Fractions

A number is a mathematical or arithmetical value used for measuring, calculating and counting. Numbers can be divided and classified into decimals, rational numbers, irrational numbers,  real numbers, natural numbers, whole numbers, fractions, etc. Fractions denote the parts or portions or sections of any set/quantity or collection. In this article, we are going to study fractions in detail. 

What Are Fractions? 

After dividing a whole into parts, each part is called a fraction of the whole. Fractions denote the parts or portions or sections of any set/quantity or collection. The word “fraction” is derived from the Latin word ‘fractus’. It means ‘broken’. 

Fraction is denoted by the “/” symbol, e.g., p/q. The upper part is called the numerator, and the lower part is the denominator.

Examples: 

• 1 ball is divided into 2 equal parts. So, each part is one-half (½). 
• 1 ball is divided into 4 equal parts. So, each part is one-fourth (¼). 

• There are a total of 5 fruits. 1 out of 5 is orange. So the fraction of oranges is one-fifths (⅕).  The other 4 fruits are apples. So the fraction of apples is four-fifths (⅘).

• A real-life example of fractions is equal slices of pizza, cake, fruits etc. 

• There is a group of 5 students. 1 out of them is a girl. So, the fraction of girls is one-fifths ( 1⁄5 ). The remaining 4 are boys. So, the fraction of boys is four-fifths ( 4⁄5 ).

Parts of Fractions

A fraction is represented in a/b form. It has two parts: Numerator and Denominator. 

Numerator: The top part of the fraction is called the numerator. It is at the top of the line. The numerator tells the sections or the number of equal parts taken in a fraction.

Denominator: The bottom part of the fraction is called the denominator. It is below the line.  It tells us the total number of equal parts in a collection. 

Properties of Fractions 

The properties of fractions are listed below: 

• Fractions obey and follow the associative property of addition, i.e., a+(b+c) = (a+b)+c

Example: 2/3 +( 7/6 + 8/9) = (2/3 + 7/6) + 8/9

• They also obey the associative property of multiplication; i.e.,  a x (b x c) = (a x b) x c

Example:  2/3 x ( 7/6 x  8/9) = (2/3 x 7/6) x 8/9

• The commutative property of addition applies to fractions as well.

 Example: 9/10 + 8/9 = 8/9 + 9/10 

• The fractions obey the commutative property of multiplication.

Example:   9/10 x 8/9 = 8/9 x 9/10 

• Identity property of addition: If we add 0 to any fraction, the answer will be the fraction itself. 

Example: (6/7)+0 = 6/7.

• Identity property of multiplication: If we multiply any fraction by 0, the answer will be 0.

 Example: (8/9) x 0 = 0. 

• The answer to the identity property of addition is 0. 

Example: (9/10)+(-9/10)= 0.

• After the identity property of multiplication, the answer is 1.

 Example: (7/8) x (8/7) = 1.

• They follow the distributive property of multiplication.

 Example: 1/3 [(6/7)+(8/9)] = [(1/3) x (6/7)]  + [(1/3) x (8/9)]

• When a and b are non-zero numbers, the inverse of a/b is b/a. 

Types of Fractions 

Fractions are divided into many types: 

• Proper fractions – The denominator is greater than the numerator.

Example: 7/9. 

• Improper fractions – The denominator is lesser than the numerator in these fractions.   

Example: 9/8.  

• Mixed fractions – It is a combination of integers and a proper fraction.                 

Example: 8 ½. 

• Like fractions – The fractions which are like each other.     

Example: 3/6 and 2/4. 

• Unlike fractions – These fractions are dissimilar from each other.                     

Example: 2/6 and 9/5. 

• Equivalent fractions – In this fraction, after simplification, either of the two fractions is equal to each other. 

Example: 6/9 and 4/6 are equivalent fractions. 

• Unit fractions – In this fraction, the numerator is equal to 1. 

Example: 1/9. 

Conclusion

This topic is a general study on fractions. After dividing a whole into parts, each part is called a fraction of the whole. Fractions denote the parts or portions or sections of any set/quantity or collection. We discussed the parts of fractions. We also studied the types of fractions and properties of fractions. This is a very crucial topic for math students and students appearing in board exams. This topic is also helpful for students or aspirants appearing in SSC exams.