Class 8: Numbers – Exercise 3A

$\displaystyle \textbf{Question 1: }\text{Write the following integers in ascending order:}$
$\displaystyle \text{(i) }-13,\ 2,\ -123,\ -3,\ 11,\ 0$
$\displaystyle \text{(ii) }143,\ -317,\ -1,\ 19,\ -63,\ -19$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }-123,\ -13,\ -3,\ 0,\ 2,\ 11$

$\displaystyle \text{(ii) }-317,\ -63,\ -19,\ -1,\ 19,\ 143$

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$\displaystyle \textbf{Question 2: }\text{Write the following integers in descending order:}$
$\displaystyle \text{(i) }17,\ 0,\ -5,\ 69,\ -124,\ -1$
$\displaystyle \text{(ii) }-3,\ -77,\ 2,\ -345,\ -49,\ -617$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }69,\ 17,\ 0,\ -1,\ -5,\ -124$

$\displaystyle \text{(ii) }2,\ -3,\ -49,\ -77,\ -345,\ -617$

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$\displaystyle \textbf{Question 3: }\text{Add the following:}$
$\displaystyle \text{(i) }64+(-27)\qquad\text{(ii) }(-89)+16\qquad\text{(iii) }(-46)+(-38)$
$\displaystyle \text{(iv) }(-47)+85+(-6)\qquad\text{(v) }348+(-121)+(-765)$
$\displaystyle \text{(vi) }(-248)+414+(-8)+77+(-19)$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }64+(-27)=64-27=37$

$\displaystyle \text{(ii) }(-89)+16=-73$

$\displaystyle \text{(iii) }(-46)+(-38)=-(46+38)=-84$

$\displaystyle \text{(iv) }(-47)+85+(-6)=85-47-6=32$

$\displaystyle \text{(v) }348+(-121)+(-765)=348-121-765=-538$

$\displaystyle \text{(vi) }(-248)+414+(-8)+77+(-19)=216$

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$\displaystyle \textbf{Question 4: }\text{Find the additive inverse of:}$
$\displaystyle \text{(i) }-987\qquad\text{(ii) }0\qquad\text{(iii) }1428$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }-987+a=0$
$\displaystyle \Rightarrow a=987.$
$\displaystyle \therefore \text{The additive inverse of }-987\text{ is }987.$

$\displaystyle \text{(ii) }0+a=0$
$\displaystyle \Rightarrow a=0.$
$\displaystyle \therefore \text{The additive inverse of }0\text{ is }0.$

$\displaystyle \text{(iii) }1428+a=0$
$\displaystyle \Rightarrow a=-1428.$
$\displaystyle \therefore \text{The additive inverse of }1428\text{ is }-1428.$

$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{Find the successor of the following integers:}$
$\displaystyle \text{(i) }-1009\qquad\text{(ii) }0\qquad\text{(iii) }-1\qquad\text{(iv) }-4321$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }-1009+1=-1008$

$\displaystyle \text{(ii) }0+1=1$

$\displaystyle \text{(iii) }-1+1=0$

$\displaystyle \text{(iv) }-4321+1=-4320$

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$\displaystyle \textbf{Question 6: }\text{Find the predecessor of the following integers:}$
$\displaystyle \text{(i) }-1009\qquad\text{(ii) }0\qquad\text{(iii) }-1\qquad\text{(iv) }-2094$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }-1009-1=-1010$

$\displaystyle \text{(ii) }0-1=-1$

$\displaystyle \text{(iii) }-1-1=-2$

$\displaystyle \text{(iv) }-2094-1=-2095$

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Question 7: A bus starts from the terminal and moves $188 \ km$ to the EAST and then $\ 343 km$ to the west. How far is the bus from the terminal? v21

Answer: $155 \ km$

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$\displaystyle \textbf{Question 8: }\text{A shopkeeper purchased a book for Rs. }345,\text{ a pencil box for Rs. }62,$
$\displaystyle \text{a notebook for Rs. }21\text{ and a pen for Rs. }79.\text{ He sold the book for Rs. }376,$
$\displaystyle \text{the pencil box for Rs. }55,\text{ the notebook for Rs. }25\text{ and the pen for Rs. }67.$
$\displaystyle \text{What is his gain or loss?}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Total Cost}=345+62+21+79=\text{Rs. }507.$

$\displaystyle \text{Total Sales}=376+55+25+67=\text{Rs. }523.$

$\displaystyle \text{Gain}=\text{Total Sales}-\text{Total Cost}=523-507=\text{Rs. }16.$

$\displaystyle \therefore \text{The shopkeeper made a gain of Rs. }16.$

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$\displaystyle \textbf{Question 9: }\text{Find an integer }a\text{ such that:}$
$\displaystyle \text{(i) }a+(-7)=0\qquad\text{(ii) }(-4)+a=0$
$\displaystyle \text{(iii) }a+12=0\qquad\text{(iv) }21+a=0$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }a+(-7)=0\Rightarrow a=7$

