 Let's solve few worded problems on fractions. Let's take an example So the question here is how much is one month as a fraction of a year? How I like to do such problems is that I always spot for the word of as you can see here Whatever that comes after of always goes in the denominator of a answer because our answer is going to be a Fraction because that's what we need to find out how much is one month as a fraction of a year So we are choosing some parts of a whole which has been divided into equal parts and we write those some parts in numerator and the quantity that represents a whole in the denominator in The denominator there will always be a quantity that comes after the word of in such English worded examples And whatever that has been asked to be found as a fraction will come in a numerator So we have one month now. These are just words We need to convert them into quantities because in the numerator We have a month and in the denominator we have a year But we know that a year is composed of 12 months, isn't it? So you may consider that a year has been divided into 12 equal parts and that's what we are writing in the denominator and in the numerator I can write one month and I can simply write this as One divided by 12 because both in numerator and denominator. We have the word months You can say that one month is one by 12 of a year and that's how we can complete our answer So if you understand this technique, let's solve one more worded problem Now consider this example if Ajay ate six slices of a pizza Which had total ten slices and remaining slices were eaten by his older sister Amrita What fraction of pizza both of them ate again? Let's first take Ajay and then we will write Amrita and I have written these two in different colors Now let's compute the fraction of pizza that Ajay has eaten So Ajay ate six slices of a pizza So this is the word of and a pizza so a whole pizza will come in the denominator While finding out this answer and how many slices did Ajay eat? He ate six slices Can I convert the denominator into slices? A whole pizza had ten slices. So I can write six slices divided by Ten slices and this gives me the answer as six over ten So Ajay has eaten six by ten of the pizza or we could say three by five of the pizza We divide six and ten by two in the numerator and denominator So Ajay has eaten three by fifth of the pizza. Now, what about Amrita? Amrita has eaten Four slices, but in the denominator first, we will again write the pizza because she has eaten the remaining slices of the whole pizza. So a pizza in the denominator and Four slices were remaining right because there were total ten slices and out of those six were eaten by Ajay So Amrita ate four slices. That means the fraction of pizza that she ate is four slices divided by Ten slices and that gives us four by ten and if we divide by two on In the numerator and denominator we get two by five As a fraction So Ajay ate three by five of the pizza and Amrita ate two by five of the pizza And I'm sure Amrita is not going to be happy Because Ajay ate more pizza. Let's look at one more problem How many hours are 15 minutes because we know that one hour also means 60 minutes Right now with the same logic two hours will be 120 minutes three hours will be 180 minutes But clearly because 15 minutes are less than 60 minutes The number of hours that 15 minutes represent is going to be less than one hour And that's how we know that the answer is going to be a fraction and because this is a fraction We want to know how much are 15 minutes as a fraction of an hour so that we can represent 15 minutes as Number of hours so we find 15 minutes as a fraction of an hour And so this is one hour in the denominator, which is nothing but 15 divided by 60 minutes, which is One over four and one by four is also known as a quarter. So how many hours are 15 minutes? Quarter hour is 15 minutes. Now, let's go for the other example in the other example We have if four friends received three chocolates each How much fraction of total chocolates each of them has received? Let's just say whatever total chocolates were there were distributed among four friends to find a fraction That each of them received we need to know total chocolates that will be in the denominator because if I spot the word of I have total chocolates after that which will come in the denominator so total chocolates in the denominator and in the numerator We want to find how much fraction of total chocolates each of them has received if we just consider anyone Friend everybody of them has received three chocolates So we will have three in the numerator and the total chocolates are four times three because everybody has got three Chocolates and there were a total four friends of total chocolates will be 12 which is in the denominator Which is four times three and that is three over twelve three over twelve can be simplified as One by four because you can divide in the numerator and denominator by three which gives us one by four So everybody got quarter of the total chocolates because there were four friends and everybody got equal share of total chocolates Each friend get equal part and thus the answer wouldn't change Even if we place any number instead of three chocolate even if we said five chocolates each The total would be five times four and in the numerator. We will have five. Let me just show you So let's say this number here three was five Our answer would be five over five times four and this would still give us one by four So even though we are writing total chocolates and the number of chocolates each one has got this numerator and denominator Is actually showing you that in the numerator We have each individual friend and in the denominator. We have total friends. So that's how we have arrived at the answer here