Question 12 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater? $\frac{5}{9},\frac{-3}{-8}$
Answer$\frac{5}{9}=\frac{5\times8}{9\times8}=\frac{40}{72}\text{ and }\frac{-3}{-8}$ $=\frac{3\times9}{8\times9}=\frac{27}{72}$ Therefore, $\frac{5}{9}>\frac{-3}{-8}$
View full question & answer→Question 22 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater?
$\frac{-4}{11},\frac{3}{11}$
Answer$\frac{-4}{11}<\frac{3}{11}$ Because every positive rational number is greater than zero and every negative rational number is smaller than zero.
View full question & answer→Question 32 Marks
Select those rational numbers which can be written as a rational number with numerator $6$:
$\frac{1}{22},\frac{2}{3},\frac{3}{4},\frac{4}{-5},\frac{5}{6},\frac{-6}{7},\frac{-7}{8}$
AnswerGiven rational numbers that can be written as a rational number with numerator $6$ are:
$\frac{1}{22}$ (On multiplying by $6$) $=\frac{6}{132}$
$\frac{2}{3}$ (On multiplying by $3$) $=\frac{6}{9}$
$\frac{3}{4}$ (On multiplying by $2$) $=\frac{6}{8}$
$\frac{-6}{7}$ (On multiplying by $1$) $=\frac{6}{-7}$
View full question & answer→Question 42 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater? $\frac{5}{2},0$
Answer$ \frac{5}{2} > 0$ Because every positive rational number is greater than zero and every negative rational number is smaller than zero.
View full question & answer→Question 52 Marks
Write of the following rational numbers in the standard form: $\frac{-15}{-35}$
AnswerThe denominator is negative. $\frac{-15\times-1}{-35\times-1}=\frac{15}{35}$ $HCF$ of $-15$ and $-35$ is $5$.
Therefore, Dividing the numerator and denominator of $\frac{-15}{-35}$ by $5$,
We get: $\frac{-15\div5}{-85\div5}=\frac{3}{7}$
View full question & answer→Question 62 Marks
Express the following numbers to the lowest form: $\frac{132}{-428}$
AnswerLowest form of: $\frac{132}{-428}$ is:
$132=2\times3\times2\times11$
$428=2\times2\times107$
$HCF$ of $132$ and $428$ is $4$.
Dividing the fraction by $4$, We get: $\frac{33}{-107}$
View full question & answer→Question 72 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater?
$\frac{-3}{8},0$
AnswerWe know that every positive rational number is greater than zero and every negative
Rational number is smaller than zero.
Thus, $ \frac{-3}{8} > 0$
View full question & answer→Question 82 Marks
Write of the following rational numbers in the standard form:
$\frac{-63}{-210}$
Answer$\frac{-63}{-210}$
The $H.C.F$ of $63$ and $210$ is $21$.
Dividing the $Nr$ and $Dr$ of $\frac{-63}{-210}$ by $21$,
We get:
$\frac{-63}{-210}=\frac{-63\div21}{-210\div21}=\frac{-3}{-10}=\frac{3 }{10}$
View full question & answer→Question 92 Marks
Write of the following rational numbers in the standard form: $\frac{-195}{275}$
Answer$\frac{68}{-119}$ The $H.C.F.$ of $195$ and $275$ is $5$.
Dividing the $Nr$ and $Dr$ of $\frac{68}{-119}$ by $17$,
We get:
$\frac{-195}{275}=\frac{-195\div5}{275\div5}=\frac{-39}{55}$
View full question & answer→Question 102 Marks
Express the following numbers to the lowest form:
$\frac{4}{22}$
AnswerLowest form of:
$\frac{4}{22}$ is:
$4=2\times2$
$22=2\times11$
$HCF$ of $4$ and $22$ is $2$.
Dividing the fraction by $2$,
We get: $\frac{2}{11}$
View full question & answer→Question 112 Marks
Write of the following rational numbers in the standard form:
$\frac{4}{-16}$
AnswerThe denominator is negative.
$\frac{4\times-1}{-16\times-1}=\frac{-4}{16}$
$HCF$ of $4$ and $16$ is $4$.
Therefore, Dividing the numerator and denominator by $4$,
We get:
$\frac{\frac{-4}{4}}{\frac{16}{4}}=\frac{-1}{4}$
View full question & answer→Question 122 Marks
Write of the following rational numbers in the standard form: $\frac{-8}{36}$
AnswerThe denominator is positive and $HCF$ of $8$ and $36$ is $4$.
Therefore, Dividing the numerator and denominator by $4$,
We get: $\frac{-8}{36}=\frac{\frac{-8}{4}}{\frac{36}{4}}=\frac{-2}{9}$
View full question & answer→Question 132 Marks
Which of the following numbers are equal? $\frac{-16}{20}\text{ and }\frac{20}{-25}$
AnswerSince, $LCM$ of $20$ and $25$ is $100.$
Therefore making the denominators equal,
$\frac{-16}{20}=\frac{-16\times5}{20\times50}$
$=\frac{-80}{100}\text{ and }\frac{20}{-25}$
$=\frac{-20\times4}{25\times4}=\frac{-80}{100}$
Therefore, $\frac{-16}{20}=\frac{20}{-25}$
View full question & answer→Question 142 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater?
