Question 11 Mark
Draw the number line and represent the following rational number on it:
$\frac{22}{-7}$
View full question & answer→Question 21 Mark
In the following state if the statement is true (T) or false (F):
Every integer is a rational number.
AnswerTrue.Solution:
Every integer can be expressed in the form of $\frac{\text{p}}{\text{q}},$ where q is not zero.
View full question & answer→Question 31 Mark
Draw the number line and represent the following rational number on it:
$\frac{3}{4}$
View full question & answer→Question 41 Mark
In the following state if the statement is true (T) or false (F):
Two rational numbers with different numerators cannot be equal.
AnswerFalse.
Solution:
They can be equal, when simplified further.
View full question & answer→Question 51 Mark
Express the following as rational number with positive denominator:
$\frac{19}{-7}$
AnswerMultiplying the number by -1,
we get:
$\frac{19}{-7}=\frac{19\times-1}{-7\times-1}=\frac{-19}{7}$
View full question & answer→Question 61 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
-49
AnswerRational number with numerator:
-49 as numerator:
$\frac{168}{6}\&\frac{-294}{6}=\frac{28}{-49}$
(Dividing the numerator and denomintor by 6)
View full question & answer→Question 71 Mark
If each of the following pairs represents a pair of equivalent rational numbers, Find the values of x:
$\frac{2}{3}\text{ and }\frac{5}{\text{x}}$
Answer$\frac{2}{3}=\frac{5}{\text{x}},\text{ then }\text{x}={5}\times\frac{3}{2}=\frac{15}{2}$
View full question & answer→Question 81 Mark
Draw the number line and represent the following rational number on it:
$\frac{-31}{3}$
View full question & answer→Question 91 Mark
Fill in the blanks:
$\frac{-6}{\dots}=\frac{3}{11}=\frac{\dots}{-55}$
AnswerHere, $\frac{\frac{-6}{2}}{\frac{-22}{-2}}=\frac{3}{11}$
Also, $\frac{-6}{-22}=\frac{3\times-5}{11\times-5}=\frac{-15}{-55}$
Therefore, $\frac{-6}{-22}=\frac{3}{11}=\frac{-15}{-55}$
View full question & answer→Question 101 Mark
Express $\frac{3}{4}$ as a rational number with numerator:
20
Answer$\frac{3}{4}$ as a rational number with denominator:
20 is:
$\frac{3\times5}{4\times5}=\frac{15}{20}$
(Multiplying numerator and denominator by 5)
View full question & answer→Question 111 Mark
In the following state if the statement is true (T) or false (F):
8 can be written as a rational number with any integer as numerator.
Question 121 Mark
Express $\frac{168}{-294}$ as a rational number with numerator:
14
AnswerRational number with numerator:
14 as numerator:
$\frac{168}{42}\&\frac{-294}{21}=\frac{-8}{14}$
(Dividing the numerator and denomintor by -21)
View full question & answer→Question 131 Mark
In the following, fill in the blanks so as to make the statement true:
If $\frac{\text{p}}{\text{q}}$ is a rational number, then q cannot be _______.
AnswerIf $\frac{\text{p}}{\text{q}}$ is a rational number, then q cannot be Zero.
View full question & answer→Question 141 Mark
Write down the rational whose numerator is the smallest three digit number and denominator is the largest four digit number.
AnswerSmallest three digit number $=100$
Largest four digit number $=9999$
Therefore rational number $=\frac{100}{9999}$
View full question & answer→Question 151 Mark
Determine whether the following rational numbers are in the lowest form or not:
$\frac{24}{128}$
AnswerWe observe that 24 and 128 is not 1.Thus, given rational number is not in its simplest form.
View full question & answer→Question 161 Mark
If each of the following pairs represents a pair of equivalent rational numbers, Find the values of x:
$\frac{13}{6}\text{ and }\frac{-65}{\text{x}}$
Answer$\frac{13}{6}=\frac{-65}{\text{x}}$
$\Rightarrow\text{Then, }\text{x}=\frac{6}{13}\times(-65)=\times(-5)=-30$
View full question & answer→Question 171 Mark
Express $\frac{3}{4}$ as a rational number with numerator:
-80
Answer$\frac{3}{4}$ as a rational number with denominator:
-80 is:
$\frac{3\times-20}{4\times-20}=\frac{-60}{-80}$
(Multiplying numerator and denominator by -20)
View full question & answer→Question 181 Mark
Which of the two rational numbers in the following pairs of rational numbers is smaller?
