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?
- $\frac{3}{-5}$
- $\frac{-11}{15}$
- $\frac{-5}{-8}$
- $\frac{37}{53}$
- $\frac{0}{3}$
- $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?
- $\frac{-15}{-4}$
- $0$
- $\frac{-5}{7}$
- $\frac{4}{-9}$
- $-6$
- $\frac{1}{-2}$
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 × 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 × (-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}$
View full question & answer→Question 512 Marks
Multiply:
$\frac{-12}{5}\text{ by }\frac{10}{-3}$
Answer$\frac{-12}{5}\text{ by }\frac{10}{-3}$
$=\frac{-12}{5}\times\frac{10}{-3}$
$=\frac{-12\times10}{5\times(-3)}$
$=\frac{-4\times2}{1\times(-1)}$
$=\frac{-8}{-1}=8$
View full question & answer→Question 522 Marks
Write the following rational numbers in standard form:
$\frac{-14}{-49}$
Answer$\frac{-14}{-49}=\frac{-14\div(-7)}{-49\div(-7)}$
(HCL of -14 and -49 = -7)
$=\frac{2}{7}$
View full question & answer→Question 532 Marks
Simplify:
$-32\times\frac{-7}{36}$
Answer$-32\times\frac{-7}{36}$
$=\frac{(-32)\times(-7)}{36}$
$=\frac{(-8)\times(-7)}{9}$
$=\frac{56}{9}$
View full question & answer→Question 542 Marks
Express $\frac{-8}{11}$ as a rational number with denominator-55
AnswerRational number $=\frac{-8}{11}$
$-55=11\times(-5)$
$\therefore\frac{-8}{11}=\frac{-8\times(-5)}{1\times(-5)}=\frac{40}{-55}$
View full question & answer→Question 552 Marks
What should be subtracted from $\frac{-2}{3}$ to get $\frac{-5}{6}?$
AnswerThe required number $=\frac{-2}{3}-\Big(\frac{-5}{6}\Big)$ (LCM of 3, 6 = 6) $=\frac{-2}{3}+\frac{5}{6}$ $=\frac{-4+5}{6}$$=\frac{1}{6}$
View full question & answer→Question 562 Marks
Evaluate:
$\frac{-3}{5}+\frac{7}{5}+\frac{-1}{5}$
Answer$\frac{-3}{5}+\frac{7}{5}+\frac{-1}{5}$
$=\frac{-3+7+(-1)}{5}$
$=\frac{-3+7-1}{5}$
$=\frac{7-4}{5}=\frac{3}{5}$
View full question & answer→Question 572 Marks
Represent the following rational numbers on the number line:
$\frac{36}{-5}$
AnswerDraw a number line and locate a point O on it. Let it represent 0. The number $\frac{36}{-5}$ has been represented on it as given below:
$\frac{36}{-5}=\frac{-36}{5}=-7\frac{1}{5}$
View full question & answer→Question 582 Marks
Represent the following rational numbers on the number line:
$\frac{-3}{4}$
AnswerDraw a number line and locate a point O on it. Let it represent 0. The number $\frac{-3}{4}$ has been represented on it is as given below: 
View full question & answer→Question 592 Marks
Express $\frac{14}{-5}$ as a rational number with numerator -70
AnswerRational number $=\frac{14}{-5}$
$-70=14\times(-5)$
$\therefore\frac{14}{-5}=\frac{14\times(-5)}{-5\times(5)}=\frac{-70}{25}$
View full question & answer→Question 602 Marks
Find x such that:
$\frac{13}{6}=\frac{-65}{\text{x}}$
Answer$\frac{13}{6}=\frac{-65}{\text{x}}$$\Rightarrow13\times\text{x}=-65\times6$
$\Rightarrow-\text{x}=\frac{-65\times6}{13}$
$=-5\times6=-30$
$\therefore\text{x}=-30$
View full question & answer→Question 612 Marks
Express $\frac{-36}{24}$ as a rational number with numerator 6
AnswerRational number $=\frac{-36}{24}$
$6=-36\div(-6)$
$\therefore\frac{-36}{24}=\frac{-36\div(-6)}{24\div(-6)}=\frac{6}{-4}$
