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Q4) Find ten rational numbers between, \frac{-2}{5}\ \&\ \frac{1}{2}

Answer:

Solution 4:

Given numbers can be written as \frac{-2\times2}{5\times2}\ \&\ \frac{1\ \times5}{2\times5}\ =\ \frac{-4}{10}\ \&\ \frac{5}{10}

Therefore, Ten rational numbers between \frac{-4}{10}\ \&\ \frac{5}{10} are,

\frac{-3}{10},\ \frac{-2}{10},\frac{-1}{10},\ 0,\ \frac{1}{10},\ \frac{2}{10},\ \frac{3}{10},\ \frac{4}{10}

Hi everyone, welcome to today's session in this session we are going to learn how to find rational numbers between the given two rational numbers, so the question for today is find10 rational numbers between minus 2 by 5and 1 by 2. now here before I solve this I want you to try solving it on your own I know it will take a minute so why don't you pause this video go solve it and come back once you're done solving all right I hope you tried solving it on your own now it's my turn to explain so let's go over the question one more time we need to find ten rational numbers that lie between minus two by five and one byte now here we can see that we have two rational numbers and both of them have different denominators so it is difficult for us to find the numbers that lie between these two numbers to make our job easy what we are going to do is we are going to make the denominators of these two rational numbers equal and how do we do that we do that by taking the lcm just a second we do that by taking the lcm of 5 and 2. so when we take lcm of 5 and 2 we get 5 so lcm becomes 5 multiplied by 2 just now it's our job to convert these rational numbers into equivalent rational numbers with the same denominator so let's start with minus 2 by 5. we want the denominator to be 10 so what we do is multiply both the numerator and the denominator by doing so the denominator will become 10 and we will get an equivalent rational number to minus 2 by 5. now we are going to use the same method to calculate to find the equivalent number of 1 by 2 whose denominator is 10 so this time we are going to multiply both the numerator and denominator with yes you guessed it right 5. so we are going to have 5 by 10 now it's damn easy for us to find the numbers between minus 4 by 10 and 5 by 10 right so we are going to start with minus 3 by 10 minus 2 by 10 minus 1 by 10 0 plus 1 by 10 plus 2 by 10 sorry plus 3 by 10 plus 4 byte how many rational numbers have we got let's count so we have one two three four five six seven eight oh we got only eight rational numbers but the question has
asked us to find out ten rational numbers so how are we going to find the other two all right now we are going to use a different method to find rational numbers between two rational numbers let's consider plus 1 by 10 plus 2 y to find the number that lies between plus 1 by 10 plus 2 by 10 we are going to use the formula a plus b by 2. so here a will be1 by 10 b will be 2 by 10 and we are going to find the number that lies exactly in the middle of these two numbers by using this formula so now since the denominators are same it's easy for us to add this becomes 3 by 10 by 2 which can also be written as 3 by 10 divided by 2 so now I'm going to keep the first fraction change the division to multiplication and flip the second to get 1 by 2. so this number the number between 1 by 10 and 2 by 10 is 3 by 20 similarly we are going to find the number that lies between 3 by 10 and 4 bytes we are going to use the same method so let us go over this 3 by 10 plus 4 by 10 the whole divided by 2 so that will be 7 by 10 by 2 which can also be written as 7 by 10 divided by 2. so now I'm going to keep the first number change the division to multiplication and flip 2 by 1 to 1 byte so this will give us 7 by 20 so apart from the eight rational numbers we found using the first method we have two more rational numbers which is 3 by 20 and 7 by 20 which lie between minus 2 by 5 and 1 byte I know some of you saw this on your own
and got the correct answer so here is an ice cream for all of you who got it right without my help all right I hope you found the session helpful and enjoyable I will see you in the next session until then bye

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