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) × 4, and whose denominator is (34 - 23) × (7 - 4).
AnswerAccording to the question:
Numerator = (-3) × 4 = -12
Denominator = (34 - 23) × (7 - 4) = 11 × 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?
$\frac{-9}{12}\text{ and }\frac{8}{-12}$
AnswerThe 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?
- $\frac{-3}{7}$
- $\frac{-5}{-8}$
- $\frac{9}{-83}$
- $\frac{-115}{-197}$
AnswerThe numbers can be rewritten as:
- $-\frac{3}{7}$
- $\frac{5}{8}$
- $-\frac{9}{83}$
- $\frac{115}{197}$
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→