Question 511 Mark
Which of the two rational numbers in the following pairs of rational numbers is smaller?
$\frac{-4}{3},\frac{8}{-7}$
Answer$\frac{-4}{3}=\frac{-4\times7}{3\times7}=\frac{-28}{21}\text{ and }\frac{8}{-7}$
$=\frac{-8\times3}{7\times3}=\frac{-24}{21}$
$\text{Therefore},\frac{-4}{3}<\frac{8}{-7}$
View full question & answer→Question 521 Mark
Express $\frac{5}{7}$ as a rational number with numerator:
-14
Answer$\frac{5}{7}$ as a rational number with denominator:
-14 is:
$\frac{5\times-2}{7\times-2}=\frac{-20}{-14}$
(Multiplying numerator and denominator by -2)
View full question & answer→Question 531 Mark
Write the following rational numbers as integers:
$\frac{7}{1},\frac{-12}{1},\frac{34}{1},\frac{-73}{1},\frac{95}{1}$
AnswerIntegers are:
7, -12, 34, -73 and 95.
View full question & answer→Question 541 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
64
AnswerRational number with numerator:
64 as numerator:
$\frac{-192}{-3}\&\frac{108}{-3}=\frac{64}{-36}$
(Dividing the numerator and denomintor by -3)
View full question & answer→Question 551 Mark
Write down the numerator of the following rational numbers:
5
Question 561 Mark
In the following, fill in the blanks so as to make the statement true:
The standard form of -1 is _______.
AnswerThe standard form of -1 is $\frac{-1}{1}$
View full question & answer→Question 571 Mark
If each of the following pairs represents a pair of equivalent rational numbers, Find the values of x:
$\frac{-3}{7}\text{ and }\frac{\text{x}}{\text{4}}$
Answer$\frac{-3}{7}=\frac{\text{x}}{\text{4}},\text{ then }\text{x}=\frac{-3}{7}\times{4}=\frac{-12}{7}$
View full question & answer→Question 581 Mark
Write down the denominator of the following rational numbers:
15
Question 591 Mark
Express the following as rational number with positive denominator:
$\frac{-28}{-11}$
AnswerMultiplying the number by -1,
we get:
$\frac{-28}{-11}=\frac{-28\times-1}{-11\times-1}=\frac{28}{11}$
View full question & answer→Question 601 Mark
Fill in the blanks:
$\frac{-5}{7}=\frac{\dots}{35}=\frac{\dots}{49}$
AnswerHere, $\frac{-5\times5}{7\times5}=\frac{-25}{35}$
Also, $\frac{-5\times7}{7\times7}=\frac{-35}{49}$
Therefore, $\frac{-5}{7}=\frac{-25}{35}=\frac{-35}{49}$
View full question & answer→Question 611 Mark
Which of the two rational numbers in the following pairs of rational numbers is greater?
$\frac{4}{-9},\frac{-3}{-7}$
Answer$\frac{-4}{9}=\frac{-4\times7}{9\times7}=\frac{-28}{63}\text{ and }\frac{-3}{-7}$
$=\frac{3\times7}{7\times9}=\frac{21}{63}$
Therefore:
$\frac{-4}{9}<\frac{-3}{-7}$
View full question & answer→Question 621 Mark
In the following state if the statement is true (T) or false (F):
Every rational number is a fraction.
AnswerFalse.
Solution:
Not necessary.
View full question & answer→Question 631 Mark
In the following, fill in the blanks so as to make the statement true:
If the integers p and q have no common divisor other than 1 and q is positive, then the rational number $\frac{\text{p}}{\text{q}}$ is said to be in the _____.
AnswerIf the integers p and q have no common divisor other than 1 and q is positive, then the rational number $\frac{\text{p}}{\text{q}}$ is said to be in the Standard rational number.
View full question & answer→Question 641 Mark
Express $\frac{2}{5}$ as a rational number with numerator:
154
Answer$\frac{2}{5}$ as a rational number with denominator:
154 is:
$\frac{2\times77}{5\times77}=\frac{154}{385}$
(Multiplying numerator and denominator by 77)
View full question & answer→Question 651 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
-16
AnswerRational number with numerator:
-16 as numerator:
$\frac{-192}{12}\&\frac{108}{12}=\frac{-16}{9}$
(Dividing the numerator and denomintor by 12)
View full question & answer→Question 661 Mark
Express the following as rational number with positive denominator:
$\frac{6}{-9}$
AnswerRational number with positive denominators:
Multiplying the number by -1,
we get:
$\frac{6}{-9}=\frac{6\times-1}{-9\times-1}=\frac{-6}{9}$
View full question & answer→Question 671 Mark
Which of the two rational numbers in the following pairs of rational numbers is smaller?
