Question 14 Marks
What rational number should be subtracted from $\frac{5}{8}$ to get $\frac{8}{5}$.
AnswerThe required number $=\frac{5}{8}-\frac{8}{5}$
$\begin{aligned} & =\frac{5 \times 5}{8 \times 5}-\frac{8 \times 8}{5 \times 8} \\ & (\because \text { L.C.M. of } 8,5=40) \\ & =\frac{25-64}{40}=-\frac{39}{40}\end{aligned}$ View full question & answer→Question 24 Marks
Evaluate: $3 \frac{5}{12}-1 \frac{2}{3}$
Answer
$\begin{aligned} & 3 \frac{5}{12}-1 \frac{2}{3} \\ & =\frac{12 \times 3+5}{12}-\frac{3 \times 1+2}{3} \\ & =\frac{41}{12}-\frac{5}{3} \quad(\because \text { L.C.M. of } 12,3=12) \\ & =\frac{41 \times 1}{12 \times 1}-\frac{5 \times 4}{3 \times 4} \\ & =\frac{41}{12}-\frac{20}{12} \\ & =\frac{41-20}{12}=\frac{21}{12}=\frac{7}{4}=1 \frac{3}{4}\end{aligned}$
View full question & answer→Question 34 Marks
Evaluate: $3 \frac{5}{12}+1 \frac{2}{3}$
Answer
$\begin{aligned} & 3 \frac{5}{12}+1 \frac{2}{3} \\ & =\frac{12 \times 3+5}{12}+\frac{3 \times 1+2}{3} \\ & =\frac{41}{12}+\frac{5}{3} \quad(\because \text { L.C.M. of } 12,3=12) \\ & =\frac{41 \times 1}{12 \times 1}+\frac{5 \times 4}{3 \times 4} \\ & =\frac{41}{12}+\frac{20}{12} \\ & =\frac{41+20}{12}=\frac{61}{12}=5 \frac{1}{12}\end{aligned}$
View full question & answer→Question 44 Marks
A bus is moving with a speed of $65 \frac{1}{2} \mathrm{~km}$ per hour. How much distance will it cover in $1 \frac{1}{3}$ hours.
Answer
$ \begin{aligned} & \text { Speed of bus per hour }=65 \frac{1}{2} \\ & =\frac{2 \times 65+1}{2}=\frac{130+1}{2}=\frac{131}{2} \mathrm{~km} \end{aligned} $
Time taken $=1 \frac{1}{3}$ hour $=\frac{4}{3}$ hour
$ =\frac{131}{2} \times \frac{4}{3} \Rightarrow \frac{131}{1} \times \frac{2}{3} $
Distance covered $=$ Speed $\times$ Time
$ =\frac{131}{2} \times \frac{4}{3} $
$ =\frac{131 \times 2}{1 \times 3}=\frac{262}{3}=87 \frac{1}{3} \mathrm{~km} $
View full question & answer→Question 54 Marks
Find the cost of $3 \frac{1}{2} \mathrm{~m}$ cloth, if one metre cloth costs ₹ $325 \frac{1}{2}$.
