Question

The sum of two rational numbers is 5 1/2. If one of the numbers is 6 3/14, find the other number.

Answer 1

`\text{The sum of two rational numbers is}\ 5(1)/(2).\\\\\text{One of the numbers is}\ 6(3)/(14).\\\\5(1)/(2)+x=6(3)/(14)\Rightarrow x=5(1)/(2)-6(3)/(14)\\\\\text{We must find the common denominator. It's 14.}\\\\14=2\cdot7\to5(1)/(2)=5(1\cdot7)/(2\cdot7)=5(7)/(14)\\\\5(7)/(14)-6(3)/(14)=-\left(6(3)/(14)-5(7)/(14)\right)=-\left(5(14+3)/(14)-5(7)/(14)\right)`

`=-\left(5(17)/(14)-5(7)/(14)\right)=-(10)/(14)=-(10:2)/(14:2)=-(5)/(7)\\\\Answer:\ -(5)/(7)\\\\Check:\\\\6(3)/(14)+\left(-(5)/(7)\right)=6(3)/(14)-(5)/(7)=6(3)/(14)-(5\cdot2)/(7\cdot2)=6(3)/(14)-(10)/(14)\\\\=5(14+3)/(14)-(10)/(14)=5(17)/(14)-(10)/(14)=5(7)/(14)=5(7:7)/(14:7)=5(1)/(2)\ \ \ CORRECT`