$\frac{-12}{5},-3$
Answer$\frac{-12}{5}\text{ and } -3=\frac{-3\times5}{1\times5}=\frac{-15}{5}$
Therefore $\frac{-12}{5}>-3$
View full question & answer→Question 191 Mark
Express $\frac{2}{5}$ as a rational number with numerator:
500
Answer$\frac{2}{5}$ as a rational number with denominator:
500 is:
$\frac{2\times250}{5\times250}=\frac{500}{1250}$
(Multiplying numerator and denominator by 250)
View full question & answer→Question 201 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
1470
AnswerRational number with numerator:
1470 as numerator:
$\frac{168\times-5}{-294\times-5}=\frac{-840}{1470}$
(Dividing the numerator and denomintor by -5)
View full question & answer→Question 211 Mark
Express the following as rational number with positive denominator:
$\frac{(-15)}{(-28)}$
AnswerRational number with positive denominators:
Multiplying the number by -1,
We get:
$\frac{-15}{28}=\frac{-15\times-1}{-28\times-1}=\frac{15}{28}$
View full question & answer→Question 221 Mark
In the following, fill in the blanks so as to make the statement true:
If m is a common divisor of a and b,
$\text{then }\frac{\text{a}}{\text{b}}=\frac{\text{a}\div\text{m}}{\dots}$
AnswerIf m is a common divisor of a and b,
$\text{then }\frac{\text{a}}{\text{b}}=\frac{\text{a}\div\text{m}}{\text{b}\div\text{m}}$
View full question & answer→Question 231 Mark
Express $\frac{2}{5}$ as a rational number with numerator:
-750
Answer$\frac{2}{5}$ as a rational number with denominator:
-750 is:
$\frac{2\times-375}{5\times-375}=\frac{-750}{-1875}$
(Multiplying numerator and denominator by -375)
View full question & answer→Question 241 Mark
In the following, find an equivalent form of the rational number having common denominator:
$\frac{3}{4}\text{ and }\frac{5}{12}$
AnswerEquivalent forms of the rational number having common denominator are:
$\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}\text{ and }\frac{5}{12}$
View full question & answer→Question 251 Mark
In the following, fill in the blanks so as to make the statement true:
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.
AnswerIf p and q are positive Integers, then $\frac{\text{p}}{\text{q}}$ is a Positive rational number rational number and $\frac{\text{p}}{-\text{q}}$ is a negative rational number rational number.
View full question & answer→Question 261 Mark
Write down the denominator of the following rational numbers:
$\frac{-15}{-82}$
View full question & answer→Question 271 Mark
Fill in the blanks by the correct symbol out of >, =, or <:
$\frac{-6}{7}\dots\frac{7}{13}$
AnswerBecause every positive number is greater than a negative number,
$\frac{-6}{7}<\frac{7}{13}$
View full question & answer→Question 281 Mark
Write down the numerator of the following rational numbers:
$\frac{-17}{-21}$
View full question & answer→Question 291 Mark
Draw the number line and represent the following rational number on it:
$\frac{-3}{16}$
View full question & answer→Question 301 Mark
In the following, fill in the blanks so as to make the statement true:
Two rational numbers are said to be equal, if they have the same ______ form.
AnswerTwo rational numbers are said to be equal, if they have the same Standard form.
View full question & answer→Question 311 Mark
Write down the numerator of the following rational numbers:
$\frac{15}{-4}$
View full question & answer→Question 321 Mark
Express $\frac{3}{5}$ as a rational number with numerator:-15
AnswerRational number with numerator:
-15 is:
$\frac{3\times-5}{5\times-5}=\frac{-15}{-25}$
(Multiplying numerator and denominator by -5)
View full question & answer→Question 331 Mark
Write down the denominator of the following rational numbers:0
Question 341 Mark
In the following state if the statement is true (T) or false (F):
8 can be written as a rational number with any integer as denominator.