Answer
$ \begin{aligned} & \text { Cost of } 1 \text { meter cloth }=\text { Rs. } 325 \frac{1}{2} \\ & \frac{2 \times 325+1}{2}=\frac{650+1}{2}=\frac{651}{2} \end{aligned} $
Now cost of $3 \frac{1}{2} \mathrm{~m}\left(\frac{2 \times 3+1}{2}=\frac{7}{2}\right) \mathrm{m}$
$ =\frac{651}{2} \times \frac{7}{2}=\frac{651 \times 7}{2 \times 2} $
$ =\frac{4557}{4}=1139 \frac{1}{4} $
View full question & answer→Question 64 Marks
Evaluate: $\left(\frac{11}{-9} \times \frac{21}{44}\right)+\left(\frac{-5}{9}\right) \times\left(\frac{63}{-100}\right)$
Answer
$\begin{aligned} & \left(\frac{11}{-9} \times \frac{21}{44}\right)+\left(\frac{-5}{9}\right) \times\left(\frac{63}{-100}\right) \\ & =\left(\frac{11}{-9} \times \frac{21}{44}\right)+\left(\frac{5}{9} \times \frac{63}{100}\right) \\ & =-\frac{1 \times 7}{3 \times 4}+\frac{1 \times 7}{1 \times 20}=-\frac{7}{12}+\frac{7}{20} \\ & =-\frac{7 \times 5}{12 \times 5}+\frac{7 \times 3}{20 \times 3} \\ & (\because \text { L.C.M. of } 12 \text { and } 20=60) \\ & =-\frac{35}{60}+\frac{21}{60}=\frac{-35+21}{60}=\frac{-14}{60}\end{aligned}$
View full question & answer→Question 74 Marks
Evaluate: $\left(-6 \times \frac{5}{18}\right)-\left(-4 \frac{2}{9}\right)$
Answer
$\begin{aligned} & \left(-6 \times \frac{5}{18}\right)-\left(-4 \frac{2}{9}\right) \\ & =\left(-1 \times \frac{5}{3}\right)-\left(\frac{-(4 \times 9+2)}{9}\right)\end{aligned}$
$\begin{aligned} & \text { L.C.M. }=9 \\ & =\frac{-5}{3}-\left(\frac{-38}{9}\right) \\ & =\frac{-5}{3}+\frac{38}{9}=\frac{-5 \times 3}{3 \times 3}+\frac{38 \times 1}{9 \times 1} \\ & =\frac{-15+38}{9} \Rightarrow \frac{23}{9}=2 \frac{5}{9}\end{aligned}$ View full question & answer→Question 84 Marks
Evaluate: $5+\frac{-3}{4}+\frac{-5}{8}$
Answer
$ \begin{aligned} & 5+\frac{-3}{4}+\frac{-5}{8} \\ & \frac{5}{1}+\frac{-3}{4}+\frac{-5}{8} \end{aligned} $
$ =\frac{5 \times 8}{1 \times 8}+\frac{(-3) \times 2}{4 \times 2}+\frac{(-5) \times 1}{8 \times 1} $
$(\because$ L.C.M. of 1,4 and $8=8$ )
$ =\frac{40}{8}+\frac{-6}{8}+\frac{-5}{8} $
$ =\frac{40-6-5}{8}=\frac{40-11}{8}=\frac{29}{8} $
View full question & answer→Question 94 Marks
Evaluate: $-\frac{2}{3}+\frac{5}{2}+2$
Answer
$\begin{aligned} & -\frac{2}{3}+\frac{5}{2}+2 \\ & =-\frac{2}{3}+\frac{5}{2}+\frac{2}{1} \\ & =\frac{-2 \times 2}{3 \times 2}+\frac{5 \times 3}{2 \times 3}+\frac{2 \times 6}{1 \times 6} \\ & (\because \text { L.C.M. of } 3,2 \text { and } 1=6) \\ & =\frac{-4}{6}+\frac{15}{6}+\frac{12}{6} \\ & =\frac{-4+15+12}{6}=\frac{23}{6}\end{aligned}$
View full question & answer→Question 104 Marks
Evaluate: $-5+\frac{5}{-8}+\frac{-5}{-12}$
Answer
$\begin{aligned} & -5+\frac{5}{-8}+\frac{-5}{-12} \\ & \frac{-5}{1}+\frac{-5}{8}+\frac{5}{12} \\ & =\frac{-5 \times 24}{1 \times 24}+\frac{-5 \times 3}{8 \times 3}+\frac{5 \times 2}{12 \times 2} \\ & (\because \text { L.C.M. of } 1,8 \text { and } 12=24) \\ & =\frac{-120}{24}+\frac{-15}{24}+\frac{10}{24} \\ & =\frac{-120-15+10}{24}=\frac{-125}{24}\end{aligned}$
