# Introduction to Fractions

Fraction is derived from the Latin word “fractus” which means “a part of” or “broken”. Fractions are integers and are used to express parts of a whole. We shall discuss this concept here in detail with some solved examples.

## Introduction to Fractions

Fractions are types of integers and are used to represent a part of the whole. For example, if I have to say I have one half of a cake, it means that I divided 1 cake into 2 equal and smaller parts and I possess one of the 2 parts. To put it simply, I have 1/2 part of the cake.

They are represented in the format of “p/q” where the “p” part is called the Numerator and the “q” part is called the Denominator. P/q means ‘p’ parts out of ‘q’ number of total parts. The value of a fraction in decimal form can be obtained by dividing the numerator by denominator.

For example ‘3/5’ means 3 parts out of 5, 1/3 means 1 part out of 3. Fractions are also used to denote division or ratios. For example, 3/5 can be read as ‘3 divided by 5’ or as a ratio of ‘3 is to 5’.

(Source: Wikimedia)

## Equivalence

2 sets of fractions can be the same although their numerators and denominators do not match. Consider the fractions 3/6, 1/2 and 9/18. In all the 3 fractions we see that the numerator is one half or 1/2 of the denominator. Thus all the fractions are easily reducible to the common form 1/2. This method is called Simplifying or reducing the fraction.

If we observe the numerator and denominator to have a common factor we eliminate that factor to reduce the fraction to a simpler form. Some of the important ones are given below.

Addition of 2 fractions can take place only when they have the same denominator. For example, if we add 3/6 and 5/6 then this is possible as both the fractions have the same denominator i.e. 6. in such additions we add only the numerators and the denominator stays the same.  Consider this as adding 3 parts out of 6 to another 5 parts out of 6. So,

3/6 + 5/6 = (3 + 5)/6 = 8/6

Consider the case when denominators of the fractions are not the same. In such a case we make the denominators of both the fractions same by multiplying the denominators with a suitable factor to form an l.c.m of the denominators and then add them. Consider the fractions 3/6 and 1/2

3/6 + 1/2

In this case, 2 and 6 have common LCM as 6. So, we make both the denominators as 6. To do this we multiply the numerator and denominator of 1/2 with 3 so as to not change the value of the fraction.

so 3/6 + 1/2 = 3/ 6 + 3/6 =6/6 =1

### Subtraction

Subtraction of fractions follows the same rule as the addition of fractions where it is necessary to have the same denominator for carrying out the operation. Consider the example 5/6 – 3/6= (5 – 3) / 6 = 2/6 = 1/3. Similarly, 5/6 -1/4 = (5 x 4) / (6 x 4) – (1 x 6) / (4 x 6) = 20/24 – 6/24 = (20 – 6) / 24 = 14 / 24 = 7/12.

### Multiplication

Multiplication of 2 fractions is performed by multiplying the numerators of the 2 numbers and multiplying the denominators of the 2 numbers separately and obtaining the final result. For example, 3/9 x 4/5 = (3 x 4) / (9 x 5) = 12/45

### Division

Division of 2 fractions again, is carried out by dividing the 2 numerators and dividing the 2 denominators separately and obtaining the final result. For example, 6/18 divided by 2/9 = (6 divided by 2) / (18 divided by 9) = 3/2

## Solved Example for You

Question 1: Obtain the result if (2/3) is added to (4/9) and is multiplied by 3

= 3x ( 6/9 + 4/9)

= 3x ( 10/9 )

= 30/9

= 10/3

Question 2: Explain what is fraction with example?

Answer: A fraction informs us how many parts of a whole we have. One can recognize a fraction by the slash that is between the two numbers. We have the numerator, a bottom number, a top number, and the denominator. For example, 1/2 happens to be a fraction. Also, 1/2 of a pie will be half a pie.

Question 3: Name the three types of fractions?

Answer: The three types of fractions are proper fraction, improper fraction, and mixed fraction.

Question 4: Explain how one can multiply fractions?

Answer: Below are the steps for carrying out multiplication of fractions:

• Carry out simplification of the fractions if not in lowest terms.
• Carry out multiplication of the numerators of the fractions in order to get the new numerator.
• Finally, carry out multiplication of the denominators of the fractions in order to get the new denominator.

Question 5: Can we say that 1 is a proper fraction?

Answer: No, 1 is not a proper fraction. This is because, in a proper fraction, the numerator happens to be smaller compared to the denominator. So, 1 and other integers are not proper fractions.

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