question_answer

Takings =\[\frac{-4}{9}\], y =\[\frac{5}{12}\] and z =\[\frac{7}{18}\], find:

(a) the rational number which when added to x gives y.

(b) the rational number which subtracted from y gives z.

(c) the rational number which when added to z gives us x.

(d) the rational number which when multiplied by y to get x.

Answer:

(a) Let we add A to x then gives y

\[A+x=y\Rightarrow A+\left( \frac{-4}{9} \right)|=\frac{5}{12}\]

\[A=\frac{5}{12}-\left( \frac{-4}{9} \right)\]

\[=\frac{5}{12}+\frac{4}{9}\]

\[=\frac{5\times 3+4\times 4}{36}\]

\[=\frac{5+16}{36}=\frac{31}{36}\]

(b) Let us subtract A from y gives z

\[yA=z\Rightarrow \frac{5}{12}-A=\frac{7}{18}\]

\[-A=\frac{7}{18}-\frac{5}{12}=\frac{7\times 2-5\times 3}{36}=\frac{14-15}{36}=\frac{-1}{6}\]

\[A=\frac{1}{6}\]

(c) Let A is added to z gives x

\[A+z=x\Rightarrow A+\frac{7}{18}=\frac{-4}{9}\]

\[A=\frac{-4}{9}-\frac{7}{18}=\frac{-4\times 2-7}{18}=\frac{-8-7}{18}=\frac{-15}{18}=\frac{-5}{6}\] [both are divided by 3]

(d) Let A be multiplied by y to get x

\[A\times \frac{5}{12}=\frac{-4}{9}\]

\[A=\frac{-4}{9}\times \frac{12}{5}\]

\[A=\frac{-16}{15}\]