Suppose mn and pq are two positive rational numbers- Where do m - pn - q lie- with respect to mn and pq-

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Standard VIII

Mathematics

Rational Numbers between Two Rational Numbers

Suppose mn ...

Question

Suppose $\frac{m}{n}$ and $\frac{p}{q}$ are two positive rational numbers. Where do $\frac{m + p}{n + q} l i e,$ with respect to $\frac{m}{n}$ and $\frac{p}{q}$ ?

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Solution

Let $\frac{m}{n} = \frac{1}{2} = 0.5$ and $\frac{p}{q} = \frac{3}{4} = 0.75$

Individually we have, $m = 1, n = 2, p = 3$ and $q = 4$ .

Now consider,

$\frac{m + p}{n + q} = \frac{1 + 3}{2 + 4} = \frac{4}{6} = \frac{2}{3} = 0.66$

Hence, the above drawn number line shows that $\frac{m + p}{n + q}$ lies between $\frac{m}{n}$ and $\frac{p}{q}$ .

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Suppose mn and pq are two positive rational numbers. Where do m+pn+qlie, with respect to mn and pq?

Let mn=12=0.5 and pq=34=0.75Individually we have, m=1,n=2,p=3 and q=4.Now consider,m+pn+q=1+32+4=46=23=0.66 Hence, the above drawn number line shows that m+pn+q lies between mn and pq.

Suppose $\frac{m}{n}$ and $\frac{p}{q}$ are two positive rational numbers. Where do $\frac{m + p}{n + q} l i e,$ with respect to $\frac{m}{n}$ and $\frac{p}{q}$ ?