$\displaystyle \text{(ii) }(-4)+a=0\Rightarrow a=4$

$\displaystyle \text{(iii) }a+12=0\Rightarrow a=-12$

$\displaystyle \text{(iv) }21+a=0\Rightarrow a=-21$

$\displaystyle \\$

$\displaystyle \textbf{Question 10: }\text{Subtract:}$
$\displaystyle \text{(i) }3715\text{ from }(-468)\qquad\text{(ii) }(-329)\text{ from }0$
$\displaystyle \text{(iii) }(-2347)\text{ from }1543\qquad\text{(iv) }(-4682)\text{ from }(-419)$
$\displaystyle \text{(v) }(-76)\text{ from the sum of }(-813)\text{ and }248$
$\displaystyle \text{(vi) The sum of }(-66)\text{ and }619\text{ from the sum of }597\text{ and }(-184)$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }(-468)-3715=-4183$

$\displaystyle \text{(ii) }0-(-329)=0+329=329$

$\displaystyle \text{(iii) }1543-(-2347)=1543+2347=3890$

$\displaystyle \text{(iv) }(-419)-(-4682)=-419+4682=4263$

$\displaystyle \text{(v) }\{(-813)+248\}-(-76)=-565+76=-489$

$\displaystyle \text{(vi) }\{597+(-184)\}-\{(-66)+619\}$
$\displaystyle =413-553=-140$

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$\displaystyle \textbf{Question 11: }\text{Simplify:}$
$\displaystyle \text{(i) }\{(-78)-(-92)\}+\{(-54)-(-21)\}$
$\displaystyle \text{(ii) }\{92-(-53)\}-\{76-(-132)\}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }\{(-78)-(-92)\}+\{(-54)-(-21)\}$
$\displaystyle =(-78+92)+(-54+21)=14+(-33)=-19$

$\displaystyle \text{(ii) }\{92-(-53)\}-\{76-(-132)\}$
$\displaystyle =(92+53)-(76+132)=145-208=-63$

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$\displaystyle \textbf{Question 12: }\text{The sum of two integers is }-29.\text{ If one of the integers is }182,$
$\displaystyle \text{find the other integer.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Let the other integer be }a.$

$\displaystyle a+182=-29$

$\displaystyle \Rightarrow a=-29-182=-211$

$\displaystyle \therefore \text{The other integer is }-211.$

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$\displaystyle \textbf{Question 13: }\text{The difference of an integer }a\text{ and }-37\text{ is }-14.$
$\displaystyle \text{Find the value of }a.$

$\displaystyle \text{Answer:}$

$\displaystyle a-(-37)=-14$

$\displaystyle \Rightarrow a+37=-14$

$\displaystyle \Rightarrow a=-14-37=-51$

$\displaystyle \therefore a=-51.$

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$\displaystyle \textbf{Question 14: }\text{During a month, the average day temperature of a desert region was }37^\circ\mathrm{C}$
$\displaystyle \text{and the average night temperature was }-4^\circ\mathrm{C}.\text{ Find the difference between the}$
$\displaystyle \text{average day temperature and the average night temperature.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Difference}=\text{Average day temperature}-\text{Average night temperature}$

$\displaystyle =37-(-4)=37+4=41^\circ\mathrm{C}$

$\displaystyle \therefore \text{The difference in temperature is }41^\circ\mathrm{C}.$

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$\displaystyle \textbf{Question 15: }\text{Find the products:}$
$\displaystyle \text{(i) }16\times25\qquad\text{(ii) }(-34)\times76\qquad\text{(iii) }26\times(-496)$
$\displaystyle \text{(iv) }(-289)\times(-173)\qquad\text{(v) }(-25)\times17\times(-42)$
$\displaystyle \text{(vi) }31\times13\times(-23)$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }16\times25=400$

$\displaystyle \text{(ii) }(-34)\times76=-2584$

$\displaystyle \text{(iii) }26\times(-496)=-12896$

$\displaystyle \text{(iv) }(-289)\times(-173)=49997$

$\displaystyle \text{(v) }(-25)\times17\times(-42)=17850$

$\displaystyle \text{(vi) }31\times13\times(-23)=-9269$

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$\displaystyle \textbf{Question 16: }\text{Divide:}$
$\displaystyle \text{(i) }893\text{ by }19\qquad\text{(ii) }(-629)\text{ by }37$
$\displaystyle \text{(iii) }224\text{ by }(-14)\qquad\text{(iv) }(-423)\text{ by }(-47)$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) }893\div19=47$

$\displaystyle \text{(ii) }(-629)\div37=-17$

$\displaystyle \text{(iii) }224\div(-14)=-16$

$\displaystyle \text{(iv) }(-423)\div(-47)=9$

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$\displaystyle \textbf{Question 17: }\text{In an examination consisting of }20\text{ questions, }5\text{ marks are awarded}$
$\displaystyle \text{for each correct answer, }(-2)\text{ marks are awarded for each incorrect answer, and }0\text{ marks}$
$\displaystyle \text{are awarded for each question left unattempted. Aditya answered }10\text{ questions correctly}$
$\displaystyle \text{and }2\text{ questions incorrectly, while Cyrus answered }12\text{ questions correctly and }8$
$\displaystyle \text{questions incorrectly. Who scored more marks and what was his score?}$