Question 13 Marks
In the following, find an equivalent form of the rational number having common denominator:
$\frac{5}{7},\frac{3}{8},\frac{9}{14}\text{ and }\frac{20}{21}$
AnswerEquivalent forms of the rational number having common denominator are:
$\Rightarrow\frac{5}{7}=\frac{5\times24}{7\times24}=\frac{120}{168}$
$\Rightarrow\frac{3}{8}=\frac{3\times21}{8\times21}=\frac{63}{168}$
$\Rightarrow\frac{9}{14}=\frac{9\times12}{14\times12}=\frac{108}{168}$ and
$\Rightarrow\frac{20}{21}=\frac{20\times8}{21\times8}=\frac{160}{168}$
$\text{Forms are }\frac{120}{168},\frac{63}{168},\frac{108}{168}\text{ and }\frac{160}{168}$
View full question & answer→Question 23 Marks
Arrange the following rational numbers in ascending order: $\frac{3}{5},\frac{-17}{30},\frac{8}{-15},-\frac{7}{10}$
AnswerAscending order: Since, $LCM$ of $5, -30, -15, 10$ is $30$.
Multiplying the numerators and denominators to get the denominator equal to the $LCM$ $\frac{3}{5}$
$=\frac{3\times6}{5\times6}=\frac{18}{30},\frac{17}{30}=\frac{17\times1}{30\times1}=\frac{17}{30}$
$\frac{8}{-15}=\frac{-8\times2}{15\times2}=\frac{-16}{30},$
$\frac{-7}{10}=\frac{-7\times3}{10\times3}=\frac{-21}{30}$
Order is $-21<-16<17<8$
Order is $\frac{-7}{10}<\frac{8}{-15}<\frac{17}{30}<\frac{3}{5}$
View full question & answer→Question 33 Marks
Arrange the following rational numbers in ascending order: $-\frac{4}{9},\frac{5}{-12},\frac{7}{-18},\frac{2}{-3}$
AnswerSince, $LCM$ of $9, -12, -18, 3$ is $36$.
Multiplying the numerators and denominators to get the denominator to get the denominator equal to the $LCM$.
$\frac{-4}{9}=\frac{-4\times4}{9\times4}=\frac{-16}{36},$
$\frac{5}{-12}=\frac{-5\times3}{12\times3}=\frac{-15}{36},$
$\frac{7}{-18}=\frac{-7\times2}{8\times2}=\frac{-14}{36},$
$\frac{2}{-3}=\frac{-2\times12}{3\times12}=\frac{-24}{36}$
Order is $-24<-16<-15<-14$
Order is $\frac{2}{-3}<\frac{-4}{9}<\frac{5}{-12}<\frac{7}{-18}$
View full question & answer→Question 43 Marks
Arrange the following rational numbers in descending order: $\frac{7}{8},\frac{64}{16},\frac{36}{-12},\frac{5}{-4},\frac{140}{28}$
AnswerWe have to arrange them in descending order.
Since, $LCM$ of $8, 16, -12, -4, 28$ is $336$.
Multiplying the numerators and denominators to get the denominator to get the denominator equal to the $LCM$,
$\frac{7}{8}$ $=\frac{7\times42}{8\times42}=\frac{294}{336},\frac{64}{16}=\frac{64\times121}{16\times21}=\frac{1344}{336}$
$\frac{36}{-12}=\frac{-36\times28}{12\times28}=\frac{-1008}{336},\frac{5}{-4}=\frac{-5\times84}{4\times84}=\frac{-420}{336},$
$\frac{140}{28}=\frac{140\times12}{28\times12}=\frac{180}{336}$
Order is: $1680>1344>294>-420>-1008$
Order is: $4>36-12$
Order is: $\frac{140}{28}>\frac{64}{16}>\frac{7}{8}>\frac{5}{-4}>\frac{36}{-12}$
View full question & answer→Question 53 Marks
Select those rational numbers which can be written as a rational number with denominator $4$:
$\frac{7}{8},\frac{64}{16},\frac{36}{-12},\frac{-16}{17},\frac{5}{-4},\frac{-140}{28}$
AnswerGiven rational numbers that can be written as a rational number with denominator $4$ are:
$\frac{7}{8}$ (On multiplying by $2$) $=\frac{3.5}{4}$
$\frac{64}{16}$ (On multiplying by $4$) $=\frac{16}{4}$
$\frac{36}{-12}$ (On multiplying by $3$) $=\frac{12}{-4}=\frac{-12}{4}$
$=\frac{-16}{17}$ Can,t be expressed with a denominator $4$.