$\frac{-6}{-13},\frac{7}{13}$
Answer$=\frac{-6}{-13}=\frac{6}{13}<\frac{7}{13}$
View full question & answer→Question 681 Mark
Which of the following statements are true:
The rational number $\frac{-21}{5}\text{ and } \frac{7}{-31}$ are on the opposite side of zero on the number line.
AnswerFalse.Solution:
They both are of same signs.
View full question & answer→Question 691 Mark
Express $\frac{3}{5}$ as a rational number with numerator:
21
AnswerRational number with numerator:
21 is:
$\frac{3\times7}{5\times7}=\frac{21}{35}$
(Multiplying numerator and denominator by 7)
View full question & answer→Question 701 Mark
In the following state if the statement is true (T) or false (F):
The quotient of two integers is always an integer.
AnswerFalse.Solution:
Not necessary.
View full question & answer→Question 711 Mark
In the following state if the statement is true (T) or false (F):
$\frac{2}{3}$ is equal to $\frac{4}{6}.$
AnswerTrue.
Solution:
In the standard form, they are equal.
View full question & answer→Question 721 Mark
Express $\frac{2}{5}$ as a rational number with numerator:
-56
Answer$\frac{2}{5}$ as a rational number with denominator:
-56 is:
$\frac{2\times-28}{5\times-28}=\frac{-56}{-140}$
(Multiplying numerator and denominator by -28)
View full question & answer→Question 731 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
32
AnswerRational number with numerator:
32 as numerator:
$\frac{-192}{-6}\&\frac{108}{-6}=\frac{32}{-18}$
(Dividing the numerator and denomintor by -6)
View full question & answer→Question 741 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
-7
AnswerRational number with numerator:
-7 as numerator:
$\frac{168}{42}\&\frac{-294}{42}=\frac{4}{-7}$
(Dividing the numerator and denomintor by 42)
View full question & answer→Question 751 Mark
Which of the following statements are true:
The rational number $\frac{29}{23}$ 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 761 Mark
Fill in the blanks:
$\frac{-4}{9}=\frac{\dots}{18}=\frac{12}{\dots}$
AnswerHere, $\frac{-4\times-2}{-9\times-2}=\frac{-25}{35}=\frac{-35}{49}$
Also, $\frac{-4\times-3}{-9\times-3}=\frac{12}{27}$
Therefore, $\frac{-4}{-9}=\frac{8}{18}=\frac{12}{27}$
View full question & answer→Question 771 Mark
Fill in the blanks by the correct symbol out of >, =, or <:
$0\dots\frac{-2}{5}$
AnswerBecause every positive number is greater than a negative number, $0>\frac{-2}{5}$
View full question & answer→Question 781 Mark
Write down the denominator of the following rational numbers:
$\frac{-4}{5}$
View full question & answer→Question 791 Mark
Express $\frac{-192}{108}$ as a rational number with numerator:
-48
AnswerRational number with numerator:
-48 as numerator:
$\frac{-192}{4}\&\frac{108}{4}=\frac{-48}{27}$
(Dividing the numerator and denomintor by 4)
View full question & answer→Question 801 Mark
In the following, find an equivalent form of the rational number having common denominator:
$\frac{2}{3},\frac{7}{6}\text{ and }\frac{11}{12}$
AnswerEquivalent forms of the rational number having common denominator are:
$\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}\text{ and }\frac{7}{6}$
$=\frac{7\times2}{6\times2}=\frac{14}{12}\text{ and }\frac{11}{12}$
$\text{Forms are }\frac{8}{12},\frac{14}{12}\text{ and }\frac{11}{12}$
View full question & answer→Question 811 Mark
Write down the numerator of the following rational numbers:
$\frac{8}{9}$
View full question & answer→Question 821 Mark
Express $\frac{5}{7}$ as a rational number with numerator:
-28
Answer$\frac{5}{7}$ as a rational number with denominator:
-28 is:
$\frac{5\times-4}{7\times-4}=\frac{-20}{-28}$
(Multiplying numerator and denominator by -4)
View full question & answer→Question 831 Mark
Draw the number line and represent the following rational number on it:
$\frac{-5}{8}$
View full question & answer→Question 841 Mark
Fill in the blanks by the correct symbol out of >, =, or <:
$\frac{-3}{5}\dots\frac{-5}{6}$
AnswerOn multiplying $\frac{-3}{5}$ by $\frac{6}{6},$ we get $\frac{-18}{30}$
On multiplying $\frac{-3}{5}$ by $\frac{6}{6},$ we get $\frac{-18}{30}$
Because $118>-25,\frac{-3}{8}>\frac{-5}{6}$
View full question & answer→Question 851 Mark
Which of the following rational numbers are positive?
