Just like ratios and percentages, a fraction is a piece of information that represents a set of data. A fraction, however, represents information with two parts, a numerator that is evaluated with respect to the denominator. This article will show you the basics of how to divide fractions.
In dividing fractions unlike when you are adding or subtracting them, you don't need the denominators to be common or the same. In fact the process for dividing fractions uses the same steps that you would in multiplying them except with a few additional parts. Interestingly enough, you will find that to divide fractions, you use no division at all.
To begin with, when you want to divide one fraction into another, consider the algebraic process involved. Let's see a quick example. Say you want to perform the following operation: (4/6) / (3/4). To start with, let's convert the fractions into decimals to illustrate a concept. We have (0.667)/(0.75) = 0.889. If we recognize the fact that dividing the divisor into the dividend is the same as multiplying the dividend by the reciprocal or inverse of the divisor, we can see how this is achieved. Let's rewrite this calculation into a couple of other forms to show this.
(0.667/1) / (0.75/1) = (0.667/1)(1/0.75) = 0.889
Or if we write this in to fractional form, we have the following:
(4/6) / (3/4) = (4/6)(4/3) = (4 x 4)/(6 x 3) =16/18 = 8/9 = 0.889
Restating this process, to divide two fractions, the dividend fraction (numerator) is multiplied by the reciprocal or inverse of the divisor fraction (denominator). The reciprocal for the divisor fraction is found by dividing it into 1 which results in a new fraction where the numerator and denominator switch places from that of the original fraction. For example, the reciprocal of 3/8 is 1/(3/8) = 8/3. As you would expect a fraction multiplied by its reciprocal is equal to 1.
Here are a couple of examples to further explain.
1.) Find the quotient of 7/10 and 12/15.
(7/10) / (12/15) = (7/10)(15/12) = (7 x 15)/(10 x 12) = 105/120 = 21/24
We recognize that when the divisor fraction is less than 1 it becomes a reciprocal or multiplier that is greater than 1 which will then increase the value of the dividend fraction.
2.) Find the quotient of 9/7 divided by 12/8.
(9/7) / (12/8) = (9/7)(8/12) = (9 x 8)/(7 x 12) = 72/84 = 6/7
From this example you can see that when the dividend fraction is divided by a larger divisor fraction, it will become a smaller reciprocal and multiplier reducing the value of the dividend fraction.