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Maths 1 Marks Question

Rational Numbers · CBSE STD 7 (CBSE - English Medium). 77 questions.

Questions · Page 2 of 2

1 Marks Question

Question 511 Mark
The standard form of $\frac{-8}{-24}$ is ______.
Answer
The standard form of $\frac{-8}{-24}$ is $\frac{-3}{4}$.Solution:
Given rational number is $\frac{-8}{-24},$ For standrad/ simplest from, $\frac{18+6}{-24+4}=\frac{3}{-4}$ $[\therefore \text{HCF of 18 and 24}=6]$ Hence, the standard from of, $\frac{18}{-24}$ is $\frac{-3}{4}.$
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Question 521 Mark
$\frac{8}{8}\Box\frac{2}{2}$
Answer
$\frac{8}{8}=\frac{2}{2}$ Solution: Given, $\frac{8}{8}=1$ and $\frac{2}{2}=1$ Hence, $\frac{8}{8}=\frac{2}{2}$
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Question 531 Mark
Write each of the following numbers in the form $\frac{\text{q}}{\text{p}},$ where $p$ and $q$ are integers.
Opposite of three-fifths.
Answer
Here, three-fifths $=\frac{3}{5}$
$\therefore$ Opposite of three-fifths $=\frac{5}{3}$
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Question 541 Mark
If $\frac{\text{P}}{\text{q}}$ is a rational number and $m$ is a non-zero integer, then $\frac{\text{P}}{\text{q}}=\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}$
Answer
e.g. Let $m = 1, 2, 3,...$ When $m = 1,$
then, $\frac{\text{P}}{\text{q}}=\frac{\text{P}\times1}{1\times\text{q}}=\frac{\text{P}}{\text{q}}$
When $m = 2,$ then,
$\frac{\text{P}}{\text{q}}=\frac{\text{P}\times2}{\text{q}\times{2}}=\frac{\text{P}}{\text{q}}$
Hence, $\frac{\text{P}}{\text{q}}=\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}$
Note: When both numerator and denominator of a rational number are multiplied/ divide by a same non-zero number, then we get the same rational number
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Question 561 Mark
$\frac{1}{2}=\frac{6}{}$
Answer
$\frac{1}{2}=\frac{6}{12}.$ Solution: Let given exprssion is written as, $\frac{1}{2}=\frac{6}{\text{x}}$ $\Rightarrow\text{x}=12$ Hence, [by cross-multiplication] $\frac{1}{2}=\frac{6}{12}.$
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Question 571 Mark
If $p$ and $q$ are positive integers, then $\frac{\text{P}}{\text{q}}$ is a ______ rational number and $\frac{\text{P}}{\text{-q}}$ is a _____ rational number.
Answer
if $p$ and $q$ are positive integers,
then $\frac{\text{P}}{\text{q}}$ is a positive rational number,
because both numerator and denominator are positive and $\frac{\text{P}}{\text{-q}}$ is a negative rational number,
because denominator is in negative.
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Question 581 Mark
In the following cases, write the rational number whose numerator and denominator are respectively as under:
$25 + 15$ and $81 ÷ 40$
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Question 591 Mark
Zero is a rational number.
Answer
e.g. Zero can be written as $0=\frac{0}{1}.$
We know that, a number of the form where $p, q$ are integers and $\text{q}\neq0$ is a rational number.
So, zero is a rational number.
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Question 601 Mark
The standard form of rational number $-1$ is ______.
Answer
$\therefore HCF$ of given rational number $-1$ is $1.$
For standard form $= -1 + 1 = -1$
Hence, the standard form of rational number $-1$ is $-1.$
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Question 611 Mark
$\frac{-9}{7}\Box\frac{4}{-7}$
Answer
$\frac{-9}{7}<\frac{4}{-7}$Solution:
Given rational numbers are $\frac{-9}{7}$ and $\frac{4}{-7}$ Since, both fractions have same denominator, the fraction which have greater numerator is greator. But in negative number, the numerator which is smailer the greater number. Hence, $\frac{-9}{7}<\frac{4}{-7}$
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Question 621 Mark
$\frac{-3}{5}+\frac{2}{3}=$ ______.
Answer
$\frac{-3}{5}+\frac{2}{3}=\frac{-1}{5}$Solution:
GIven, $\frac{-3}{5}+\frac{2}{3}=\frac{-3+2}{5}$
Hence, $\frac{-3}{5}+\frac{2}{3}=\frac{-1}{5}$
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Question 631 Mark
Zero is the smallest rational number.
Answer
False.
Solution:
Rational numbers can be negative and negative rational numbers are smaller than zero.
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Question 641 Mark
Write the following as rational numbers in their standard forms. $1.2$
Answer
Here, $1.2=\frac{12}{10}=\frac{12\div2}{10\div2}=\frac{6}{5}$
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Question 651 Mark
$\frac{-1}{2}$ is ____ then $\frac{1}{5.}$
Answer
Given rational numbers are $\frac{-1}{2}$ and $\frac{1}{5}.$
$LCM$ of their denominatoes, i.s. $2$ and $5 = 10$
$\therefore\frac{-1\times5}{2\times5}=\frac{-5}{10}$ and $\frac{1\times2}{5\times2}=\frac{2}{10}$
$\because2>-5$
So, $\frac{1}{5}>\frac{-1}{5}$
Hence, $\frac{-1}{2}$ is smaller than $\frac{1}{5.}$
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Question 661 Mark
$\frac{-2}{9}-\frac{7}{9}=$ ______.
Answer
$\frac{-2}{9}-\frac{7}{9}=-1.$ Solution: Given, $=\frac{-2}{9}-\frac{7}{9}=\frac{-2-7}{9}$ $=\frac{-9}{9}=-1$ Hence, $\frac{-2}{9}-\frac{7}{9}=-1$
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Question 671 Mark
On a number line, $\frac{3}{4}$ is to the ______ of Zero$(0).$
Answer
On a number line, $\frac{3}{4}$ is to the right of Zero$(0).$

