Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it’s dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it’s all illuminated and you can see exactly where you were. Then you enter the next dark room.
Andrew Wiles
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Division of fractions is an important concept in lower school mathematics. The procedure requires two step involvement – reciprocate and then multiply. Let us call this as known method.
Known Method – Some Key Points
To achieve the solution by this method, follow the steps given:
- Step 1. Consider the second fraction and take the reciprocal.
- Step 2. Change the ÷ symbol between first and second fraction by × symbol.
- Step 3. Multiply the numerators and the denominators.
- Step 4. Simplify the fraction, if possible.
Mathematical analysis of the known result is given below:
Following example will help us to understand the concept better.
In the proposed method, we will divide the numbers in numerators and the numbers in the denominators, maintaining the given order. Therefore,
Proposed Method – Some Key Points
Following the above discussion, we need to consider the below steps while solving by the proposed method:
- Step 1. Consider the numerators and denominators of the two fractions.
- Step 2. Divide the numerators and denominators.
- Step 3. Simplify the fraction, if possible.
Mathematical analysis of the known result is given below. Without any difficulty, we can write
Following example will help us to understand the concept better.
Now what happened, if the numbers do not divide each other? Of course, we are talking about the numerators and denominators. This is the most crucial point to understand. Recall that, when we were adding or subtracting two unlike fractions, our first task (may be) is to make the fractions like. Here also, we need to convert them into like fractions. Therefore, following changes are necessary in the proposed method.
Proposed Method – Changed Version
From the above discussion, few changes are required while dividing the fractions. These are given below:
- Step 1. Consider the denominators of the two fractions.
- Step 2. Take the L.C.M of the denominators.
- Step 3. Multiply the numerators suitably, to convert them into like fractions.
- Step 4. Divide the numerators and denominators.
- Step 5. Simplify the fraction, if possible.
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