$\frac{5}{-8},\frac{-7}{12}$
Answer $\frac{-7}{12}=\frac{-7\times2}{12\times2}=\frac{-14}{24}\text{ and }\frac{-5}{8}$
$=\frac{-5\times3}{8\times3}=\frac{-15}{24}$
Therefore, $\frac{7}{12}>\frac{5}{-8}$
View full question & answer→Question 152 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater? $\frac{-5}{8},\frac{3}{-4}$
Answer$\frac{-5}{8}\text{ and }\frac{3}{-4}=\frac{-3\times2}{4\times2}=\frac{-6}{8}$ Therefore: $\frac{-5}{8}<\frac{3}{-4}$
View full question & answer→Question 162 Marks
Write of the following rational numbers in the standard form: $\frac{2}{10}$
AnswerThe denominator is positive and $HCF$ of $2$ and $10$ is $2$.
Therefore, Dividing the numerator and denominator by $2$,
We get: $\frac{2}{10}=\frac{\frac{2}{2}}{\frac{10}{2}}=\frac{1}{5}$
View full question & answer→Question 172 Marks
Write down the rational number whose numerator is $(-3) \times 4,$ and whose denominator is $(34 - 23) \times (7 - 4)$.
AnswerAccording to the question:
Numerator $= (-3) \times 4 = -12$
Denominator $= (34 - 23) \times (7 - 4) = 11 \times 3 = 33$
Therefore, Rational number $= -1232$
View full question & answer→Question 182 Marks
Write of the following rational numbers in the standard form:
$\frac{68}{-119}$
Answer$\frac{68}{-119}$The $H.C.F.$ of $68$ and $119$ is $17$.
Dividing the $Nr$ and $Dr$ of $\frac{68}{-119}$ by $17$,
We get:
$\frac{68}{-119}=\frac{68\div17}{119\div17}=\frac{4}{-7}$
View full question & answer→Question 192 Marks
Which of the two rational numbers in the following pairs of rational numbers is greater? $\frac{-7}{12},\frac{5}{-8}$
Answer$\frac{7}{12}=\frac{-7\times12}{12\times2}=\frac{-14}{24}\text{ and }\frac{-5}{8}$ $=\frac{-5\times3}{8\times3}=\frac{-15}{24}$ Therefore: $-\frac{7}{12}>\frac{5}{-8}$
View full question & answer→Question 202 Marks
Which of the following numbers are equal? $\frac{-8}{14}\text{ and }\frac{13}{21}$
AnswerSince, $LCM$ of $14$ and $21$ is $42$.
Therefore making the denominators equal,
$\frac{-8}{-14}=\frac{-8\times3}{-14\times3}$
$=\frac{-24}{-12}\text{ and }\frac{13}{21}$
$=\frac{13\times2}{21\times2}=\frac{26}{42}$
Therefore, $\frac{-8}{14}$ is not equal to $=\frac{13}{21}.$
View full question & answer→Question 212 Marks
Seperate positive and negative rational numbers from the following rational numbers: $\frac{-5}{-7},\frac{12}{-5},\frac{7}{4},\frac{13}{-9},0,\frac{-18}{-7},\frac{-95}{116},\frac{-1}{-9}$
AnswerGiven rational numbers can be rewritten as:
$\frac{5}{7}.\frac{-12}{7},\frac{7}{4},-\frac{13}{9},0,\frac{18}{7},-\frac{95}{116},\frac{1}{9}$
Thus, positive rational numbers are: $\frac{5}{7},\frac{7}{4},\frac{18}{7},\frac{1}{9}$
Negative rational numbers are:$−\frac{12}{5} , -\frac{13}{9} , -\frac{95}{116}$
View full question & answer→Question 222 Marks
Which of the following numbers are equal?
$\frac{-9}{12}\text{ and }\frac{8}{-12}$
Answer The standard form of $\frac{-9}{12}\text{ is }\frac{\frac{-9}{3}}{\frac{12}{3}}=\frac{-3}{4}$
The standard form of $\frac{8}{-12}\text{ is }\frac{\frac{8}{-4}}{\frac{-12}{-4}}=\frac{-2}{3}$
Since, the standard forms of two rational numbers are not same. Hence, they are not equal.
View full question & answer→Question 232 Marks
Arrange the following rational numbers in descending order: $\frac{-3}{10},\frac{17}{30},\frac{7}{-15},\frac{-11}{20}$
AnswerSince, $LCM$ of $10, -30, -15, 20$ is $60.$
Multiplying the numerators and denominators, to get the denominator equal to $LCM,$
$\frac{-3}{10}=\frac{-3\times6}{10\times6}=\frac{-18}{60},\frac{17}{-30}=\frac{-17\times2}{30\times2}=\frac{-34}{60}$
$\frac{7}{-15}=\frac{-7\times4}{15\times4}=\frac{-28}{60},\frac{-11}{20}=\frac{-11\times3}{20\times3}=\frac{-33}{60}$
Order is, $-18>-28>-33>-34$
Order is, $\frac{-3}{10}>\frac{7}{-15}>\frac{-11}{20}>\frac{17}{-30}$
View full question & answer→Question 242 Marks
Determine whether the following rational numbers are in the lowest form or not: $\frac{-15}{32}$
AnswerWe observe that $-15$ and $32$ have no common factor ie., their $HCF$ is $1$.