View full question & answer→Question 114 Marks
Evaluate: $\frac{-9}{4}+\frac{13}{3}+\frac{25}{6}$
Answer$\frac{-9}{4}+\frac{13}{3}+\frac{25}{6}$
LCM of $4,3$ and $6$ is $12 .$
$ \frac{-9}{4} \Rightarrow \frac{-9}{4} \times \frac{3}{3}=\frac{-27}{12}$
$\frac{13}{3} \Rightarrow \frac{13}{3} \times \frac{4}{4}=\frac{52}{12}$
$\frac{25}{6} \Rightarrow \frac{25}{6} \times \frac{2}{2}=\frac{50}{12}$
$=\frac{-27+52+50}{12} $
$=\frac{75}{12}=\frac{25}{4}$
$\therefore \frac{-9}{4}+\frac{13}{3}+\frac{25}{6}=\frac{25}{4}$
View full question & answer→Question 124 Marks
Evaluate: $-\frac{11}{18}+\frac{-3}{9}+\frac{2}{-3}$
Answer
$\begin{aligned} & -\frac{11}{18}+\frac{-3}{9}+\frac{2}{-3} \\ & =\frac{-11}{18}+\frac{-3}{9}+\frac{-2}{3} \\ & =\frac{-11 \times 1}{18 \times 1}+\frac{-3 \times 2}{9 \times 2}+\frac{-2 \times 6}{3 \times 6} \\ & (\because \text { L.C.M. of } 3,9 \text { and } 18=18) \\ & =\frac{-11}{18}+\frac{-6}{18}+\frac{-12}{18} \\ & =\frac{-11-6-12}{18}=\frac{-29}{18}\end{aligned}$
View full question & answer→Question 134 Marks
Evaluate: $\frac{-11}{12}+\frac{5}{16}+\frac{-3}{8}$
Answer
$\begin{aligned} & \frac{-11}{12}+\frac{5}{16}+\frac{-3}{8} \\ & =\frac{-11 \times 4}{12 \times 4}+\frac{5 \times 3}{16 \times 3}+\frac{-3 \times 6}{8 \times 6} \quad \text { ( } \because \text { L.C.M. of 8, 12, 16 =48) } \\ & =\frac{-44}{48}+\frac{15}{48}+\frac{-18}{48} \\ & =\frac{-44+15-18}{48} \\ & =\frac{-62+15}{48}=\frac{-47}{48}\end{aligned}$
View full question & answer→Question 144 Marks
Evaluate: $-2+\frac{2}{5}+\frac{-2}{15}$
Answer
$\begin{aligned} & -2+\frac{2}{5}+\frac{-2}{15} \\ & \frac{-2}{1}+\frac{2}{5}+\frac{-2}{15} \\ & =\frac{-2 \times 15}{1 \times 15}+\frac{2 \times 3}{5 \times 3}+\frac{-2 \times 1}{15 \times 1} \quad(\because \text { L.C.M. of } 1,5,15=15) \\ & =\frac{-30}{15}+\frac{6}{15}+\frac{-2}{15} \\ & =\frac{-30+6-2}{15} \\ & =\frac{-32+6}{15}=\frac{-26}{15}\end{aligned}$
View full question & answer→Question 154 Marks
Evaluate: $\frac{-7}{6}+\frac{4}{-15}+\frac{-4}{-30}$
Answer
$\begin{aligned} & \frac{-7}{6}+\frac{4}{-15}+\frac{-4}{-30} \\ & =\frac{-7}{6}+\frac{-4}{15}+\frac{4}{30} \\ & =\frac{-7 \times 5}{6 \times 5}+\frac{-4 \times 2}{15 \times 2}+\frac{4 \times 1}{30 \times 1} \quad(\because \text { L.C.M. of } 6,15,30=30) \\ & =\frac{-35}{30}+\frac{-8}{30}+\frac{4}{30} \\ & =\frac{-35-8+4}{30} \\ & =\frac{-43+4}{30}=\frac{-39}{30}\end{aligned}$
View full question & answer→Question 164 Marks
What should be subtracted from $\frac{5}{9}$ to get $\frac{9}{5} ?$
AnswerLet the first number be $x$
Other number $=\frac{5}{9}$
Difference of two number $=\frac{9}{5}$
According to question,
$ \begin{aligned} & \therefore \frac{5}{9}-\mathrm{x}=\frac{9}{5} \\ & \mathrm{x}=\frac{5}{9}-\frac{9}{5} \\ & \mathrm{x}=\frac{5 \times 5}{9 \times 5}-\frac{9 \times 9}{5 \times 9} \\ & (\because \text { L.C.M. of } 9 \text { and } 5=45) \\ & \mathrm{x}=\frac{25}{45}-\frac{81}{45} \\ & \mathrm{x}=\frac{25-81}{45}=-\frac{56}{45} \end{aligned} $
