Question 90 (c)

Given that, $\frac{p}{q}$ and $\frac{r}{s}$ are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers, we say that
$\frac{☐}{☐} < \frac{☐}{☐}$ , if $p \times s > r \times q$

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Solution

Given, $p \times s > r \times q$
$\Rightarrow \frac{p}{q} > \frac{r}{s}$ [by transferring sides]

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Question 90 (a)

Given that, $\frac{p}{q}$ and $\frac{r}{s}$ are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers, we say that
$\frac{☐}{☐} < \frac{☐}{☐}$ , if $p \times s < r \times q$

In each of the following, fill in the blanks so as to make the statement true:

(i) A number which can be expressed in the form $p q$ , where $p$ and $q$ are integers and $q$ is not equal to zero, is called a .....

(ii) If the integers $p$ and $q$ have no common divisor other than 1 and $q$ is positive, then the rational number $p q$ is said to be in the ....

(iii) Two rational numbers are said to be equal, if they have the same .... form.

(vi) $\frac{a}{b} = \frac{a \div m}{b \div}$

(v) If $p$ and $q$ are positive integers, then $p q$ is a ..... rational number and $p - q$ is a ..... rational number.

(vi) The standard form of −1 is ...

(vii) If $p q$ is a rational number, then $q$ cannot be ....

(viii) Two rational numbers with different numerators are equal, if their numerators are in the same .... as their denominators.

Question 5
The points P, Q R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S