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

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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 $\frac{p}{q}$ ?

Open in App

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 $\frac{p}{q}$ .

Suggest Corrections

Similar questions

Suppose m/n and p/q are two positive rational numbers. Where does lie, with respect to m/n and p/q?

Q. If two positive integers m and n are expressible in the form m = pq³ and n = p³q², where p, q are prime numbers, then HCF (m, n) =
(a) pq
(b) pq2
(c) p³q²
(d) p²q²

Q. Consider the following relations:
R = {(x, y) | x, y are real numbers and x = wy for some rational number w};
S = {

(\frac{m}{n}, \frac{p}{q})

| m, n, p and q are integers such that n, q

\neq

0 and qm = pn}.
Then

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as:
(Here, n and m are non-negative integers.)

Q. Let n =

P^{2} q

, where p and q are distinct prime numbers. How many numbers m satisfy

1 \leq m \leq

n and gcd (m , n) = 1? Note that gcd (m,n) is the greatest common divisor of m and n.

Join BYJU'S Learning Program

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 $\frac{p}{q}$ ?