View full question & answer→Question 174 Marks
What should be added to $\frac{-7}{12}$ to get $\frac{3}{8} ?$
AnswerLet the required rational number be $=x$
Other number $=\frac{-7}{12}$
Sum of two numbers $=\frac{3}{8}$
$ \begin{aligned} & \therefore \frac{-7}{12}+\mathrm{x}=\frac{3}{8} \\ & \Rightarrow \mathrm{x}=\frac{3}{8}-\frac{-7}{12} \\ & =\frac{3 \times 3}{8 \times 3}+\frac{7 \times 2}{12 \times 2} \end{aligned} $
$(\because$ L.C.M. of 8 and $12=24)$
$ \begin{aligned} & =\frac{9}{24}+\frac{14}{24} \\ & =\frac{9+14}{24}=\frac{23}{24} \end{aligned} $
View full question & answer→Question 184 Marks
What should be added to $-\frac{3}{6}$ to get $-\frac{11}{24} ?$
AnswerLet the required rational number be $x$
Other number $=-\frac{3}{16}$
Sum of two number $=\frac{11}{24}$
According to question,
$ \begin{aligned} & -\frac{3}{16}+\mathrm{x}=\frac{11}{24} \\ & \Rightarrow \mathrm{x}=\frac{11}{24}+\frac{3}{16} \\ & \mathrm{x}=\frac{11 \times 2}{24 \times 2}+\frac{3 \times 3}{16 \times 3} \end{aligned} $
$(\because$ L.C.M. of 16 and $24=48)$
$ \begin{aligned} & x=\frac{22}{48}+\frac{9}{48} \\ & x=\frac{22+9}{48}=\frac{31}{48} \end{aligned} $
View full question & answer→Question 194 Marks
Arrange the given rational numbers in descending order:
$\frac{3}{-10}, \frac{-13}{30} \text { and } \frac{8}{-20}$
Answer
$\begin{aligned} & \frac{3}{-10}, \frac{-13}{30} \text { and } \frac{8}{-20} \\ & =\frac{-3}{10}, \frac{-13}{30} \text { and } \frac{-8}{20} \\ & =\frac{-3 \times 6}{10 \times 6}, \frac{-13 \times 2}{30 \times 2} \text { and } \frac{-8 \times 3}{20 \times 3} \\ & (\because \text { LCM of } 10,20 \text { and } 30=60)=\frac{-18}{60}, \frac{-26}{60} \text { and } \frac{-24}{60} \\ & =\frac{-18}{60}, \frac{-26}{60} \text { and } \frac{-24}{60}\end{aligned}$
Since, $-18>-24>-26$
$
\begin{aligned}
& \therefore \frac{-18}{60}>\frac{-24}{60}>\frac{-26}{60} \\
& \Rightarrow \frac{-3}{10}>\frac{-8}{20}>\frac{-13}{30}
\end{aligned}
$ View full question & answer→Question 204 Marks
Arrange the given rational numbers in descending order:
$\frac{5}{8}, \frac{13}{-16} \text { and } \frac{-7}{12}$
Answer
$\begin{aligned} & \frac{5}{8}, \frac{13}{-16} \text { and } \frac{-7}{12} \\ & =\frac{5}{8}, \frac{-13}{16} \text { and } \frac{-7}{12} \\ & =\frac{5 \times 6}{8 \times 6}, \frac{-13 \times 3}{16 \times 3} \text { and } \frac{-7 \times 4}{12 \times 4} \\ & (\because \text { LCM of } 8,16 \text { and } 12=48) \\ & =\frac{30}{48}, \frac{-39}{48} \text { and } \frac{-28}{48}\end{aligned}$
Since, $30>-28>-39$
$
\begin{aligned}
& \therefore \frac{30}{48}>\frac{-28}{48}>\frac{-39}{48} \\
& \Rightarrow \frac{5}{8}>\frac{-7}{12}>\frac{-13}{16}
\end{aligned}
$ View full question & answer→Question 214 Marks
Arrange the given rational numbers in ascending order:
$\frac{4}{-9}, \frac{-5}{12} \text { and } \frac{2}{-3}$