View full question & answer→Question 622 Marks
Express $\frac{13}{-8}$ as a rational number with denominator 32
AnswerRational number $=\frac{13}{-8}$
$32=-8\times(-4)$
$\therefore\frac{13}{-8}=\frac{13\times(-4)}{-8\times5}=\frac{-52}{32}$
View full question & answer→Question 632 Marks
By what number should $-4\frac{3}{8}$ be divided to obtain $-3\frac{1}{2}?$
AnswerLet the required number be x
$-4\frac{3}{8}\div\text{x}=-3\frac{1}{2}$
$\Rightarrow\text{x}=\frac{-35}{8}\times\frac{2}{-7}$
$=\frac{5}{4}$
Hence, the require numbers is $\frac{5}{4}$
View full question & answer→Question 642 Marks
Write the following rational numbers in standard form:
$\frac{-68}{119}$
Answer$\frac{-68}{119}=\frac{-68\div17}{119\div17}$
(HCL of 68 and 119 = 17)
$=\frac{-4}{7}$
View full question & answer→Question 652 Marks
Find x such that:
$\frac{3}{5}=\frac{\text{x}}{-25}$
Answer$\frac{3}{5}=\frac{\text{x}}{-25}$$\Rightarrow5\times\text{x}=3\times(-25)$
$\Rightarrow-\text{x}=\frac{3(-25)}{5}$
$=3\times(-5)=-15$
$\therefore\text{x}=-15$
View full question & answer→Question 662 Marks
Find the multiplicative inverse, or reciprocal of the following:-16
AnswerReciprocal of $-16=\frac{1}{-16}$
$=\frac{1\times(-1)}{-16\times(-1)}=\frac{-1}{16}$
View full question & answer→Question 672 Marks
Find five rational numbers between -1 and 1.
AnswerWe can write $-1=\frac{-3}{3}\text{ and }1\frac{3}{3}$
$\frac{-3}{3}<\frac{-2}{3}<\frac{-1}{3}<\frac{0}{3}<\frac{1}{3}<\frac{2}{3}<\frac{3}{3}$
$\therefore$ Five rational between -1 and 1 are
$\frac{-2}{3}<\frac{-1}{3}<\frac{0}{3}<\frac{1}{3}<\frac{2}{3}$
View full question & answer→Question 682 Marks
Simplify:
$\frac{-9}{8}\times\frac{-16}{3}$
Answer$\frac{-9}{8}\times\frac{-16}{3}$
$=\frac{(-9)\times(-16)}{8\times3}$
$=\frac{(-3)\times(-2)}{1\times1}$
$=\frac{6}{1}=6$
View full question & answer→Question 692 Marks
Find the additive inverse of:
$\frac{15}{-4}$
Answer$\frac{15}{-4}=\frac{15\times(-1)}{-4\times(-1)}=\frac{-15}{4}$
$\therefore$ Additive inverse of $\frac{-15}{4}=-\Big(\frac{-15}{4}\Big)$
$=\frac{15}{4}$
View full question & answer→Question 702 Marks
Add the following rational numbers:
$\frac{-17}{9}\text{ and }\frac{-11}{9}$
Answer$\frac{-17}{9}\text{ and }\frac{-11}{9}$
$=\frac{-17}{9}+\frac{-11}{9}$
$=\frac{-17-11}{9}$
$=\frac{-28}{9}$
View full question & answer→Question 712 Marks
Represent the following rational numbers on the number line:
$\frac{2}{7}$
AnswerDraw a number line and locate a point O on it. Let it represent 0. The number $\frac{2}{7}$ has been represented on the number line given below:
View full question & answer→Question 722 Marks
Simplify:
$-13\times\frac{17}{26}$
Answer$-13\times\frac{17}{26}$$=\frac{-13}{1}\times\frac{17}{26}$
$=\frac{-1\times17}{1\times2}$
$=\frac{-17}{2}$
View full question & answer→Question 732 Marks
Express $\frac{84}{-147}$ as a rational number with denominator 7
AnswerDenominator of $\frac{84}{-147}\text{ is }-147$$\therefore-147\div(-21)=7$
Dividing both the numerator and the denominator by -21
$\frac{84\div(-21)}{-147\div(-21)}=\frac{-4}{7}$
$=\frac{8}{-147}=\frac{-4}{7}$
