Chapter 2 – Fractions and Decimals

Let’s say you ordered a pizza. So, in general, a complete pizza is sliced into 6 parts, and you consumed 3 such slices. So in a fraction, you consumed 3/6 of a pizza where 3 is the numerator and 6 is the denominator.

The decimal represented by a dot (.) is the decimal separator of 2 numbers, such as 1.5. In this, 1 is an integral part, whereas 5 is the fractional part. You can make a note the fractional part always represents a number or unit less than 1.

Remember you ate a pizza less than a minute ago and consumed 3 slices out of 6. So, if you want to represent it in decimals, you’ll have to divide 3/6 to obtain 0.5.

Interesting right, your consumption was easily represented as a fraction as well as a decimal. Well, actually, it is worth noting that fractions and decimals can be denoted as one another, just like you did in the example above.

Now that you know the basics, let’s take you to the important topics and their implementation.

So far, you’ve understood what fractions are and how to represent them. Let’s take the first topic and begin with multiplying them.

Now, there are several cases of multiplication of fractions; here, you’ll be learning about the most common yet important ones.

• Multiplication Of A Fraction By A Whole Number
  Under this, the numerator of the fraction is multiplied by the whole number. Take a look at this example:
  (1/2) x 7 = 7/2.
  or it can also be written as,
  (1/2) x (7/1) = 7/2.

Since the denominator of a whole number is always 1, the final product’s denominator in a multiplication of a fraction by a whole number remains unchanged.

• Multiplication Of A Fraction By A Fraction
  In this, numerators of both the fractions are multiplied together, and denominators of both the fractions are multiplied together to obtain the final output. Do have a look at the below example to understand this better.
  Example: (2/5) X (4/7) = (2 x 4) / (5 x 7) = 8/35
  Simple, isn’t it? We are confident that now you can handle any such problem that involves the multiplication of a fraction by a fraction.

Let’s take you to the division of fractions with a few important scenarios and examples.

• Division of a whole number by a fraction
  Consider this example, 54 ÷ (6/9). In such a situation, the concept of reciprocation comes into the picture.
  In reciprocation, the reciprocal of the original number of the fraction is obtained when 1 is divided by that number or fraction.
  So, if you need to find the reciprocal of 2/5, then it is interpreted as 1 ÷ (2/5), and the final result becomes (5/2).
  At this point, do not confuse yourself with what just happened and how it happened, as this is the concept of reciprocation.
  So, using this, the original problem of division of a whole number by a fraction, 54 ÷ (6/9), can be written as 54 x (9/6), and the result becomes (54 x 9) / 6 = 81.

• Division of a fraction by a whole number
  Under this, a fraction is to be divided by a whole number. However, you can once again use reciprocals and multiply the fraction by the reciprocal of the whole number. Try out this example to understand the division of a fraction by a whole number better:
  (2/5) ÷ (9) can be represented as (2/5) x (1/9), and as you already know how to solve this, the final answer obtained will be 2/45.

In this module, you learnt what fractions and decimals are and that they can be interpreted in terms of one another. You also learnt about the various mathematical situations that you have to face and how to solve them using multiplication, division, and reciprocation. These basics about fractions and decimals can help you solve further critical calculations with ease and expertise.