Question 12 Marks
Add the following rational numbers: $\frac{3}{-8}\text{ and }\frac{1}{8}$
Answer$\frac{3}{-8}\text{ and }\frac{1}{8}$
$=\frac{3\times(-1)}{-8\times(-1)}+\frac{1}{8}$
$=\frac{-3}{8}+\frac{1}{8}$
$=\frac{-3+1}{8}=\frac{-2}{8}$
$\frac{-1}{4} ($Dividing by $2)$
View full question & answer→Question 22 Marks
Find x such that: $\frac{-1}{5}=\frac{8}{\text{x}}$
Answer$\frac{-1}{5}=\frac{8}{\text{x}}$$\Rightarrow-1\times\text{x}=8\times5$
$\Rightarrow-\text{x}=40$
$\Rightarrow\text{x}=-40$
$\therefore\text{x}=-40$
View full question & answer→Question 32 Marks
Which of the following are pairs of equivalent rational number? $\frac{9}{4},\frac{-36}{16}$
Answer$\frac{9}{4},\frac{-36}{16}$
$\frac{-36}{16}=\frac{-36\div(-4)}{-16\div(-4)}=\frac{9}{4} (HCF$ of $36$ and $16 = 4)$
$\therefore\frac{9}{4}\text{ and }\frac{-36}{-16}$ are equivalent rational numbers.
View full question & answer→Question 42 Marks
What should be added to $\frac{-5}{7}$ to get $\frac{-2}{3}?$
AnswerThe required number $=3-\Big(\frac{-12}{5}\Big)$ $=\frac{3}{1}+\frac{12}{5}=\frac{15+12}{5}$ $=\frac{27}{5}$
View full question & answer→Question 52 Marks
How many pieces, each of length $3\frac{3}{4}\text{m}$ can be cut from a rope of length $45m?$
AnswerLength of rope $= 45m$
Number of pieces $=45\div3\frac{3}{4}$
$=45\div\frac{15}{4}$
$=45\times\frac{4}{15}$
$=12$
View full question & answer→Question 62 Marks
Which of the following are positive rational numbers$?$
$i. \frac{3}{-5}$
$ii. \frac{-11}{15}$
$iii. \frac{-5}{-8}$
$iv. \frac{37}{53}$
$v. \frac{0}{3}$
$vi. 8$
AnswerAccording to the definition, a rational number is positive if both of numerator and denominator have same signs.
Therefore $(iii), (iv)$ and $(vi)\ 8$ are positive rational numbers.
View full question & answer→Question 72 Marks
Add the following rational numbers: $\frac{-5}{11}\text{ and }\frac{-7}{-11}$
Answer$\frac{-5}{11}\text{ and }\frac{-7}{-11}$ $\frac{7}{-11}=\frac{7\times(-1)}{-11\times(-1)}+\frac{-7}{11}$ $\therefore\frac{-5}{11}+\frac{-5-7}{11}=\frac{-12}{11}$
View full question & answer→Question 82 Marks
Write the following rational numbers in standard form: $\frac{-27}{45}$
Answer$\frac{-27}{45}=\frac{-27\div9}{45\div9} (HCL$ of $-27$ and $45 = 9)$
$=\frac{-3}{5}$
View full question & answer→Question 92 Marks
Somplify: $\Big(\frac{-65}{14}\Big)\div\Big(\frac{13}{-7}\Big)$
Answer$\Big(\frac{-65}{14}\Big)\div\Big(\frac{13}{-7}\Big)$ $=\frac{65}{14}\times\frac{(-7)}{13}$ $=\Big(\frac{-5}{2}\Big)\times\Big(\frac{-1}{1}\Big)$ $=\frac{5}{2}$
View full question & answer→Question 102 Marks
Find the additive inverse of: $\frac{-11}{15}$
AnswerAdditive inverse of $\frac{-11}{15}=-\Big(\frac{11}{15}\Big)$ $=\frac{11}{15}$
View full question & answer→Question 112 Marks
Express $\frac{13}{-8}$ as a rational number with denominator $-40$
AnswerRational number $=\frac{13}{-8}$
$-40=-8\times5$
$\therefore\frac{13}{-8}=\frac{13\times5}{-8\times5}=\frac{65}{-40}$
View full question & answer→Question 122 Marks
What should be added to $\frac{-5}{7}$ to get $\frac{-2}{3}?$
AnswerThe required number $=\frac{-2}{3}-\Big(\frac{-5}{7}\Big)$
$=\frac{-2}{3}+\frac{5}{7}=\frac{-14+15}{21}$
$(LCM$ of $3, 7 = 21)$
$=\frac{1}{21}$
View full question & answer→Question 132 Marks
Simplify: $\frac{-3}{4}\times\frac{4}{3}$
Answer$\frac{-3}{4}\times\frac{4}{3}$$=\frac{-3}{4}\times\frac{4}{3}$
$=\frac{-3\times4}{4\times3}$
$=\frac{-12}{12}=-1$
View full question & answer→Question 142 Marks
Which of the following are negative rational numbers$?$
$i. \frac{-15}{-4}$
$ii. 0$
$iii. \frac{-5}{7}$
$iv. \frac{4}{-9}$
$v. -6$
$vi. \frac{1}{-2}$
AnswerAccording to the definition, a rational number is negative if numerator and denominator have opposite sign.
