What should be added to twice the rational number −73 to get 37?

Hint: Assume that the number that should be added is x. Now, first find the value of twice the rational number −73 by multiplying the numerator with 2. Now, take the sum of the obtained rational number with x and equate it with 37 to form a linear equation in x. Solve this equation for the value of x to get the answer. Complete step by step solution: Here we have been asked to find the number that must be added to twice the rational number −73 to get 37 as the resultant fraction. Now, let us assume that the number that should be added is x. The meaning of twice of −73 means we need to multiply the numerator of this rational number with 2, so we get, ⇒2×(−73)=−143 So we need to add −143 with x to get 37, therefore the expression will be given as: ⇒x+(−143)=37 Clearly this is a linear equation in x so we need to solve for the value of x. Leaving x in the L.H.S and taking all other terms to the R.H.S we get, ⇒x=37−(−143) We know that (−1)×(−1)=1 so we get, ⇒x=37+143 Taking the L.C.M of 7 and 3 which is 21 we get, ⇒x=(3×3)+(14×7)21⇒x=9+9821∴x=10721 Hence the required number that must be added is 10721. Note: You must remember how to add and subtract two rational numbers. To find the value of twice the rational number always multiply the numerator with 2 and not the denominator. Note that to add fractions we take the L.C.M of their denominators and not numerators. Here both 3 and 7 were prime numbers and we know that the L.C.M of two prime numbers is simply their product.