- $\frac{-8}{7}$
- $\frac{9}{8}$
- $\frac{-19}{-13}$
- $\frac{-21}{13}$
AnswerThe numbers can be rewritten as:
- $-\frac{8}{7}$
- $\frac{9}{8}$
- $\frac{19}{13}$
- $-\frac{21}{13}$
View full question & answer→Question 861 Mark
Determine whether the following rational numbers are in the lowest form or not:
$\frac{65}{84}$
AnswerWe observe that 65 and 84 have no common factor their HCF is 1.
Thus, $\frac{65}{84}$ is in its lowest form.
View full question & answer→Question 871 Mark
Fill in the blanks:
$\frac{6}{-13}=\frac{-12}{\dots}=\frac{24}{\dots}$
AnswerHere, $\frac{6\times-2}{-13\times-2}=\frac{-12}{26}$
Also, $\frac{6\times4}{-13\times4}=\frac{24}{-52}$
Therefore, $\frac{6}{-13}=\frac{-12}{26}=\frac{24}{-52}$
View full question & answer→Question 881 Mark
Write the following integers as rational numbers with denominator 1:
-15, 17, 85, -100
AnswerRational numbers of given integers with denominator 1 are:
$-\frac{15}{1}, \frac{17}{1}, \frac{85}{1}, -\frac{100}{1}$
View full question & answer→Question 891 Mark
Express $\frac{3}{5}$ as a rational number with numerator:
-27
AnswerRational number with numerator:
-27 is:
$\frac{3\times-9}{5\times-9}=\frac{-27}{-45}$
(Multiplying numerator and denominator by -9)
View full question & answer→Question 901 Mark
In the following, fill in the blanks so as to make the statement true:
Two rational numbers with different numerators are equal, if their numerators are in the same ______ as their denominators.
AnswerTwo rational numbers with different numerators are equal, if their numerators are in the same Ratio as their denominators.
View full question & answer→Question 911 Mark
Write $\frac{-14}{42}$ in a form so that the numerator with denominator:
-70
AnswerRational number with numerator:
-70 is:
$\frac{-14\times5}{42\times5}=\frac{-70}{210}$
(Dividing numerator and denominator by 5)
View full question & answer→Question 921 Mark
In the following state if the statement is true (T) or false (F):
Every fraction is a rational number.
AnswerTrue.
Solution:
Every fraction can be expressed in the form of $\frac{\text{p}}{\text{q}},$ where q is not zero.
View full question & answer→Question 931 Mark
Which of the following statements are true:
The rational number $\frac{-12}{-5}\text{ and } \frac{-7}{17}$ are on the opposite side of zero on the number line.
AnswerTrue.Solution:
They are of opposite signs.
View full question & answer→Question 941 Mark
Determine whether the following rational numbers are in the lowest form or not:
$\frac{-56}{-32}$
AnswerHCF of 56 and 32 is 8.
Thus, given rational number is not in its simplest form.
View full question & answer→Question 951 Mark
Write $\frac{-14}{42}$ in a form so that the numerator with denominator:
7
AnswerRational number with numerator:7 is:
$\frac{-14}{-2}\&\frac{42}{-2}=\frac{7}{-21}$ (Dividing numerator and denominator by -2)
View full question & answer→Question 961 Mark
Write $\frac{-14}{42}$ in a form so that the numerator with denominator:
-2
AnswerRational number with numerator:
-2 is $\frac{\frac{-14}{7}}{\frac{42}{7}}=\frac{-2}{6}$ (Dividing numerator and denominator by 7)
View full question & answer→Question 971 Mark
Express $\frac{5}{7}$ as a rational number with numerator:
70
Answer$\frac{5}{7}$ as a rational number with denominator:
70 is:
$\frac{5\times10}{7\times10}=\frac{50}{70}$
(Multiplying numerator and denominator by 10)
View full question & answer→Question 981 Mark
In the following state if the statement is true (T) or false (F):
Every rational number is an integer.
AnswerFalse.
Solution:
Not necessary.
View full question & answer→Question 991 Mark
Express $\frac{5}{7}$ as a rational number with numerator:
-84
Answer$\frac{5}{7}$ as a rational number with denominator:
-84 is:
$\frac{5\times-12}{7\times-12}=\frac{-60}{-80}$
(Multiplying numerator and denominator by -12)
View full question & answer→