Therefore $(iii), (iv), (v), (vi)$ are all negative rational numbers.
View full question & answer→Question 152 Marks
Add the following rational numbers: $\frac{-3}{7}\text{ and }\frac{5}{-7}$
Answer$\frac{-3}{7}\text{ and }\frac{5}{-7}$ $\frac{5}{-7}=\frac{5\times(-1)}{-7\times(-1)}=\frac{-5}{7}$ $\therefore \ \frac{-3}{7}+\frac{-5}{7}=\frac{-3-5}{7}$ $=\frac{-8}{7}$
View full question & answer→Question 162 Marks
Somplify: $\frac{-65}{14}\div\Big(\frac{13}{-7}\Big)$
Answer$\frac{-65}{14}\div\Big(\frac{13}{-7}\Big)$ $=\frac{65}{14}\times\frac{(-7)}{13}$ $=\frac{-5}{2}\times\Big(\frac{-1}{1}\Big)$ $=\frac{5}{2}$
View full question & answer→Question 172 Marks
Simplify: $\frac{-9}{16}\times\frac{-64}{27}$
Answer$\frac{-9}{16}\times\frac{-64}{27}$$=\frac{-9\times-64}{16\times27}$
$=\frac{-1\times4}{1\times3}$ $=\frac{4}{3}$
View full question & answer→Question 182 Marks
Which of the following are pairs of equivalent rational number$? \frac{7}{15},\frac{-28}{60}$
Answer$\frac{7}{15},\frac{-28}{60}$
$\frac{-28}{60}=\frac{-28\div(-4)}{60\div(-4)}=\frac{7}{-15}$
$(HCF$ of $28$ and $60 = 4)$
$\therefore\frac{7}{-15}\text{ and }\frac{-28}{60}$ are not equivalent rational numbers.
View full question & answer→Question 192 Marks
Find the additive inverse of:
$\frac{1}{-6}$
Answer $\frac{1}{-6}=\frac{1\times(-1)}{-6\times(-1)}=\frac{-1}{6}$
$\therefore$ Additive inverse of $\frac{-1}{6}=-\Big(-\frac{1}{6}\Big)$
$=\frac{1}{6}$
View full question & answer→Question 202 Marks
Express $\frac{4}{7}$ as a rational number with denominator $-35$
AnswerRational number $=\frac{4}{7}$
$-35=7\times(-5)$
$\therefore\frac{4}{7}=\frac{4\times(-5)}{7\times(-5)}=\frac{-20}{-35}$
View full question & answer→Question 212 Marks
Which of the following are pairs of equivalent rational number? $\frac{3}{12},\frac{-1}{4}$
Answer$\frac{3}{12},\frac{-1}{4}$
$\frac{3}{12}=\frac{3\div3}{12\div3}=\frac{1}{4}$
$(HCF$ of $3$ and $12 = 3)$
$\therefore\frac{3}{12}\text{ and }\frac{1}{4}$ are not equivalent rational numbers.
View full question & answer→Question 222 Marks
Express $\frac{84}{-147}$ as a rational number with denominator $-49$
AnswerDenominator of $\frac{84}{-147}\text{ is }-147$
$\therefore-147\div3=-49$
Dividing both the numerator and the denominator by $3$
$\frac{84\div3}{-147\div3}=\frac{28}{-49}$
$=\frac{84}{147}=\frac{28}{-49}$
View full question & answer→Question 232 Marks
Which of the following rational number are equal? $\frac{-8}{-14}\text{ and }\frac{15}{21}$
Answer$\frac{-8}{-14}\text{ and }\frac{15}{21}$ will be equal $\text{ if }-8\times21=-14\times15$ $\text{if }-168=-210$ which is not true $\therefore\frac{-8}{-14}\text{ and }\frac{15}{21}$ are not equal.
