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Multiplying and dividing integers - class-VI

Description: multiplying and dividing integers
Number of Questions: 97
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Tags: negative numbers numbers : revision number system maths the integers integers integers, powers and roots multiplication and division of integers integer, power and roots
Attempted 0/97 Correct 0 Score 0

The value of $\displaystyle\ \frac{15\times (-24)\times-18}{-(27)\times (20)}$ is

  1. -16

  2. -15

  3. -12

  4. 12


Correct Option: C
Explanation:

As there are $ 2 $ negative numbers in the numerator and $ 1 $ in the denominator, the answer will be negative. 

Cancelling out the common factors and simplifying we get 


$ \dfrac { 15\times (-24)\times -18 }{ -(27)\times (20) } =\dfrac {3 \times 8 \times 18}{-9\times 4}=-3\times 2\times2 = -12 $


The value of $-5\times-12\times 2\times-3$ is

  1. -360

  2. -380

  3. -400

  4. 360


Correct Option: A
Explanation:

As there are $ 3 $ negative numbers, which is an odd number, the product will be negative.

So, $ -5 \times -12 \times 2\times -3 = - 360 $

Multiply $4\times(-3)\times (-2) \ and\  6\times(-5)$

  1. -720

  2. -70

  3. -270

  4. 720


Correct Option: A
Explanation:

$4 \times (-3)\times (-2)\times 6\times (-5)$
$=24\times -30$
$=-720$

Divide:
$(-60 \times -72)  \  by\    (36\times (-15))$

  1. -8

  2. -16

  3. 8

  4. 16


Correct Option: A
Explanation:

Given, $

\dfrac { (-60)\times (-72) }{ 36\times (-15) } $

As there are $ 2 $ negative numbers in the numerator and $ 1 $ in the

denominator, the answer will be negative.

Cancelling out the common factors and simplifying we get

$ \dfrac { (-60)\times (-72) }{ 36\times (-15) }=-4\times 2  = - 8 $

The value of $-5\times -2\times -2\times-3$  is

  1. 80

  2. 65

  3. 60

  4. -60


Correct Option: C
Explanation:

As there are $ 4 $ negative numbers, which is an even number, the product

will be positive.





So, $ -5 \times -2 \times -2\times -3 = 60 $

Multiply:
$(-5)\times 8$ and $3\times (-2)$

  1. 240

  2. 420

  3. -240

  4. -420


Correct Option: A
Explanation:

$ (-5)\times 8 = - 40 $

$ 3\times (-2) = -6 $

Hence, $ ((-5)\times 8 ) \times (3\times (-2)) = -40 \times -6 = 240 $

Evaluate $\displaystyle\ \frac{(-8)\times8\times(-8)\times(-8)}{(-4)\times(-4)\times(-4)\times(-4)}$

  1. -1

  2. -6

  3. -16

  4. 16


Correct Option: C
Explanation:

Given, $

\dfrac { (-8) \times 8 \times (-8) \times (-8) }{ (-4)\times (-4) \times (-4) \times (-4) } $

As there are $ 3 $ negative numbers in the numerator and $ 4 $ in the denominator, the answer will be negative.

Canceling out the common factors and simplifying we get

$ \dfrac { (-8) \times 8 \times (-8) \times (-8) }{ (-4)\times (-4) \times (-4) \times (-4) }   =2\times -2\times2\times2 = - 16 $

Divide $(-54) \times (64) \ by \  (-27) \times (-128)$

  1. -1

  2. 1

  3. 5

  4. -4


Correct Option: A
Explanation:

$(-54)\times (64)\div (-27)\times (-128)$
$=-3456 \div 3456$
$=-1$

Find the value of $(-144)\div(+16)$

  1. $+9$

  2. $+11$

  3. $-9$

  4. $-11$


Correct Option: C
Explanation:

$(-144)\div (+16)=\dfrac { -144 }{ 16 } \ =-(\dfrac { 144 }{ 16 } )\ =-(9)$

So correct answer will be option C

Evaluate  $\displaystyle\ \frac {(-16)\times (-8)\times (-81)}{(-18)\times 32}$

  1. $-18$

  2. $18$

  3. $16$

  4. $-16$


Correct Option: B
Explanation:

Given, $

\dfrac { (-16)\times (-8) \times (-81) }{ (-18)\times 32 } $

As there are $ 3 $ negative numbers in the numerator and $ 1 $ in the denominator, the answer will be positive. 