Question 351 Mark
Draw the number line and represent the following rational number on it:
$\frac{3}{8}$
View full question & answer→Question 361 Mark
In the following, fill in the blanks so as to make the statement true:
A number which can be expressed in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and q is not equal to zero, is called a ______.
AnswerA number which can be expressed in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and q is not equal to zero, is called a Rational number.
View full question & answer→Question 371 Mark
Which of the following statements are true:
The rational number $\frac{3}{4}$ lies to the left of zero on the number line.
View full question & answer→Question 381 Mark
Fill in the blanks by the correct symbol out of >, =, or <:
$\frac{-2}{3}\dots\frac{5}{-8}$
AnswerOn multiplying $\frac{-2}{3}$ by $\frac{8}{8},$ we get $\frac{-16}{24}$
On multiplying $\frac{5}{-8}$ by $\frac{3}{3},$ we get $\frac{15}{-24}=\frac{-15}{24}$
Because $-15>-16,\frac{-2}{3}<\frac{5}{-8}$
View full question & answer→Question 391 Mark
Draw the number line and represent the following rational number on it:
$\frac{-7}{3}$
View full question & answer→Question 401 Mark
Write down the denominator of the following rational numbers:
$\frac{11}{-34}$
View full question & answer→Question 411 Mark
Which of the following statements are true:
The rational number $\frac{-3}{-5}$ is on the right of $\frac{-4}{7}$ on the number line.
AnswerTrue.Solution:
they both are of opposite signs and positive number is greater than the negative number.
Thus, it is on the right of the negative number.
View full question & answer→Question 421 Mark
Express $\frac{3}{4}$ as a rational number with numerator:
44
Answer$\frac{3}{4}$ as a rational number with denominator:
44 is:
$\frac{3\times11}{4\times11}=\frac{33}{44}$
(Multiplying numerator and denominator by 11)
View full question & answer→Question 431 Mark
Which of the two rational numbers in the following pairs of rational numbers is smaller?
$\frac{16}{-5},3$
View full question & answer→Question 441 Mark
Which of the following statements are true:
The rational number $\frac{-12}{-17}$ lies to the left of zero on the number line.
AnswerFalse.Solution:
It lies to the right of zero because it is a positive number.
View full question & answer→Question 451 Mark
Express $\frac{3}{4}$ as a rational number with numerator:
36
Answer$\frac{3}{4}$ as a rational number with denominator:
36 is:
$\frac{3\times9}{4\times9}=\frac{27}{36}$
(Multiplying numerator and denominator by 9)
View full question & answer→Question 461 Mark
Draw the number line and represent the following rational number on it:
$\frac{2}{3}$
View full question & answer→Question 471 Mark
Write $\frac{-14}{42}$ in a form so that the numerator with denominator:
42
AnswerRational number with numerator:
42 is:
$\frac{-14\times-3}{7\times-3}=\frac{42}{-21}$
(Dividing numerator and denominator by -3)
View full question & answer→Question 481 Mark
Express $\frac{3}{5}$ as a rational number with numerator:
6
AnswerRational number with numerator:
6 is:
$\frac{3\times2}{5\times2}=\frac{6}{10}$
(Multiplying numerator and denominator by 2)
View full question & answer→Question 491 Mark
In the following state if the statement is true (T) or false (F):
If $\frac{\text{a}}{\text{b}}$ is a rational number and m any integer,
$\text{Then}\frac{\text{a}}{\text{b}}=\frac{\text{a}\times\text{m}}{\text{b}\times\text{m}}$
View full question & answer→Question 501 Mark
If each of the following pairs represents a pair of equivalent rational numbers, Find the values of x:
$\frac{3}{5}\text{ and }\frac{\text{x}}{-25}$
Answer$\frac{3}{5}=\frac{\text{x}}{-25},$
$\Rightarrow\text{Then, }\text{x}=\frac{3}{5}\times(-25)=\frac{-75}{5}=-15$
View full question & answer→