Note: All the positive numbers lie on the right side of zero on the number line.
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Question 681 Mark
If $\frac{\text{P}}{\text{q}}$ is a rational number and $m$ is a non-zerocommon divisor of $p$ and $q,$ then, $\frac{\text{P}}{\text{q}}=\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}$
Answer
e.g. Let $m = 1, 2, 3,...$ When $m = 1,$
then, $\frac{\text{P}}{\text{q}}=\frac{\text{P}+1}{\text{q}+1}=\frac{\text{P}}{\text{1}}\div\frac{\text{q}}{\text{1}}=\frac{\text{P}}{\text{1}}\times\frac{1}{\text{q}}=\frac{\text{P}}{\text{q}}$
When $m = 2,$
then, $\frac{\text{P}}{\text{q}}=\frac{\text{P}+2}{\text{q}+2}=\frac{\text{P}}{\text{2}}\div\frac{\text{q}}{\text{2}}=\frac{\text{P}}{\text{2}}\times\frac{2}{\text{q}}=\frac{\text{P}}{\text{q}}$
Hence, $\frac{\text{P}}{\text{q}}=\frac{\text{P}+\text{m}}{\text{q}+\text{m}}$
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Question 691 Mark
Express $\frac{3}{4}$ as a rational number with denominator: $36$
Answer
To make the denominator $36,$ we have to multiply numerator and denominator by $9.$
$\therefore\frac{\text{3}\times9}{4\times9}=\frac{27}{36}$
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Question 701 Mark
$\frac{-3}{8}$ is a ____ rational number.
Answer
The given rational number $\frac{-3}{8}$ is a negative number,
because its numerator is negative integer.
Hence, $\frac{-3}{8}$ is a negative rational number.
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MCQ 711 Mark
Find the odd one out of the following and give reason.
  • ✓
    $\frac{-3}{7}$
  • B
    $\frac{-9}{15}$
  • C
    $\frac{24}{20}$
  • D
    $\frac{35}{25}$
Answer
Correct option: A.
$\frac{-3}{7}$
From the above given rational numbers, we can see that $\frac{-3}{7}$ is in its lowest form while others have common factor in numerator and denominator.
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Question 721 Mark
The standard form of $\frac{-8}{-36}$ is ______.
Answer
The standard form of $\frac{-8}{-36}$ is $\frac{2}{9}$.

