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Ratio Ratio Ratio means relations between two numbers are called ration or in other words comparison between two numbers or quantities are called ratio and we can also represent ration in terms of fraction. Suppose that if we have two numbers M and N then we want to represent these two numbers in ratio then M: N or M/N This is the way we are represent the ration of two numbers or quantities and as we seen above M/N is rational number and first representation is ratio representation and in second representation there is other representation of ration that is in fraction. Now we elaborate What is a Ratio In mathematics ratio means relation between numbers or quantities or we take some examples to make you understand the meaning of ratio.

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Suppose there are 5 pens and 3 pencils then if we want to express pens and pencils in ratio form and pen is represent by M and pencil is represent by N then M: N = Pen: pencil = 5: 3 or M/N = pen/pencil = 5/3 Now to understand ratio more clearly we are going to find out the ratio so taking one question in which we find the ratio so if we have value of N = 4 and value of ratio of M: N is 3: 6 then find we have to find the value of M So we saw that value of M: N is equal to 3: 6 so we express M: N as M/N so M/N = 3/6 Now we also know that value of N = 4 so we have to put the value of N in above equation then M/4 = 3/6 Then, after cross multiplication M = 12/6 After simplify the above equation M=2 So the value of M is 2 now we represent M: N = 2: 4 Then we can say that ration between M and N is 2 and 4 respectively. Now if we are going to multiply the above ratio by any number then we have to kept in mind tha.

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when we multiplying any ratio by any number we have to multiply both the sides so that after simplification we get the same ration that we have in question or given problem. Let’s take an example of ratio in which we are going to multiply the given ratio and after solving it again we get the original ratio as we have in starting. Suppose we have a ratio M: N is 5:10 Now if we are going to multiply the above ratio by 5 then we have to multiply the ratio both the sides. So, multiply above ratio by 5 M × 5: N × 5 Now putting the values of M and N 5 × 5: 10 × 5 Then we have 25: 50 Now if we are going to prove that the given ratio is equal to the result ratio which we get after multiplying the ratio so, 5: 10 = 25: 50 Now if we going to simplify both the sides then we get 1:2 = 1:2 So we can say that both results are same.

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