Thus, $\frac{-15}{32}$ is in its lowest form.
View full question & answer→Question 252 Marks
Which of the following rational numbers are negative?
$i. \frac{-3}{7}$
$ii. \frac{-5}{-8}$
$iii. \frac{9}{-83}$
$iv. \frac{-115}{-197}$
AnswerThe numbers can be rewritten as:
$i. -\frac{3}{7}$
$ii. \frac{5}{8}$
$iii. -\frac{9}{83}$
$iv. \frac{115}{197}$
Negative rational numbers are $(i)$ and $(iii)$ .
View full question & answer→Question 262 Marks
Which of the following numbers are equal? $\frac{-7}{21}\text{ and }\frac{3}{-9}$
AnswerSince, $LCM$ of $21$ and $9$ is $63$.
Therefore making the denominators equal,
$\frac{-7}{21}=\frac{-7\times3}{21\times3}$
$=\frac{-21}{63}\text{ and }\frac{3}{-9}=\frac{-3\times7}{9\times7}=\frac{-21}{63}$
View full question & answer→Question 272 Marks
Write the following rational numbers in the standard form: $\frac{299}{-161}$
AnswerThe denominator is negative. $\frac{299\times-1}{-161\times-1}$
The $H.C.F.$ of $299$ and $-161$ is $23$.
Dividing the $Nr$ and $Dr$ of $\frac{299}{-161}$ by $23$,
We get: $\frac{299}{-161}=\frac{299\div23}{-161\div23}=\frac{13}{-7}$
View full question & answer→Question 282 Marks
Express the following numbers to the lowest form: $\frac{-32}{-56}$
AnswerLowest form of: $\frac{-32}{-56}$ is: $32=2\times2\times2\times2\times2$
$56=2\times2\times2\times7$ $HCF$ of $32$ and $56$ is $8$.
Dividing the fraction by $8$, We get: $\frac{4}{7}$
View full question & answer→Question 292 Marks
Express the following numbers to the lowest form: $\frac{-36}{180}$
AnswerLowest form of: $\frac{-36}{180}$ is: $36=3\times3\times2\times2$
$180=5\times3\times3\times2\times2$
$HCF$ of $36$ and $180$ is $36$.
Dividing the fraction by $36$, We get: $\frac{-1}{5}$
View full question & answer→Question 302 Marks
Which of the two rational numbers in the following pairs of rational number is smaller?
$\frac{-12}{5},-3$
View full question & answer→Question 312 Marks
Which of the two rational numbers in the following pairs of rational number is smaller?
$\frac{-4}{3}, \frac{8}{-7}$
View full question & answer→Question 322 Marks
Which of the two rational numbers in the following pairs of rational number is smaller?
$\frac{16}{-5}, 3$
View full question & answer→Question 332 Marks
Which of the two rational numbers in the following pairs of rational number is smaller?
$\frac{-6}{-13}, \frac{7}{13}$
View full question & answer→Question 342 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{5}{-8}, \frac{-7}{12}$
View full question & answer→Question 352 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{5}{9}, \frac{-3}{-8}$
View full question & answer→Question 362 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{-5}{8}, \frac{3}{-4}$
View full question & answer→Question 372 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{4}{-9}, \frac{-3}{-7}$
View full question & answer→Question 382 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{-7}{12}, \frac{5}{-8}$
View full question & answer→Question 392 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{-4}{11}, \frac{3}{11}$
View full question & answer→Question 402 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{5}{2}, 0$
View full question & answer→Question 412 Marks
Which of the two rational numbers in the following pairs of rational number is greater?
$\frac{-3}{8}, 0$
View full question & answer→Question 422 Marks
Draw the number line and represent the following rational number on it:
$\frac{-31}{3}$
View full question & answer→Question 432 Marks
Draw the number line and represent the following rational number on it:
$\frac{22}{-7}$
View full question & answer→Question 442 Marks
Draw the number line and represent the following rational number on it:
$\frac{-7}{3}$
View full question & answer→Question 452 Marks
Draw the number line and represent the following rational number on it:
$\frac{-3}{16}$
View full question & answer→Question 462 Marks
Draw the number line and represent the following rational number on it:
$\frac{-5}{8}$
View full question & answer→Question 472 Marks
Draw the number line and represent the following rational number on it:
$\frac{3}{8}$
View full question & answer→Question 482 Marks
Draw the number line and represent the following rational number on it:
$\frac{3}{4}$
View full question & answer→Question 492 Marks
Draw the number line and represent the following rational number on it:
$\frac{2}{3}$
View full question & answer→Question 502 Marks
Write $\frac{-14}{42}$ in a form so that the numerator is equal to:
-70
View full question & answer→