[5 marks sum] - MATHS STD 7 Questions - Vidyadip

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[5 marks sum]

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18 questions · timed · auto-graded

Question 15 Marks

Evaluate: $\left(\frac{-13}{7} \times \frac{-35}{39}\right)-\left(\frac{-7}{45} \times \frac{9}{14}\right)$

Answer

$\begin{aligned} & \left(\frac{-13}{7} \times \frac{-35}{39}\right)-\left(\frac{-7}{45} \times \frac{9}{14}\right) \\ & \Rightarrow \frac{-13 \times(-35)}{7 \times 39}+\frac{7 \times 9}{45 \times 14} \\ & \Rightarrow \frac{-1 \times(-5)}{1 \times 3}+\frac{1 \times 1}{5 \times 2} \\ & \Rightarrow \frac{5}{3}+\frac{1}{10}\end{aligned}$

2	3,10
3	3,5
5	1,5
	1,1

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} $

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Question 25 Marks

Evaluate: $\left(\frac{18}{33} \times \frac{-22}{27}\right)+\left(\frac{13}{25} \times \frac{-75}{26}\right)$

Answer

$\begin{aligned} & \left(\frac{18}{33} \times \frac{-22}{27}\right)+\left(\frac{13}{25} \times \frac{-75}{26}\right) \\ & \Rightarrow \frac{18 \times(-22)}{33 \times 27}-\frac{13 \times(-75)}{25 \times 26} \\ & \Rightarrow \frac{2 \times(-2)}{3 \times 3}-\frac{1 \times-3}{1 \times 2} \\ & \Rightarrow \frac{-4}{9}-\left(\frac{-3}{2}\right)=\frac{-4}{9}+\frac{3}{2}\end{aligned}$

2	9,2
3	9,1
3	3,1
	1,1

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} $

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Question 35 Marks

Evaluate: $\left(\frac{8}{15} \times \frac{-25}{16}\right)+\left(\frac{-18}{35} \times \frac{5}{6}\right)$

Answer

$\begin{aligned} & \left(\frac{8}{15} \times \frac{-25}{16}\right)+\left(\frac{-18}{35} \times \frac{5}{6}\right) \\ & \Rightarrow \frac{8 \times(-25)}{15 \times 16}+\frac{-18 \times 5}{35 \times 6} \\ & \Rightarrow \frac{1 \times(-5)}{3 \times 2}+\frac{-3 \times 1}{7 \times 1} \\ & \Rightarrow \frac{-5}{6}-\frac{3}{7}\end{aligned}$

2	6,7
3	3,7
7	1,7
	1,1

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} $

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Question 45 Marks

Evaluate: $\left(\frac{7}{8} \times \frac{24}{21}\right)+\left(\frac{-5}{9} \times \frac{6}{-25}\right)$

Answer

$\begin{aligned} & \left(\frac{7}{8} \times \frac{24}{21}\right)+\left(\frac{-5}{9} \times \frac{6}{-25}\right) \\ & \Rightarrow \frac{7 \times 24}{8 \times 21}+\frac{-5 \times 6}{9 \times(-25)} \\ & \Rightarrow \frac{1 \times 3}{1 \times 3}+\frac{1 \times 2}{3 \times 5} \\ & \Rightarrow \frac{3}{3}+\frac{2}{15}\end{aligned}$

3	3,15
5	1,5
	1,1

$(\because$ L.C.M. of 3 and $15=15)$
$\begin{aligned} & \Rightarrow \frac{3 \times 5}{3 \times 5}+\frac{2 \times 1}{15 \times 1} \\ & \Rightarrow \frac{15+2}{15}=\frac{17}{15}=1 \frac{2}{15}\end{aligned}$

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Question 55 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} $

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Question 65 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 $=\frac{-3}{8}-\frac{3}{16}$

2	8,16
2	4,8
2	2,4
2	1,2
	1,1

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 $=\frac{-9}{16}$

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Question 75 Marks

Evaluate: $-1+\frac{2}{-3}+\frac{5}{6}$

Answer

$-1+\frac{2}{-3}+\frac{5}{6}$

2	3,6
3	3,3
	1,1

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} $

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Question 85 Marks

Evaluate: $\frac{7}{26}+2+\frac{-11}{13}$

Answer

$\begin{aligned} & \frac{7}{26}+2+\frac{-11}{13} \\ & \Rightarrow \frac{7}{26}+\frac{2}{1}+\frac{-11}{13}\end{aligned}$

2	26,13
13	13,13
	1,1

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} $

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Question 95 Marks

Evaluate: $-\frac{5}{7}-\left(-\frac{3}{8}\right)$

Answer

$\begin{aligned} & -\frac{5}{7}-\left(-\frac{3}{8}\right) \\ & -\frac{5}{7}+\frac{3}{8}\end{aligned}$

2	7,8
2	7,4
2	7,2
7	7,1
	1

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} $

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Question 105 Marks

Evaluate: $-\frac{2}{3}-\left(\frac{-5}{7}\right)$

Answer

$\begin{aligned} & -\frac{2}{3}-\left(\frac{-5}{7}\right) \\ & \Rightarrow-\frac{2}{3}+\frac{5}{7}\end{aligned}$

3	3,7
7	1,7
	1,1

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} $

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Question 115 Marks

Evaluate: $\frac{7}{-26}+\frac{16}{39}$

Answer

$\frac{7}{-26}+\frac{16}{39}$

2	26,39
3	13,39
13	13,13
	1,1

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}
$

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Question 125 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} $

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Question 135 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} $

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Question 145 Marks

Evaluate: $\frac{-3}{8}+\frac{-5}{12}$

Answer

$\frac{-3}{8}+\frac{-5}{12}$

2	8,12
2	4,6
2	2,3
3	1,3
	1,1

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} $

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Question 155 Marks

Evaluate: $\frac{7}{-27}+\frac{11}{18}$

Answer

$\frac{7}{-27}+\frac{11}{18}$

2	27,18
3	27,9
3	9,3
3	3,1
	1,1

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} $

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Question 165 Marks

Evaluate: $\frac{-2}{3}+\frac{3}{4}$

Answer

$\frac{-2}{3}+\frac{3}{4}$

3	3,4
4	1,4
	1,1

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} $

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Question 175 Marks

Evaluate: $\left(3 \frac{5}{12}+1 \frac{2}{3}\right) \div\left(3 \frac{5}{12}-1 \frac{2}{3}\right)$

Answer

$\begin{aligned} & \left(3 \frac{5}{12}+1 \frac{2}{3}\right) \div\left(3 \frac{5}{12}-1 \frac{2}{3}\right) \\ & =\left(\frac{12 \times 3+5}{12}+\frac{3 \times 1+2}{3}\right) \div\left(\frac{12 \times 3+5}{12}-\frac{3 \times 1+2}{3}\right) \\ & =\left(\frac{41}{12}+\frac{5}{3}\right) \div\left(\frac{41}{12}-\frac{5}{3}\right) \\ & (\because \text { L.C.M. of } 12,3=12) \\ & =\left(\frac{41+20}{12}\right) \div\left(\frac{41-20}{12}\right) \\ & =\frac{61}{12} \div \frac{21}{12} \Rightarrow \frac{61}{12} \times \frac{12}{21} \\ & =\frac{61}{21}=2 \frac{19}{21}\end{aligned}$

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Question 185 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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[5 marks sum] - MATHS STD 7 Questions - Vidyadip