 Hello and welcome to the session. In this session we will discuss percentage. Percentage is basically a way of comparing quantities. We know that percent means hundred and basically the percentages are the numerators of fractions with denominator hundred. Now let's discuss the meaning of percentage. We already have seen that percent means hundred and this percent is represented by the symbol this and it means hundreds that is if we say that 92 percent marks this means that 92 marks out of hundred or we can also say that 92 percent is equal to 92 upon hundred or 0.92. Now we have percentage when total is not hundred. Now if the total items do not add to hundred then to find out the percentage of item we have to convert the fraction to an equivalent fraction with denominator hundred. Suppose that a student obtains marks 20 out of 50. Now here as you can see that the total is not hundred instead is 50. Let's find out the percentage of marks obtained by the student. Now this can be done by three methods. Let's see what is the first method of doing so. First let's write the fraction so that would be 20 upon 50. Now we multiply this fraction by hundred upon hundred. This would give us 40 upon hundred so that is equal to 40 percent that is the student obtains 40 percent marks. Now let's see the next method next is the unitary method. In this we have that the marks out of 50 is equal to 20 then we need to find out the marks out of hundred and this would be equal to 20 upon 50 into 100. So this is equal to 40 that is the student obtains 40 marks out of 100 thus the percentage of marks does obtain this 40 percent. Now the next method let's consider the fraction again that is 20 upon 50. We need to convert this denominator 50 to 100. So for this we multiply the numerator and denominator of this fraction by 2 so this is equal to 40 upon 100 which gives us that the marks obtained by the student is 40 percent. So any of these three methods can be used to find out the percentages when total is not hundred. Next we have converting fractional numbers to percentage. Now we know that the fractional numbers can have different denominators. When we need to compare the fractional numbers we should have the common denominator and it is always convenient to make the denominator hundred to do the comparison of the fractional numbers that is we convert the fractional numbers to the percentages. Consider the fraction number 3 upon 5 we need to convert this fraction number to percentage. So for this we multiply this number 3 upon 5 that is the fractional number by 100 percent and this comes out to be equal to 60 percent. So this fraction number 3 upon 5 is converted to the percentage that is 60 percent. Next we need to convert decimals to percentage like you consider the decimal 0.95 we need to convert this to percentage. So for this we multiply this decimal by 100 percent. So this would be equal to 95 upon 100 into 100 percent and this is equal to 95 percent. So this decimal is converted to percentage that is 95 percent. Next we discuss converting percentages to fractions or decimals. Consider 3 percent let's see how we write this 3 percent in fraction. In fraction it is written as 3 upon 100 then in decimal it is written as 0.03. We should remember one thing that parts always add to give a whole that is when we add all the parts that form a whole we get 100 percent. So if we are given one part we can definitely find out the other part like suppose in an office percentage of girls working there is 30 percent then the percentages of boys can be find out by 100 minus 30 percent which is equal to 70 percent. Next we have fun with estimation percentages help us to estimate the parts of an area. Consider this figure we need to find the percent of figure that is shaded. For this first we need to find the fraction of the figure that is shaded. Now as you can see that this figure has five parts and out of these five parts three parts are shaded. So the fraction that we obtain is 3 upon 5. Now we convert this fraction to percent by multiplying this by 100 percent so this gives us 60 percent that is we say that 60 percent of the figure is shaded. So this completes the session hope you have understood the concept of percentages.