View full question & answer→Question 742 Marks
Express $\frac{4}{7}$ as a rational number with denominator 21
AnswerRational number $=\frac{4}{7}$
$21=7\times3$
$\therefore\frac{4}{7}=\frac{4\times3}{7\times3}=\frac{12}{21}$
View full question & answer→Question 752 Marks
Find the multiplicative inverse, or reciprocal of the following:
$\frac{-3}{-5}$
AnswerReciprocal of $\frac{-3}{-5}=\frac{-5}{-3}$
$=\frac{-5\times(-1)}{-3\times(-1)}=\frac{5}{3}$
View full question & answer→Question 762 Marks
Find the multiplicative inverse, or reciprocal of the following:
$\frac{-17}{12}$
AnswerReciprocal of $\frac{-17}{12}=\frac{12}{-17}$
$=\frac{12\times(-1)}{-17\times(-1)}=\frac{-12}{17}$
View full question & answer→Question 772 Marks
Find x such that:
$\frac{16}{\text{x}}-4$
Answer$\frac{16}{\text{x}}-4$$\Rightarrow-4\times\text{x}=16$
$\Rightarrow-\text{x}=\frac{16}{-4}=-4$
$\therefore\text{x}=-4$
View full question & answer→Question 782 Marks
Simplify:
$\frac{-13}{5}\times-10$
Answer$\frac{-13}{5}\times-10$$=\frac{-13}{5}\times\frac{-10}{1}$
$=\frac{(-13)\times(-10)}{5\times1}$
$=\frac{(-13)\times(-2)}{1\times1}$ $=26$
View full question & answer→Question 792 Marks
Simplify:
$\frac{-19}{36}\times16$
Answer$\frac{-19}{36}\times16$$=\frac{-19}{36}\times\frac{16}{1}$
$=\frac{-19\times16}{36\times1}$
$=\frac{-19\times4}{9\times1}=\frac{-76}{9}$
View full question & answer→Question 802 Marks
Find the multiplicative inverse, or reciprocal of the following:
$\frac{-6}{19}$
AnswerReciprocal of $\frac{-6}{19}=\frac{19}{-6}$
$=\frac{19\times(-1)}{-6\times(-1)}=\frac{-19}{6}$
View full question & answer→Question 812 Marks
Express $\frac{14}{-5}$ as a rational number with numerator 56
AnswerRational number $=\frac{14}{-5}$
$56=14\times4$
$\therefore\frac{14}{-5}=\frac{14\times4}{-5\times4}=\frac{56}{20}$
View full question & answer→Question 822 Marks
Write the following rational numbers in standard form:
$\frac{299}{-161}$
Answer$\frac{299}{-161}=\frac{299\div23}{161\div23}$
(HCL of 299 and 161 = 23)
$=\frac{13}{-7}$
View full question & answer→Question 832 Marks
Express $\frac{-12}{13}$ as a rational number with numerator -48
AnswerRational number $=\frac{-12}{13}$
$-48=-12\times4$
$\therefore\frac{-12}{13}=\frac{-12\times4}{13\times4}=\frac{-48}{52}$
View full question & answer→Question 842 Marks
Represent the following rational numbers on the number line:
$\frac{22}{7}$
AnswerDraw a number line and locate a point O on it. Let it represent 0. The number $\frac{22}{7}$ has been represented on it as given below:
View full question & answer→Question 852 Marks
Fill in the blank:
$\frac{-6}{11}=\frac{-18}{\dots}=\frac{\dots}{-18}$
Answer$\frac{-6}{11}=\frac{-18}{\dots}=\frac{\dots}{44}$
$-18=-6\times3$
$\therefore\frac{-6}{11}=\frac{-6\times3}{11\times3}=\frac{-18}{33}$
$\therefore\frac{-6}{11}=\frac{-6\times3}{11\times3}=\frac{-18}{33}$
$44=11\times4$
$\therefore\frac{-6}{11}=\frac{-6\times4}{11\times4}=\frac{-24}{44}$
$\therefore\frac{-6}{11}=\frac{-18}{33}=\frac{-24}{44}$
View full question & answer→Question 862 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 Now $\frac{1}{3}$ has been presented on the number line given below.