Answer
$
\begin{aligned}
& \frac{4}{-9}, \frac{-5}{12} \text { and } \frac{2}{-3} \\
& =\frac{-4}{9}, \frac{-5}{12} \text { and } \frac{-2}{3} \\
& =\frac{-4 \times 4}{9 \times 4}, \frac{-5 \times 3}{12 \times 3} \text { and } \frac{-2 \times 12}{3 \times 12}
\end{aligned}
$
( $\because$ LCM of 9,12 and $3=36$ )
$
=\frac{-16}{36}, \frac{-15}{36}, \frac{-24}{36}
$
$\begin{aligned} & \text { Since, }-24<-16<-15 \\ & \therefore \frac{-24}{36}<\frac{-16}{36}<\frac{-15}{36} \\ & \Rightarrow \frac{2}{-3}<\frac{4}{-9}<\frac{-5}{12}\end{aligned}$ View full question & answer→Question 224 Marks
Arrange the given rational numbers in ascending order:
$\frac{7}{10}, \frac{-11}{-30} \text { and } \frac{5}{-15}$
Answer
$\begin{aligned} & \frac{7}{10}, \frac{-11}{-30} \text { and } \frac{5}{-15} \\ & =\frac{7}{10}, \frac{11}{30} \text { an d } \frac{-5}{15} \\ & =\frac{7 \times 3}{10 \times 3}, \frac{11}{30} \text { and } \frac{-5 \times 2}{15 \times 2} \\ & (\because \text { LCM of } 10,30 \text { and } 15=30) \\ & =\frac{21}{30}, \frac{11}{30}, \frac{-10}{30}\end{aligned}$
Since, $-10<11<21$
$
\begin{aligned}
& \therefore \frac{-10}{30}<\frac{11}{30}<\frac{21}{30} \\
& \Rightarrow \frac{5}{-15}<\frac{-11}{-30}<\frac{7}{10}
\end{aligned}
$ View full question & answer→Question 234 Marks
Find $x$, such that: $\frac{-2}{3}=\frac{6}{x}$
Answer
$\begin{aligned} & \frac{-2}{3}=\frac{6}{x} \\ & -2 x=6 \times 3 \\ & x=\frac{6 \times 3}{-2}=-3 \times 3=-9 \\ & \therefore \frac{-2}{3}=\frac{6}{-9}=-\frac{6}{9} \\ & \text { OR } \\ & \frac{-2}{3}=\frac{6}{x} \\ & \Rightarrow \frac{-2 \times 3}{-3 \times 3}=\frac{6}{x} \\ & \Rightarrow \frac{6}{-9}=\frac{6}{x} \\ & \Rightarrow x=-9\end{aligned}$
View full question & answer→Question 244 Marks
Evaluate: $\left(\frac{-13}{7} \times \frac{-35}{39}\right)-\left(\frac{-7}{45} \times \frac{9}{14}\right)$
Answer
$\begin{aligned} & \left(\frac{-13}{7} \times \frac{-35}{39}\right)-\left(\frac{-7}{45} \times \frac{9}{14}\right) \\ & \Rightarrow \frac{-13 \times(-35)}{7 \times 39}+\frac{7 \times 9}{45 \times 14} \\ & \Rightarrow \frac{-1 \times(-5)}{1 \times 3}+\frac{1 \times 1}{5 \times 2} \\ & \Rightarrow \frac{5}{3}+\frac{1}{10}\end{aligned}$
L.C.M. of 3 and $10=2 \times 3 \times 5=10$
$ \begin{aligned} & \Rightarrow \frac{5 \times 10}{3 \times 10}+\frac{1 \times 3}{10 \times 3} \\ & (\because \text { L.C.M. of } 3 \text { and } 10=30) \\ & \Rightarrow \frac{50+3}{30}=\frac{53}{30}=1 \frac{23}{30} \end{aligned} $ View full question & answer→Question 254 Marks
Evaluate: $\left(\frac{18}{33} \times \frac{-22}{27}\right)+\left(\frac{13}{25} \times \frac{-75}{26}\right)$
Answer
$\begin{aligned} & \left(\frac{18}{33} \times \frac{-22}{27}\right)+\left(\frac{13}{25} \times \frac{-75}{26}\right) \\ & \Rightarrow \frac{18 \times(-22)}{33 \times 27}-\frac{13 \times(-75)}{25 \times 26} \\ & \Rightarrow \frac{2 \times(-2)}{3 \times 3}-\frac{1 \times-3}{1 \times 2} \\ & \Rightarrow \frac{-4}{9}-\left(\frac{-3}{2}\right)=\frac{-4}{9}+\frac{3}{2}\end{aligned}$