Solution:

Given rational number is $\frac{-8}{-36},$

For standrad/ simplest from,

$\frac{-8+4}{-36+4}=\frac{-2}{-9}=\frac{2}{9}$

$[\therefore \text{HCF of 8 and 36}=4]$

Hence, the standard from of,

$\frac{-8}{-36}$ is $\frac{2}{9}.$

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Question 731 Mark
$\frac{-16}{24}$ and $\frac{20}{-15}$ reoresent _____ rational numbers.
Answer
$\frac{-16}{24}$ and $\frac{20}{-15}$ reoresent diffferent rational numbers.
Solution:
Given numbers are,
$\frac{-16}{24}=\frac{-4}{6}=\frac{-2}{3}$
and $\frac{20}{-16}=\frac{-5}{4}$
$\because\frac{-16}{24}\neq\frac{20}{-16}$
Hence, $\frac{-16}{24}$ and $\frac{20}{-16}$ represent different rational numbers.
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Question 741 Mark
Express $\frac{3}{4}$ as a rational number with denominator: $-80$
Answer
To make the denominator $-80,$ we have to multiply numerator and denominator by $-20.$
$\therefore\frac{{3}\times(-20)}{4\times(-20)}=\frac{-60}{-80}$
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Question 751 Mark
$\frac{-3}{5}$ is ____ then $0.$
Answer
Since, $\frac{-3}{5}$ lies on the left side of zero $(0).$
On the number kine, $\frac{-3}{5}$ is smaller than $0$ i.e. $\frac{3}{5}<0.$
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Question 761 Mark
Match the following:
  Column $I$   Column $II$
$(i)$ $\frac{\text{a}}{\text{b}}\div\frac{\text{a}}{\text{b}}$ $(a)$ $\frac{-\text{a}}{\text{b}}$
$(ii)$ $\frac{\text{a}}{\text{b}}\div\frac{\text{c}}{\text{d}}$ $(b)$ $-1$
$(iii)$ $\frac{\text{a}}{\text{b}}\div(-1)$ $(c)$ $1$
$(iv)$ $\frac{\text{a}}{\text{b}}\div\frac{-\text{a}}{\text{b}}$ $(d)$ $\frac{\text{bc}}{\text{ad}}$
$(v)$ $\frac{\text{b}}{\text{a}}\div\Big(\frac{\text{d}}{\text{c}}\Big)$ $(e)$ $\frac{\text{ad}}{\text{bc}}$
Answer
  Column $I$   Column $II$
$(i)$ $\frac{\text{a}}{\text{b}}\div\frac{\text{a}}{\text{b}}$ $(c)$ $1$
$(ii)$ $\frac{\text{a}}{\text{b}}\div\frac{\text{c}}{\text{d}}$ $(e)$ $\frac{\text{ad}}{\text{bc}}$
$(iii)$ $\frac{\text{a}}{\text{b}}\div(-1)$ $(a)$ $\frac{-\text{a}}{\text{b}}$
$(iv)$ $\frac{\text{a}}{\text{b}}\div\frac{-\text{a}}{\text{b}}$ $(b)$ $-1$
$(v)$ $\frac{\text{b}}{\text{a}}\div\Big(\frac{\text{d}}{\text{c}}\Big)$ $(d)$ $\frac{\text{bc}}{\text{ad}}$
$i. $ Given, $\frac{\text{a}}{\text{b}}+\frac{\text{a}}{\text{b}}$
$=\frac{\text{a}}{\text{b}}\times\frac{\text{b}}{\text{a}}$
$=1$
$ii.$ Given, $\frac{\text{a}}{\text{b}}+\frac{\text{c}}{\text{d}}$
$=\frac{\text{a}}{\text{b}}\times\frac{\text{d}}{\text{c}}$
$=\frac{\text{ad}}{\text{bc}}$
$iii.$ Given, $\frac{\text{a}}{\text{b}}+(-1)$
$=\frac{\text{a}}{\text{b}}\times(-1)$
$=\frac{-\text{a}}{\text{b}}$
$iv.$ Given, $\frac{\text{a}}{\text{b}}+\frac{-\text{a}}{\text{b}}$
$=\frac{\text{a}}{\text{b}}\times\Big(\frac{-\text{b}}{\text{a}}\Big)$
$=-1$
$v.$ Given, $\frac{\text{b}}{\text{a}}+\Big(\frac{\text{d}}{\text{c}}\Big)$
$=\frac{\text{b}}{\text{a}}\times\frac{\text{c}}{\text{d}}$
$=\frac{\text{bc}}{\text{ad}}$
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Question 771 Mark
Sum of two rational numbers is always a rational number.
Answer
True.Solution:
Sum of two rational numbers is always a rational number, it is true. $\frac{1}{2}+\frac{2}{3}=\frac{3+4}{6}=\frac{7}{6}$
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