Subtracting Rational Numbers How can a number be a rational one?! Any number could be a rational if it represents a ratio between two integers A and B where B is the denominator which doesn't equal zero. like for example, 3 over 4, 17 over 45 and 101 over 585 .. This term was first to be released by the Italian Mathematician: Giuseppe Peano. Case 1: If we are subtracting 3 from 7, the result is concretely 4 but, if I won't to maximize this 4 to make it equal to 4 over 5, you would try to multiply (7-3) by 1 over 5. We can distribute this as 7 over 5 minus 3 over 5 which equals 4 over 5 surely. The note here is that: in case of having a same denominator, we fix this denominator and add the numerators easily. Case 2: If we have two different denominators like 12 and 18, we look for their H.C.F which is 6 as 12= 6*2 and 18= 6*3, so we discard this 6.. so we are left with 2 and 3 where 2 is odd for 18, and 3 is odd for 12. We multiply 1/18 with 2/2 which actually equals 1 and it doesn't change its quantity. and 1/12 with 3/3.. we get 3/36 - 2/36 = 1/36. Case 3: If we have denominators that are not equal or share a common factor, we try the general and most popular case. in the example 3/5 - 3/7, denominators 5 and 7 are odd to each other so, we try saying that: 3/5 * 7/7 and 3/7 * 5/5 equals 21/35 - 15/35 which equals 6/35 and here it is. Exercises: I) 6/7 - 5/9 II) 1/2 - 1/4 III) 5 - 3/5 IV) 7/10 - 1/5 V) 60/61 - 60/62 Answers: I) 19/63 II) 1/4 III) 22/5 IV) 1/2 V) 60/3782 or 30/1891 (The Hardest)

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