View full question & answer→Question 242 Marks
Add the following rational numbers: $\frac{-2}{9}\text{ and }\frac{-5}{9}$
Answer $\frac{-2}{9}\text{ and }\frac{-5}{9}$ $=\frac{-2}{9}+\frac{-5}{9}$
$=\frac{-2-5}{9}$
$=\frac{-7}{9}$
View full question & answer→Question 252 Marks
Find x such that:
$\frac{7}{-3}=\frac{\text{x}}{6}$
Answer $\frac{7}{-3}=\frac{\text{x}}{6}$ $\Rightarrow-3\times\text{x}=7\times6$
$\Rightarrow-3\text{x}=42$
$\Rightarrow\text{x}=\frac{42}{-3}=-14$
$\therefore\text{x}=-14$
View full question & answer→Question 262 Marks
Which of the following are pairs of equivalent rational number? $\frac{3}{-8},\frac{-6}{16}$
Answer$\frac{3}{-8},\frac{-6}{16}$
$\frac{-6}{16}=\frac{16\div(-2)}{16\div(-2)}=\frac{3}{-8}$
$(HCF$ of $6$ and $16 = 2)$
$\therefore\frac{3}{-8}\text{ and }\frac{-6}{16}$ are equivalent rational numbers.
View full question & answer→Question 272 Marks
Which of the following rational number are equal? $\frac{-3}{9}\text{ and }\frac{7}{-21}$
Answer$\frac{-3}{9}\text{ and }\frac{7}{-21}$ will be equal $\text{ if }-3 \times(-21)=7\times9$ $\text{if }63=63$ which is true $\therefore\frac{-3}{9}\text{ and }\frac{-7}{-21}$ are equal.
View full question & answer→Question 282 Marks
Represent the following rational numbers on the number line: $\frac{38}{8}$
AnswerDraw a number line and locate a point $O$ on it. Let it represented $0.$ The number $\frac{38}{8}$ has been represented on it as given below: $\frac{22}{7}=3\frac{1}{7}$
View full question & answer→Question 292 Marks
Represent the following rational numbers on the number line:
$\frac{7}{3}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0.$ The number $\frac{7}{3}$ has been represented on the number line given below:
View full question & answer→Question 302 Marks
Simplify: $\frac{4}{9}\div\Big(\frac{-5}{12}\Big)$
Answer$\frac{4}{9}\div\Big(\frac{-5}{12}\Big)$$=\frac{4}{9}\times\frac{12}{(-5)}$
$=\frac{4\times4}{3\times(-5)}$
$=\frac{-16}{15}$
View full question & answer→Question 312 Marks
Write the following rational numbers in standard form: $\frac{-91}{-78}$
Answer$\frac{-91}{-78}=\frac{91\div13}{-78\div13}$
$(HCL$ of $91$ and $-78 = 13)$
$=\frac{7}{-6}$
View full question & answer→Question 322 Marks
Multiply:
$\frac{-13}{15}\text{ by }\frac{-25}{26}$
Answer $\frac{-13}{15}\text{ by }\frac{-25}{26}$
$=\frac{(-13)\times(-25)}{-15\times26}$
$=\frac{(-1)\times(-5)}{3\times2}$
$=\frac{5}{6}$
View full question & answer→Question 332 Marks
Evaluate: $\frac{-12}{7}+\frac{3}{7}+\frac{-2}{7}$
Answer$\frac{-12}{7}+\frac{3}{7}+\frac{-2}{7}$ $=\frac{-12+3+(-2)}{7}$ $=\frac{-12+3-2}{7}$ $=\frac{-12-2+3}{7}$ $=\frac{-14+3}{7}=\frac{-11}{7}$
View full question & answer→Question 342 Marks
Find x such that: $\frac{-48}{\text{x}}=2$
Answer$\frac{-48}{\text{x}}=2$$\Rightarrow2\text{x}=-48$
$\Rightarrow\text{x}=\frac{-48}{2}=-24$
View full question & answer→Question 352 Marks
Express $\frac{5}{8}$ as a rational number with numerator $15$
AnswerRational number $=\frac{5}{8}$
Numerator $= 15 = 5 \times 3$
$\therefore\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}$
View full question & answer→Question 362 Marks
Find the additive inverse of: $-9$
AnswerAdditive inverse of $-9 = - (-9) = 9$
View full question & answer→Question 372 Marks
Find the cost of $3\frac{1}{3}\text{m}$ of cloth at $\text{Rs. }121\frac{1}{2}\text{/m}.$
AnswerCost of $1\ m$ cloth $\text{Rs. }121\frac{1}{2}$
Cost of $3\frac{1}{3}\text{m}$ cloth
$=121\frac{1}{2}\times3\frac{1}{3}$
$=\frac{243}{2}\times\frac{10}{3}$
$=\text{Rs. }405$
View full question & answer→Question 382 Marks
Fill in the blank:
$\frac{-9}{5}=\frac{\dots}{20}=\frac{27}{\dots}=\frac{-45}{\dots}$
Answer $\frac{-9}{5}=\frac{\dots}{20}=\frac{27}{\dots}=\frac{-45}{\dots}$
$\therefore20=5\times4$
$\therefore\frac{-9}{5}=\frac{-9\times4}{5\times4}=\frac{-36}{20}$
$27=-9\times(-3)$
$\therefore\frac{-9}{5}=\frac{-9\times-3}{5\times-3}=\frac{27}{-15}$
$-45=-9\times5$
$\therefore\frac{-9}{5}=\frac{-9\times5}{5\times5}=\frac{-45}{25}$
$\therefore\frac{-9}{5}=\frac{-36}{20}=\frac{27}{-15}=\frac{-45}{25}$
View full question & answer→Question 392 Marks
Which of the following rational number are equal? $\frac{8}{-12}\text{ and }\frac{-10}{15}$
Answer$\frac{8}{-12}\text{ and }\frac{-10}{15}$ will be equal $\text{ if }8 \times15 = (-10)\times(-12)$ $\text{if }120=120$ which is true $\therefore\frac{8}{-12}\text{ and }\frac{-10}{15}$ are equal.