 
Canceling out the common factors and simplifying we get

$ \dfrac { (-16)\times (-8) \times (-81) }{ (-18)\times 32 }=\dfrac{4 \times 81}{9 \times2}   = 18 $

Divide $96×(−25)\ by\ (−75)×(−16)$

  1. -2

  2. 2

  3. -5

  4. 5


Correct Option: A
Explanation:

$96\times (-25) \div (-75)\times (-16)$
$=-2400\div 1200$
$=-2$

Sign of the product of 231 negative integers and 9 positive integer is 

  1. negative

  2. positive

  3. 0

  4. none


Correct Option: A
Explanation:

Since $231$ is an odd number, the product of $231$ negative integers will be negative.

The product of all positive integers is a positive number. Hence, the product of $9$ positive integers will be a positive integer.
Therefore, the product of the two integers ($231$ negative and $9$ positive) of unlike signs will be negative. 

The positive integer whose product with $-1$ is 

  1. positive

  2. negative

  3. $0$

  4. none


Correct Option: B
Explanation:

The positive integer whose product with $-1$ is negative.

For example: $2\times (-1)=-2$ and $2.5\times (-1)=-2.5$

Product of two integers with unlike signs is

  1. Negative

  2. 0

  3. Positive

  4. None of these


Correct Option: A
Explanation:

Let us take two integers, one with positive sign and one with negative sign that is $+2$ and $-5$ then the product of these integers with different/unlike signs is:


$(+2)\times (-5)=-(2\times 5)=-10$ which is a negative integer.

Hence, product of two integers with unlike signs is always negative.

Product of two integers with like signs is

  1. Negative

  2. Positive

  3. 0

  4. None of these


Correct Option: B
Explanation:

Let us take two integers with positive signs that is $+2$ and $+5$ then the product of these integers with same/like signs is:


$(+2)\times (+5)=2\times 5=10$ which is also a positive integer.

Now, let us take two integers with negative signs that is $-2$ and $-5$ then the product of these integers with same/like signs is:

$(-2)\times (-5)=2\times 5=10$ which is also a positive integer.


Hence, product of two integers with like signs is always positive.

-112 $\times$ _______= +112

  1. +1

  2. 0

  3. -1

  4. +112


Correct Option: C
Explanation:

$-112 \times (-1) = +112$

$(+132) $ $\div$ $ (-12)$

  1. $+ 101$

  2. $-101$

  3. $+ 11$

  4. $-11$


Correct Option: D
Explanation:

$(132)\div (-12)=\frac{132}{-12}$
                             $=\frac{12\times11}{-12}$
                             $=-1\times11$
                             $=-11$
Option D is correct.

Multiplication of a negative integer for even number of times gives a _________ number.

  1. negative

  2. 0

  3. positive

  4. none of these


Correct Option: C
Explanation:

(-1) $\times$ (-1) $\times$ (-I)......evensign = Positive

(-12) $\times$ (-3) $\times$ (+4) $\times$ (-6) =

  1. -144

  2. -908

  3. +864

  4. -864


Correct Option: D
Explanation:

There are $3$ negative signs . So, the resultant of $3$ multiplications would be negative.


$\therefore (-12) \times (-3) \times(+4) \times (-6) = 36\times 4\times (-6)$
$\Rightarrow 144\times (-6)=-864$

68 $\times$ ____ = -68

  1. 0

  2. 1

  3. -1

  4. None of these


Correct Option: C
Explanation:

$68 \times (-1) = -68$

If the dividend and divisor have unlike signs then the quotient will be___.

  1. Positive

  2. Negative

  3. Zero

  4. none of these


Correct Option: B
Explanation:

If the dividend and divisor have unlike signs then the quotient will be negative.
For eg- $\displaystyle \frac{-132}{12}=-11$

If the dividend and divisor have like signs then the quotient will be_____.

  1. Positive

  2. Negative

  3. Zero

  4. none of these


Correct Option: A
Explanation:

If the dividend and divisor have same  signs then the quotient will be positive.
For eg- $\displaystyle \frac{132}{12}=11$ and $\displaystyle \frac {-132}{-12}= 11$

Multiplying a negative integer for odd number of times gives a _______number.

