Equivalent FractionsWhy do I need to know about equivalent fractions? That’s the exact question I asked when I was first introduced to converting fractions into its equivalent form. Today, many years later I am writing this article explaining people how important it is not only for better grades but also in your daily life to understand the concepts and applications. Let me give you some understanding of the importance of an equivalent fraction in the physical word. Assume that you have a black forest cake in your fridge (but you can’t have it all, mind you!). You got strict instructions that you can have one third of the cake. The rest is for your younger brother. Some unexpected guests turn up and it so happens that you guys have to accommodate them as well with the same black forest lying out there in the fridge. You know as such you were having a small portion of the cake so it’s your brother who will have to share his part with the guests. Earlier you had planned to divide the cake into three parts of which one would have been yours and the rest would have gone to your bro. Now that these guests are there it’s not possible to divide that way. So you will have to make more number of parts of the cake. Let’s say you make nine parts of the whole cake. Now this is where you need to understand of the nine parts of the cake how much is your share. Do you get to eat 1, 3 or 5 parts of the 9 pieces? Thus you got to know what part of the 9 pieces is equivalent to the one piece out of three that was planned earlier. This is a very practical application of the concept of fractions that are equivalent. By the way if you are wondering about your share of the cake then read on to understand the method to arrive at the answer. Creating Equivalent Fractions So how do you go about creating a fraction that is equivalent to a given fraction? There are two basic techniques that we will discuss here. If you look closely then these techniques are based on the same principle and are mere variations of each other. They are presented as different techniques to enable you to understand them better. Multiplying Numerator and Denominator Technique Let’s assume that we have the fraction 1/3 and we are asked to find its equivalents. In this method the idea is to multiply the numerator and the denominator with the same number. You may choose the number as per your requirement. However this works just fine for any arbitrarily chosen number. Let’s select 2 as the multiplier. When I multiply 2 to the numerator it becomes 2 and on multiplying to the denominator it becomes 6. Thus the new numerator is 2 and the new denominator is 6. The fraction becomes 2/6. If I choose the multiplier as 3 then the equivalent fraction is 3/9, for 4 it is 4/12 and so on. This method works fine for any fraction. Dividing Numerator and Denominator Technique In this method you divide the numerator and the denominator with a common factor to arrive at the equivalent form. Caution: This method works only when the fraction is not in its simplest form. If the fraction is in its simplest form then it is a good idea to go for the multiplication method. Hope you understand the concepts and ideas behind equivalent fractions. Have a great time with the other study materials out here.
|