$\frac{5}{-4}$ (On multiplying by $-1$) $=\frac{-5}{4}$
$\frac{140}{28}$ (On multiplying by $7$) $=\frac{20}{4}$
View full question & answer→Question 63 Marks
Arrange the following rational numbers in descending order:
$\frac{-3}{10}, \frac{17}{-30}, \frac{7}{-15}, \frac{-11}{20}$
Answer$\frac{-3}{10}>\frac{7}{-15}>\frac{-11}{20}>\frac{17}{-30}$
View full question & answer→Question 73 Marks
Arrange the following rational numbers in descending order:
$\frac{7}{8}, \frac{64}{16}, \frac{36}{-12}, \frac{5}{-4}, \frac{140}{28}$
Answer$\frac{140}{28}>\frac{64}{16}>\frac{7}{8}>\frac{5}{-4}>\frac{36}{-12}$
View full question & answer→Question 83 Marks
Arrange the following rational number in ascending order:
$\frac{-4}{9}, \frac{5}{-12}, \frac{7}{-18}, \frac{2}{-3}$
Answer$\frac{2}{-3}<\frac{-4}{9}<\frac{5}{-12}<\frac{7}{-18}$
View full question & answer→Question 93 Marks
Arrange the following rational number in ascending order:
$\frac{3}{5}, \frac{-17}{-30}, \frac{8}{-15}, \frac{-7}{10}$
Answer$\frac{-7}{10}<\frac{8}{-15}<\frac{-17}{30}<\frac{3}{5}$
View full question & answer→Question 103 Marks
If the following pairs represent a pair of equivalent rational numbers, find the values of x:
$\frac{13}{6}$ and $\frac{-65}{x}$
View full question & answer→Question 113 Marks
If the following pairs represent a pair of equivalent rational numbers, find the values of x:
$\frac{3}{5}$ and $\frac{x}{-25}$
View full question & answer→Question 123 Marks
If the following pairs represent a pair of equivalent rational numbers, find the values of x:
$\frac{-3}{7}$ and $\frac{x}{4}$
View full question & answer→Question 133 Marks
If the following pairs represent a pair of equivalent rational numbers, find the values of x:
$\frac{2}{3}$ and $\frac{5}{x}$
View full question & answer→Question 143 Marks
Write the following rational number in the standard form:
$\frac{-195}{275}$
View full question & answer→Question 153 Marks
Write the following rational number in the standard form:
$\frac{68}{-119}$
View full question & answer→Question 163 Marks
Write the following rational number in the standard form:
$\frac{-63}{-210}$
View full question & answer→Question 173 Marks
Write the following rational number in the standard form:
$\frac{299}{-161}$
View full question & answer→Question 183 Marks
Write the following rational number in the standard form:
$\frac{-15}{-35}$
View full question & answer→Question 193 Marks
Write each of the following rational number in the standard form:
$\frac{4}{-16}$
View full question & answer→Question 203 Marks
Write the following rational number in the standard form:
$\frac{-8}{36}$
View full question & answer→Question 213 Marks
Write the following rational number in the standard form:
$\frac{2}{10}$
View full question & answer→Question 223 Marks
Express the following rational number to the lowest form:
$\frac{-32}{-56}$
View full question & answer→Question 233 Marks
Expressthe following rational number to the lowest form:
$\frac{132}{-428}$
View full question & answer→Question 243 Marks
Express the following rational number to the lowest form:
$\frac{-36}{180}$
View full question & answer→Question 253 Marks
Express the following rational number to the lowest form:
$\frac{4}{22}$
View full question & answer→Question 263 Marks
Determine whether the following rational numbers are in the lowest form or not:
(i) $\frac{65}{84}$
(ii) $\frac{-15}{32}$
(iii) $\frac{24}{128}$
(iv) $\frac{-56}{-32}$
View full question & answer→Question 273 Marks
Express the following as a rational number with positive denominator:
$\frac{19}{-7}$
View full question & answer→Question 283 Marks
Express the following as a rational number with positive denominator:
$\frac{-28}{-11}$
View full question & answer→Question 293 Marks
Express the following as a rational number with positive denominator:
$\frac{6}{-9}$
View full question & answer→Question 303 Marks
Express the following as a rational number with positive denominator:
$\frac{-15}{-28}$
View full question & answer→Question 313 Marks
In the following, find of equivalent form of the rational number having a common denominator:
$\frac{5}{7}, \frac{3}{8}, \frac{9}{14}$ and $\frac{20}{21}$
Answer$\frac{120}{168}, \frac{63}{168}, \frac{108}{168}$ and $\frac{160}{168}$
View full question & answer→Question 323 Marks
In the following, find of equivalent form of the rational number having a common denominator:
$\frac{2}{3}, \frac{7}{6}$ and $\frac{11}{12}$
Answer$\frac{8}{12}, \frac{14}{12}$ and $\frac{11}{12}$
View full question & answer→Question 333 Marks
In the following, find of equivalent form of the rational number having a common denominator:
$\frac{3}{4}$ and $\frac{5}{12}$
Answer$\frac{9}{12}$ and $\frac{5}{12}$
View full question & answer→Question 343 Marks
Write down the rational number whose numerator is the smallest three digit number and denominator is the largest four digit number.
Question 353 Marks
Write the following integers as rational numbers with denominator 1:-15,17,85,-100
Answer$\frac{-15}{1}, \frac{17}{1}, \frac{85}{1}, \frac{-100}{1}$
View full question & answer→Question 363 Marks
Write down the rational number whose numerator is $(-3) \times 4$, and whose denominator is $(34-23) \times(7-4)$.
View full question & answer→