Fractions are a very important expression of numbers in Mathematics. They are used in many computations including those that can relate to real life situations. Fractions are by themselves a division of two values or simply a representation of the parts of a division. You can be able to compute many operations using the fraction including addition, subtraction, multiplication, and division. In the article, we will consider division involving fractions.
Before getting into details of division involving fractions, it is important to understand the constituents of a fraction itself. A fraction should always be in its simplest form. In case the fraction is a mixed fraction, the first step should be to make it an improper fraction. The number on top is called the numerator while that at the bottom is the denominator.
Another important terminology to understand is the reciprocal. This operation is very important when performing computations that involve division of fractions. Note that if the sign before a fraction is division, the reciprocal of the fraction is determined and consequently, the sign changes to become multiplication. You will have to recall this Mathematical operation when dividing fractions.
Dividing a number by a fraction
It is mandatory to note that the knowledge of multiplying fractions is important when dividing fractions. The first thing to do before the division of a number by a fraction is to ensure that the fraction is not a mixed fraction, meaning it does not contain a whole number but is either a proper or improper fraction. Once this is ensured, find the reciprocal of the fraction and proceed to simply multiply the number by the reciprocated fraction.
The steps above can be summarized in the following steps:
1. Ensure the fraction is either a proper or an improper fraction
2. Find the reciprocal of the fraction
3. Multiply the number by the reciprocated fraction
4. Simplify the resultant fraction to its simplest form.
Once you have found the product, simplify it, if the product is a fraction, by finding a common divisor of both the numerator and the denominator. You can always check if you are correct by multiplying the numerator and the denominator by the divisor and getting the original fraction.
Dividing a fraction by fraction
The procedure used in the division of a fraction by another fraction is more or less that same as that of the division of a number by a fraction. The first fraction, in this case, is treated as the whole number. The knowledge of reciprocals is equally important when dividing a fraction by another fraction. The first step is to ensure that both fractions are either in their proper or improper forms. Mixed fractions can cause complications later in the computations.
Once both the fractions are in the desired forms, find the reciprocal of the second fraction and then proceed to multiply the two fractions. As a reminder, multiplication of fractions is very simple. Simply multiply the numerator of the first fraction by the numerator of the second reciprocated fraction and do the same with the denominators. Simplify the resultant fraction.
The steps for the division of a fraction by another fraction can be summarized as below:
1. Express both fractions into either proper or improper forms
2. Find the reciprocal of the second fraction
3. Multiply the two fractions
4. Simplify the resultant fraction