Ex.9.1 Q7 Rational-Numbers Solution - NCERT Maths Class 7

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Question

Rewrite the following rational numbers in the simplest form:

(i) \(\begin{align}\frac{ - 8}{6}\end{align}\) 

(ii) \(\begin{align}\frac{25}{45}\end{align}\)

(iii) \(\begin{align}\frac{ -44}{72}\end{align}\)

(iv)  \(\begin{align}\frac{ -8}{10}\end{align}\)

Text Solution

What is known?

Rational numbers.

What is unknown?

Simplest form of the given rational numbers.

Reasoning:

While solving such type of questions find the \(\begin{align}H.C.F\end{align}\) of numerator and denominator and then divide both numerator and denominator by the \(\begin{align}H.C.F\end{align}\). After dividing it you will get the simplest form of the rational number.
 

Steps:

(i) \(\begin{align}\frac{ - 8}{6}\end{align}\) 
\(\begin{align}H.C.F\end{align}\).of \(\begin{align}8\end{align}\) and \(\begin{align}6\end{align}\) is two. Dividing the numerator and denominator by \(\begin{align}H.C.F\end{align}\)., we get

\[\begin{align}\frac{{ - 8 \div 2}}{{6 \div 2}} = \frac{{ - 4}}{3}\end{align}\]

 

(ii) \(\begin{align}\frac{25}{45}\end{align}\)
\(\begin{align}H.C.F\end{align}\) of \(\begin{align}25\end{align}\) and \(\begin{align}45\end{align}\) is \(\begin{align} 5\end{align}\). Dividing the numerator and denominator by \(\begin{align}H.C.F\end{align}\)., we get,

\[\begin{align}\frac{{25 \div 5}}{{45 \div 25}} = \frac{5}{9}\end{align}\]

 

(iii) \(\begin{align}\frac{ -44}{72}\end{align}\)
\(\begin{align}H.C.F\end{align}\) of \(\begin{align}44\end{align}\) and \(\begin{align}72\end{align}\) is \(\begin{align}4\end{align}\). Dividing the numerator and denominator by \(\begin{align}H.C.F\end{align}\)., we get,

\[\begin{align}\frac{{ - 44 \div 4}}{{72 \div 4}} = \frac{{ - 11}}{{18}}\end{align}\]

(iv)  \(\begin{align}\frac{ -8}{10}\end{align}\)
\(\begin{align}H.C.F\end{align}\) of \(\begin{align}8\end{align}\) and \(\begin{align}10\end{align}\) is \(\begin{align}2\end{align}\). Dividing the numerator and denominator by \(\begin{align}H.C.F\end{align}\)., we get,

\[\begin{align}\frac{{ - 8 \div 2}}{{10 \div 2}} = \frac{{ - 4}}{5}\end{align}\]