Question

express each of the following as the sum of a integer and a rational number.
(a) 12/5
(b) -25/9​

Answer 1

How to solve the question?

To turn an improper fraction into a mixed fraction, we first divide the denominator by the numerator. The denominator remains the same, the remainder becomes the numerator and the quotient becomes the whole number. We'll solve this question using the same method through which we turn an improper fraction into a mixed fraction.

$\bf{(a)\:\dfrac{12}{5}}$

$\sf\qquad\quad2\\ \begin{array}{cc} \cline{2 - 2}\sf 5 )&\sf \ 12\\&\sf - 10 \\ \cline{2-2} & \sf \ \002 \\ \cline{2-2} \end{array}$

$\sf\longrightarrow{Quotient\:=\:2}$

$\sf\longrightarrow{Remainder\:=\:2}$

$\sf\longrightarrow{Rational\:number\:formed\:=\:2\dfrac{2}{5}}$

$\sf{Thus,\:\dfrac{12}{5}\:=\:2\:+\:\dfrac{2}{5}}$

$\bf{(b)\:\dfrac{-25}{9}}$

$\sf\qquad\quad2\\ \begin{array}{cc} \cline{2 - 2}\sf 9 )&\sf \ 25\\&\sf - 18 \\ \cline{2-2} & \sf \ \007 \\ \cline{2-2} \end{array}$

$\sf\longrightarrow{Quotient\:=\:2}$

$\sf\longrightarrow{Remainder\:=\:7}$

$\sf\longrightarrow{Rational\:number\:formed\:=\:-2\dfrac{7}{9}}$

$\sf{Thus,\:\dfrac{-25}{9}\:=\:-2\:+\:\dfrac{7}{9}}$