L.C.M. of 9 and $2=2 \times 3 \times 3=18$
$ \Rightarrow \frac{-4 \times 2}{9 \times 2}+\frac{3 \times 9}{2 \times 9} $
$(\because$ L.C.M. of 9 and $2=18$ )
$ \Rightarrow \frac{-8+27}{18}=\frac{19}{18}=1 \frac{1}{18} $ View full question & answer→Question 264 Marks
Evaluate: $\left(\frac{8}{15} \times \frac{-25}{16}\right)+\left(\frac{-18}{35} \times \frac{5}{6}\right)$
Answer
$\begin{aligned} & \left(\frac{8}{15} \times \frac{-25}{16}\right)+\left(\frac{-18}{35} \times \frac{5}{6}\right) \\ & \Rightarrow \frac{8 \times(-25)}{15 \times 16}+\frac{-18 \times 5}{35 \times 6} \\ & \Rightarrow \frac{1 \times(-5)}{3 \times 2}+\frac{-3 \times 1}{7 \times 1} \\ & \Rightarrow \frac{-5}{6}-\frac{3}{7}\end{aligned}$
L.C.M. of 6 and $7=2 \times 3 \times 7=42$
$(\because$ L.C.M. of 6 and $7=42)$
$ \Rightarrow \frac{-5 \times 7}{6 \times 7}+\frac{3 \times 6}{7 \times 6} $
$ \Rightarrow \frac{-35-18}{42}=\frac{-53}{42} $ View full question & answer→Question 274 Marks
Evaluate: $\left(\frac{7}{8} \times \frac{24}{21}\right)+\left(\frac{-5}{9} \times \frac{6}{-25}\right)$
Answer
$\begin{aligned} & \left(\frac{7}{8} \times \frac{24}{21}\right)+\left(\frac{-5}{9} \times \frac{6}{-25}\right) \\ & \Rightarrow \frac{7 \times 24}{8 \times 21}+\frac{-5 \times 6}{9 \times(-25)} \\ & \Rightarrow \frac{1 \times 3}{1 \times 3}+\frac{1 \times 2}{3 \times 5} \\ & \Rightarrow \frac{3}{3}+\frac{2}{15}\end{aligned}$
$(\because$ L.C.M. of 3 and $15=15)$
$\begin{aligned} & \Rightarrow \frac{3 \times 5}{3 \times 5}+\frac{2 \times 1}{15 \times 1} \\ & \Rightarrow \frac{15+2}{15}=\frac{17}{15}=1 \frac{2}{15}\end{aligned}$ View full question & answer→Question 284 Marks
What rational number should be added to $-\frac{3}{16}$ to get $\frac{11}{24}$
Answer
Sum of two numbers $=\frac{11}{24}$
One number $=-\frac{3}{16}$
$\therefore$ The required number $=\frac{11}{24}-\left(\frac{-3}{16}\right) \Rightarrow \frac{11}{24}+\frac{3}{16}$| 2 | 24,16 |
| 2 | 12,8 |
| 2 | 6,4 |
| 2 | 3,2 |
| 3 | 3,1 |
| | 1 |
L.C.M. of 16 and $24=2 \times 2 \times 2 \times 2 \times 3=48$
$ \begin{aligned} & (\because \text { L.C.M. of } 24,16=48) \\ & =\frac{11 \times 2}{24 \times 2}-\frac{3 \times 3}{16 \times 3} \end{aligned} $
$ =\frac{22+9}{48}=\frac{31}{48} $ View full question & answer→Question 294 Marks
The sum of two rational numbers is $\frac{-3}{8}$. If one of them is $\frac{3}{16}$ find the other,
Answer
Sum of two numbers $=\frac{-3}{8}$
One number $=\frac{3}{16}$
$\therefore$ Second number $=\frac{-3}{8}-\frac{3}{16}$
L.C.M. of 8 and $16=2 \times 2 \times 2 \times 2=16$
$ =\frac{-3 \times 2}{8 \times 2}-\frac{3 \times 1}{16 \times 1} $
$(\because$ L.C.M. of 8 and $16=16)$
$ =\frac{-6-3}{16}=\frac{-9}{16} $
$\therefore$ Second number $=\frac{-9}{16}$ View full question & answer→Question 304 Marks
Evaluate: $-1+\frac{2}{-3}+\frac{5}{6}$