View full question & answer→Question 402 Marks
Express $\frac{5}{8}$ as a rational number with numerator $-10$
AnswerRational number $=\frac{5}{8}$
Numerator $= -10 = 5 \times (-2)$
$\therefore\frac{5}{8}=\frac{5\times(-2)}{8\times(-2)}=\frac{-10}{-16}$
View full question & answer→Question 412 Marks
Multiply: $\frac{-7}{10}\text{ by }\frac{-40}{21}$
Answer$\frac{-7}{10}\text{ by }\frac{-40}{21}$$=\frac{-7}{10}\times\frac{-40}{21}$
$=\frac{(-7)\times(-40)}{10\times21}$
$=\frac{(-1)\times(-4)}{1\times3}=\frac{4}{3}$
View full question & answer→Question 422 Marks
Write the following rational numbers in standard form: $\frac{8}{-36}$
Answer$\frac{8}{-36}=\frac{8\div4}{-36\div4}$
$(HCL$ of $8$ and $-36 = 4)$
$=\frac{2}{-9}$
View full question & answer→Question 432 Marks
What should be subtracted from $\frac{-3}{4}$ to get $1?$
AnswerLet $x$ be subtracted from $\frac{-3}{4}$
$\therefore\frac{-3}{4}-\text{x}=1$
$\Rightarrow\text{x}=\frac{-3}{4}-1$
$=\frac{-3-4}{4}=\frac{-7}{4}$
$\therefore\frac{-7}{4}$ is to be subtracted.
View full question & answer→Question 442 Marks
Represent the following rational numbers on the number line:
$\frac{-1}{3}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0.$ The number $\frac{-1}{3}$ has been represented on it as given below:
View full question & answer→Question 452 Marks
Write the following rational numbers in standard form: $\frac{-87}{116}$
Answer$\frac{-87}{116}=\frac{-87\div29}{116\div29}$
$(HCL$ of $68$ and $116 = 29)$
$=\frac{-3}{4}$
View full question & answer→Question 462 Marks
Write the following rational numbers in standard form: $\frac{35}{49}$
Answer$\frac{35}{49}=\frac{35\div7}{49\div7}$
$(HCL$ of $35$ and $49 = 7)$
$=\frac{5}{7}$
View full question & answer→Question 472 Marks
Represent the following rational numbers on the number line: $\frac{-12}{7}$
AnswerDraw a number line and locate a point on it. Let it represent $0.$ The number $\frac{-12}{7}$ has been represented on it as given below:
View full question & answer→Question 482 Marks
Somplify:
$\frac{-16}{35}\div\Big(\frac{-15}{14}\Big)$
Answer $\frac{-16}{35}\div\Big(\frac{-15}{14}\Big)$
$=\frac{-16}{35}\times\frac{14}{(-15)}$
$=\frac{-32}{-75}$
$=\frac{32}{75}$
View full question & answer→Question 492 Marks
Express $\frac{-12}{13}$ as a rational number with numerator $60$
AnswerRational number $=\frac{-12}{13}$
$60=-12\times(-5)$
$\therefore\frac{-12}{13}=\frac{-12\times(-5)}{13\times(-5)}=\frac{60}{-65}$
View full question & answer→Question 502 Marks
Express $\frac{-8}{11}$ as a rational number with denominator $22$
AnswerRational number $=\frac{-8}{11}$
$22=11\times2$
$\therefore\frac{-8}{11}=\frac{-8\times2}{11\times2}=\frac{-16}{22}$
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