixed fraction.

Examples: 2 1/3, 5 2/7 and more.

Fraction to Decimal Form

Simply said, there are two distinct ways to express numbers less than one: fractions and decimal numbers. There are precise mathematical equations that allow you to determine the equivalent of a fraction in decimal form, and vice versa, because any number less than one can be expressed with either a fraction or a decimal.

The process of changing a number expressed as p/q, where p and q are whole numbers and q is not equal to zero, into a decimal form can be described as the process of either changing the denominator to a power of 10 or using the long division method.

Methods to Convert Fraction to Decimal Form

1. Long Division Method.

2. By Converting the Denominator of Fraction into the Power of 10.

Long Division Method

We utilise the Long Division Method to change a number from its fractional form, p/q, into its decimal form. In this situation, we divide the denominator by the numerator.

Example: Convert the 4/19 into a decimal form.

1. Let, the numerator 4 as the dividend & the denominator 19 as divisor in the given fraction 4/19. The numerator < denominator in this instance.

2. By putting a 0 next to 4 and the quotient, respectively, we may make the dividend (4) larger than the numerator (19). As of right now, the dividend is 40. (40>19).

3. It is crucial to place a decimal (.) after 0 and begin the division in the quotient part.

4. Multiply 19 by another integer such that the result is not greater than 40. We are aware that 19 multiplied by 2 equals 38. The remainder is 2, which is the digit that appears in the quotient. After adding decimal to the quotient, we can add a 0 at each divisional step.

5. The new dividend is now twenty (20). A number should be multiplied by 19 so that the result is less than or equal to 20. It is 19 times one. Now that the quotient has an additional digit of 1, making it 0.21, the remaining number is 1.

6. Repeat the steps until we get the remainder as 0 or at least 3 decimal places in quotient.

By Converting the Denominator of Fraction into the Power of 10

By changing the denominator of a fraction to the power of 10 such as 10, 100, 1000, etc., you may also convert the fraction form to a decimal form. 

Example: Convert the 7/8 into a decimal form.

1. In order to get a power of 10 in the denominator, we must first come up with a number by which to multiply the denominator & the numerator.

2. 8 is the denominator (8 times of 125 is equal to 1000).

3. Multiply the numerator & the denominator with the same number which is 125.

4. Multiply the numerator by 125, then we get 7×125=875.

5. Now, after the completion of multiplication, we get the denominator in the form of power of 10, that is 875/1000.

6. Before the number of places in the denominator that are equal to zeros, place a decimal point. Since the denominator in this case contains three zeros, the decimal point is added before three places, counting from right side. So, 875/1000 equals 0.875.

Conclusion

In mathematics, a fraction is a numerical value which expresses a portion of a total. The term “whole” can refer to any number, a certain value, or an object. The fraction symbol is written as p/q. For instance, 1/3, 2/5, 7/9, and more.

There are following types of fractions;

• Proper fractions

• Improper Fraction

• Unit fraction

• Equivalent Fraction

• Mixed Fraction

• Like Fraction

• Unlike Fraction

There are two methods which are used to convert the fraction into the form of a decimal:

1. Long Division Method.

2. By Converting the Denominator of Fraction into the Power of 10.