Answer
$-1+\frac{2}{-3}+\frac{5}{6}$
L.C.M. of 3 and $6=2 \times 3=6$
$ \begin{aligned} & \Rightarrow \frac{-1 \times 6}{1 \times 6}-\frac{2 \times 2}{3 \times 2}+\frac{5 \times 1}{6 \times 1} \\ & (\because \text { L.C.M. of } 3 \text { and } 6=6) \end{aligned} $
$ \Rightarrow \frac{-6-4+5}{6} $
$ =\frac{-10+5}{6}=-\frac{5}{6} $ View full question & answer→Question 314 Marks
Evaluate: $\frac{7}{26}+2+\frac{-11}{13}$
Answer
$\begin{aligned} & \frac{7}{26}+2+\frac{-11}{13} \\ & \Rightarrow \frac{7}{26}+\frac{2}{1}+\frac{-11}{13}\end{aligned}$
L.C.M. of 26 and $13=2 \times 13=26$
$ \Rightarrow \frac{7 \times 1}{26 \times 1}+\frac{2 \times 26}{1 \times 26}-\frac{11 \times 2}{13 \times 2} $
$(\because$ L.C.M. of 26 and $13=26)$
$ \Rightarrow \frac{7+52-22}{26} $
$ =\frac{59-22}{26}=\frac{37}{26} $ View full question & answer→Question 324 Marks
Evaluate: $-\frac{5}{7}-\left(-\frac{3}{8}\right)$
Answer
$\begin{aligned} & -\frac{5}{7}-\left(-\frac{3}{8}\right) \\ & -\frac{5}{7}+\frac{3}{8}\end{aligned}$
L.C.M. of 7 and $8=2 \times 2 \times 2 \times 7=56$
$ \Rightarrow \frac{-5 \times 8}{7 \times 8}+\frac{3 \times 7}{8 \times 7} $
$(\because$ L.C.M. of 7 and $8=56)$
$ =\frac{-40+21}{56}=\frac{-19}{56} $ View full question & answer→Question 334 Marks
Evaluate: $-\frac{2}{3}-\left(\frac{-5}{7}\right)$
Answer
$\begin{aligned} & -\frac{2}{3}-\left(\frac{-5}{7}\right) \\ & \Rightarrow-\frac{2}{3}+\frac{5}{7}\end{aligned}$
L.C.M. of 3 and $7=3 \times 7=21$
$ \begin{aligned} & \Rightarrow \frac{-2 \times 7}{3 \times 7}+\frac{5 \times 3}{7 \times 3} \\ & (\because \text { L.C.M. of } 3 \text { and } 7=21)
\end{aligned} $
$ =\frac{-14+15}{21}=\frac{1}{21} $ View full question & answer→Question 344 Marks
Evaluate: $\frac{7}{-26}+\frac{16}{39}$
Answer$\frac{7}{-26}+\frac{16}{39}$
L.C.M. of 26 and $39=2 \times 3 \times 13=78$
$ \begin{aligned} & \Rightarrow \frac{-7 \times 3}{26 \times 3}+\frac{16 \times 2}{39 \times 2} \\ & (\because \text { L.C.M. of }-26 \text { and } 39=78) \end{aligned} $
$ =\frac{-21+32}{78}=\frac{11}{78}
$ View full question & answer→Question 354 Marks
Evaluate: $\frac{-5}{9}+\frac{-7}{12}+\frac{11}{18}$
Answer$\frac{-5}{9}+\frac{-7}{12}+\frac{11}{18}$| 2 | 9,12,18 |
| 2 | 9,6,9 |
| 3 | 9,3,9 |
| 3 | 3,1,3 |
| | 1,1,1 |
L.C.M. of 9,12 and $18=2 \times 2 \times 3 \times 3=36$
$ \begin{aligned} & \Rightarrow \frac{-5 \times 4}{9 \times 4}+\frac{7 \times 3}{12 \times 3}+\frac{11 \times 2}{18 \times 2} \\ & (\because \text { L.C.M. of } 9,12 \text { and } 18=36) \end{aligned} $
$(\because$ L.C.M. of 9,12 and $18=36$ )
$ \begin{aligned} & \Rightarrow \frac{-20-21+22}{36} \\ & =\frac{-41+22}{36}=\frac{-19}{36} \end{aligned} $ View full question & answer→Question 364 Marks
Evaluate: $\frac{9}{-16}+\left(-\frac{5}{-12}\right)$
Answer
$\begin{aligned} & \frac{9}{-16}+\left(-\frac{5}{-12}\right) \\ & =\frac{9}{-16}+\left(\frac{5}
{12}\right)\end{aligned}$| 2 | 16,12 |
| 2 | 8,6 |