View full question & answer→Question 872 Marks
Somplify:
$\frac{-12}{7}\div(-18)$
Answer$\frac{-12}{7}\div(-18)$
$=\frac{12}{7}\times\Big(\frac{-1}{18}\Big)$
$=\frac{2}{21}$
View full question & answer→Question 882 Marks
What should be subtracted from $\frac{-3}{4}$ to get $\frac{5}{6}?$
AnswerThe required number $=\frac{-3}{4}-\frac{5}{6}$
(LCM of 4, 6 = 12)
$=\frac{-9-10}{12}$
$=-\frac{19}{12}$
View full question & answer→Question 892 Marks
Somplify:
$-8\div\Big(\frac{-5}{16}\Big)$
Answer$-8\div\Big(\frac{-5}{16}\Big)$
$=-8\times\frac{-16}{5}$
$=\frac{128}{5}$
View full question & answer→Question 902 Marks
Which of the following are pairs of equivalent rational number?
$\frac{-13}{7},\frac{39}{-21}$
Answer$\frac{-13}{7},\frac{39}{-21}$
$\frac{39}{-21}=\frac{39\div3}{-21\div3}=\frac{13}{-7}$
$=\frac{13\times(1)}{-7\times(-1)}=\frac{-13}{7}$
(HCF of 39 and 21 = 3)
$\therefore\frac{-13}{7}\text{ and }\frac{29}{-21}$ are equivalent rational numbers.
View full question & answer→Question 912 Marks
Represent the following rational numbers on the number line:
$\frac{-43}{9}$
View full question & answer→Question 922 Marks
What should be added to $\frac{2}{9}$ to get -1?
AnswerThe required number $=\frac{-1}{1}-\frac{2}{9}$
$=\frac{-9-2}{9}$
$=\frac{-11}{9}$
View full question & answer→Question 932 Marks
Find the additive inverse of:
$\frac{-18}{-13}$
Answer$\frac{-18}{-13}=\frac{-18\times(-1)}{-13\times(-1)}=\frac{18}{13}$
$\therefore$ Additive inverse of $\frac{18}{13}=-\Big(\frac{18}{13}\Big)$
$=\frac{-18}{13}$
View full question & answer→Question 942 Marks
Simplify:
$\frac{3}{20}\times\frac{4}{5}$
Answer$\frac{3}{20}\times\frac{4}{5}$
$=\frac{3\times4}{20\times5}$
$=\frac{3\times1}{5\times5}$
$=\frac{3}{25}$
View full question & answer→Question 952 Marks
Simplify:
$\frac{7}{24}\times-48$
Answer$\frac{7}{24}\times-48$
$=\frac{7}{24}\times\frac{(-48)}{1}$
$=\frac{7\times(-48)}{24\times1}$
$=\frac{7\times(-2)}{1\times1}=-14$
View full question & answer→Question 962 Marks
Express $\frac{-36}{24}$ as a rational number with numerator -9
AnswerRational number $=\frac{-36}{24}$
$-9=-36\div4$
$\therefore\frac{-36}{24}=\frac{-36\div4}{24\div4}=\frac{-9}{6}$
View full question & answer→Question 972 Marks
Add the following rational numbers:
$\frac{9}{-13}\text{ and }\frac{-11}{-13}$
Answer$\frac{9}{-13}\text{ and }\frac{-11}{-13}$
$\frac{9}{-13}=\frac{9\times(-1)}{-13\times(-1)}=\frac{-9}{13}$
$\frac{-11}{-13}=\frac{-11\times(-1)}{-13\times(-1)}=\frac{11}{13}$
$\therefore\frac{-9}{13}+\frac{11}{13}=\frac{-9+11}{13}$
$=\frac{2}{13}$
View full question & answer→Question 982 Marks
Which of the two rational numbers is greater in the following pairs?
$\frac{-6}{11}\text{ or }\frac{-5}{11}$
Answer$\frac{-6}{11}\text{ or }\frac{-5}{11}$ $\Rightarrow\frac{-6}{11}\text{ or }\frac{5\times(-1)}{-11\times(-1)}$ (Making denominator positive) $\Rightarrow\frac{-6}{11}\text{ or }\frac{-5}{11}$$\frac{-5}{11}$ is greater as (-5) is greater than (-6)
$\therefore\frac{5}{-11}>\frac{-6}{11}$
View full question & answer→Question 992 Marks
Simplify:
$\frac{-7}{30}\times\frac{5}{15}$
Answer$\frac{-7}{30}\times\frac{5}{15}$
$=\frac{-7\times5}{30\times14}$
$=\frac{-1\times1}{6\times2}$
$=\frac{-1}{2}$
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