Fractions

Fractions represent a part of a whole. They are usually expressed in this form: ab, where ‘a’ and ‘b’ are called the numerator and denominator, respectively. Out of the whole, numerator represents a part of the whole while, denominator denotes the whole number. Together, they tell us how much of something we have.  

A fraction represents how to divide a whole into equal parts. For example, if a circle is divided into 12 equal parts and one piece of the circle is represented as 1/12, it is read as one-twelfth. 
 

Fractions are categorized based on the relationship between the numerator and denominator. Let's take a look at the types of fractions:

• Proper Fraction

• Improper Fraction

• Unit Fraction

• Mixed Fraction

• Equivalent Fraction

• Like Fraction

• Unlike Fraction

Proper Fractions: In proper fractions, the numerator is less than the denominator. For instance, 2/8, 6/15, 7/9, … 

Improper Fractions: The numerator is greater than or equal to the denominator
For instance, 8/2, 5/3, 15/6, …

Unit Fractions: In a fraction, where the numerator is always 1, it is called a unit fraction. Unit fractions have a numerator of 1 and are always proper fractions (e.g., 1/5, 1/9, 1/12).

Mixed Fractions: A mixed fraction consists of a whole number and a proper fraction. For example, 614, here, 6 is the whole number and ¼ is the proper fraction. 

Equivalent Fractions: Equivalent fractions are two or more fractions with different numbers but the same value. For example, 1/2 = 2/4 = 3/6. Here, 1/2, 2/4, and 3/6 share the same value because they all represent half of a whole. Equivalent fractions are resulted by multiplying or dividing the numerator and denominator by the same number (e.g., 1/2 × 2/2 = 2/4).

Like Fractions: The fractions with the same denominators are called fractions. For example, 5/17, 6/17, 9/17,… 

Unlike Fractions: Fractions with different denominators. E.g., 5/12, 6/18, 9/11, …  
 

The visual representation of numbers using a horizontal straight line is the number line. A fraction on a number line helps students to understand how the number is divided into parts between the two whole numbers. The denominator represents the number of parts the number line will be divided into.

Fractions share properties with other numbers. Here, we are going to discuss some of the properties of fractions. 

• Commutative property: When multiplying and adding fractions, the order of the values does not affect the result. That is a/b + c/d = c/d + a/b and a/b × c/d = c/d ×a/b. 

• Associative property: The way of grouping the fractions in addition and multiplication doesn’t affect the result. For example, (a/b + c/d) + e/f = a/b + (c/d + e/f)  and (a/b × c/d) × e/f  = a/b × (c/d × e/f)

• Identity property: The product of a fraction multiplied by 1 is the fraction itself. For example, a/b × 1 = a/b. Adding 0 to a fraction has no effect on the final outcome. So, a/b + 0 = a/b

• Multiplicative inverse: Multiplying a fraction by its reciprocal yields 1, that is (a/b) × (b/a) = 1

• Distributive property: The product of multiplying a fraction by the sum of two fractions is equal to the sum of the product multiplied by each addend separately. That is a/b × (c/d + e/f) = a/b × c/d + a/b × e/f
   

Fractions play an important role in our everyday lives. In fact, we use them often even without realizing it. Fractions are used daily in tasks like cooking, measuring, and calculating discounts.

 Take a look at the below-mentioned scenarios where fractions are used:

• In cooking and baking, we use fractions to adjust the ingredients that are added in the right proportions. 

• Since fractions help us express values accurately, we use them to measure land areas and distances where precise measurements are required. 

• We also use fractions to calculate the discounts and interest rates. 

• To express the score for students, fractions are used.