| 2 | 4,3 |
| 2 | 2,3 |
| 3 | 1,3 |
| | 1,1 |
L.C.M. of 16 and $12=2 \times 2 \times 2 \times 2 \times 3=48$
$ \Rightarrow \frac{9 \times 3}{16 \times 3}+\frac{5 \times 4}{12 \times 4} $
$(\because$ L.C.M. of 16 and $12=48$ )
$ \Rightarrow \frac{-27+20}{48}=-\frac{7}{48} $ View full question & answer→Question 374 Marks
Evaluate: $\frac{-3}{8}+\frac{-5}{12}$
Answer$\frac{-3}{8}+\frac{-5}{12}$
L.C.M. of 8 and $12=2 \times 2 \times 2 \times 3=24$
$ \Rightarrow \frac{-3 \times 3}{8 \times 3}+\frac{-5 \times 2}{12 \times 2} $
$(\because$ L.C.M. of 8 and $12=24)$
$ \Rightarrow \frac{-9-10}{24}=-\frac{19}{24} $ View full question & answer→Question 384 Marks
Evaluate: $\frac{7}{-27}+\frac{11}{18}$
Answer$\frac{7}{-27}+\frac{11}{18}$
L.C.M. of 27 and $18=2 \times 3 \times 3 \times 3=54$
$ \begin{aligned} & \Rightarrow \frac{7 \times 2}{-27 \times 2}+\frac{11 \times 3}{18 \times 3} \\ & (\because \text { L.C.M. of }-27 \text { and } 18=54) \\ & \Rightarrow \frac{-14+33}{54}=\frac{19}{54} \mathrm{} \end{aligned} $
View full question & answer→Question 394 Marks
Evaluate: $\frac{-2}{3}+\frac{3}{4}$
Answer$\frac{-2}{3}+\frac{3}{4}$
L.C.M. of 3 and $4=3 \times 4=12$
$ \begin{aligned} & \Rightarrow \frac{-2 \times 4}{3 \times 4}+\frac{3 \times 3}{4 \times 3} \\ & (\because \text { L.C.M. of } 3 \text { and } 4=12) \end{aligned} $
$ \Rightarrow \frac{-8+9}{12}=\frac{1}{12} $ View full question & answer→Question 404 Marks
Evaluate: $\left(3 \frac{5}{12}+1 \frac{2}{3}\right) \div\left(3 \frac{5}{12}-1 \frac{2}{3}\right)$
Answer
$\begin{aligned} & \left(3 \frac{5}{12}+1 \frac{2}{3}\right) \div\left(3 \frac{5}{12}-1 \frac{2}{3}\right) \\ & =\left(\frac{12 \times 3+5}{12}+\frac{3 \times 1+2}{3}\right) \div\left(\frac{12 \times 3+5}{12}-\frac{3 \times 1+2}{3}\right) \\ & =\left(\frac{41}{12}+\frac{5}{3}\right) \div\left(\frac{41}{12}-\frac{5}{3}\right) \\ & (\because \text { L.C.M. of } 12,3=12) \\ & =\left(\frac{41+20}{12}\right) \div\left(\frac{41-20}{12}\right) \\ & =\frac{61}{12} \div \frac{21}{12} \Rightarrow \frac{61}{12} \times \frac{12}{21} \\ & =\frac{61}{21}=2 \frac{19}{21}\end{aligned}$
View full question & answer→Question 414 Marks
Evaluate: $\left(\frac{-4}{5} \times \frac{3}{2}\right)+\left(\frac{9}{-5} \times \frac{10}{3}\right)-\left(\frac{-3}{2} \times \frac{-1}{4}\right)$
Answer
$\begin{aligned} & \left(\frac{-4}{5} \times \frac{3}{2}\right)+\left(\frac{9}{-5} \times \frac{10}{3}\right)-\left(\frac{-3}{2} \times \frac{-1}{4}\right) \\ & =\left(\frac{-2 \times 3}{5 \times 1}\right)+\left(\frac{3 \times 2}{-1 \times 1}\right)-\left(\frac{-3 \times(-1)}{2 \times 4}\right) \\ & =\left(\frac{-6}{5}\right)+\left(\frac{-6}{1}\right)-\left(\frac{3}{8}\right) \\ & =\frac{-6 \times 8}{5 \times 8}-\frac{6 \times 40}{1 \times 40}-\frac{3 \times 5}{8 \times 5} \\ & =\frac{-48-240-15}{40} \\ & =\frac{-288-15}{40} \\ & =\frac{-303}{40}\end{aligned}$
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