  1. positive

  2. negative

  3. 0

  4. none of these


Correct Option: B
Explanation:

(-1) $\times$ (-1) $\times$ (-I) ......odd times = Negative sign

Square of any -ve integer is

  1. Negative

  2. Positive

  3. 0

  4. none of these


Correct Option: B
Explanation:

$(-ve\, integer)^2$ = Positive integer

$5. { 63 } \ \times 11$ is equal to

  1. $62$

  2. $83.\overline { 93 } $

  3. $83.9\overline { 3 } $

  4. $83.93$


Correct Option: A
Explanation:

$5.\overline { 63 } $
$=5.636363...$
Let $x=5.6363$  (i)
$\therefore 100x=563.6363$  (ii)
Subtracting (i) from (ii) we get,
$=>99x=558$
$=>x=\dfrac{558}{99}$
Now,$5.\overline { 63 }\times 11$
$=>\frac{558}{99}\times 11$
$=>62$

(-32)  $\div$ (-4)=____

  1. +8

  2. -18

    • 18
  3. -8


Correct Option: A
Explanation:

Given, $(-32) \div (-4)$

$\therefore (-32)\div (-4)=-32\times (-\displaystyle \frac{1}{4})$
$=8$
$2$ negative signs will give resultant division positive.

Positive of a negative integer is____.

  1. negative

  2. positive

  3. zero

  4. none of these


Correct Option: A
Explanation:

Positive of a negative integer is negative. 
Example: $+(-40)= -40$

$(-144) $$\div$$ (+16)$

  1. $+9$

  2. $+11$

  3. $-9$

  4. $-11$


Correct Option: C
Explanation:

$(-144)\div (16)=\dfrac{-1\times16\times9}{16}$


                             $=-1\times9$

                             $=-9$
Option C is correct.

The product of two factors with unlike signs is ...........

  1. positive

  2. negative

  3. cannot be determined

  4. none of these


Correct Option: B
Explanation:

Let 2 and -3 be the two factors.
Clearly, $2\times-3=-6$, which is negative.
Hence, Option B is correct.

The value of $\displaystyle \frac{1\div\frac{2}{3}\times \frac{3}{4} }{1\div \frac{2}{3}\times \frac{3}{4}}$ on simplification is

  1. $\displaystyle \frac{3}{16}$

  2. $\displaystyle \frac{9}{16}$

  3. $\displaystyle \frac{1}{16}$

  4. $\displaystyle \frac{7}{16}$


Correct Option: B
Explanation:

$\frac{1\div \frac{2}{3}\times \frac{3}{4}}{1+\div \frac{2}{3}of\frac{4}{3}}$

$\frac{1\div \frac{2}{3}\times \frac{3}{4}}{1\div \frac{2}{3}\times \frac{4}{3}}$
$\frac{1\times \frac{1}{2}}{1\times \frac{8}{9}}$
$\Rightarrow \frac{1\times 2}{1\times \frac{8}{9}}$
$\Rightarrow \frac{\frac{1}{2}}{\frac{8}{9}} =\frac{9}{16}$

The value of $\displaystyle \frac{0.9\times 0.9\times 0.9+0.1\times 0.1\times 0.1}{0.9\times 0.9-0.9\times 0.1+0.1\times 0.1}$ on simplification is

  1. 0

  2. -1

  3. 2

  4. 1


Correct Option: D
Explanation:
$\frac{0.9\times 0.9\times 0.9+0.1\times 0.1\times 0.1}{0.9\times 0.9-0.9\times 0.1+0.1\times 0.1}$
=$\frac{(0.9)^{3}+(0.1)^{3}}{(0.9)^{2}-0.9\times 0.1+(0.1)^{2}}$
We know that$ a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$
Then $\frac{(0.9+0.1)\left [ (0.9)^{2}-0.9\times 0.1+(0.1)^{2} \right ]}{(0.9)^{2}-0.9\times 0.1+(0.1)^{2}}=(0.9+0.1)=1$

The simplified value of $\displaystyle y^{4}\div y$ of $\displaystyle y^{3}\div y^{2}\times y^{5}\div y^{3}$ is

  1. 2

  2. 0

  3. -1

  4. 1


Correct Option: D
Explanation:
$y^{4}\div y ofy^{3}\div y^{2}\times y^{5}\div y^{3}$
=$y^{4}\div y\times y^{3}\div y^{2}\times y^{2}$
=$\frac{y^{4}}{y^{4}}\times \frac{y^{4}}{y^{4}}=1\times 1=1$

The product of any number and "0" is ___

  1. $1$

  2. $0$

  3. number itself

  4. none of these


Correct Option: B
Explanation:
The product of any number and zero is zero. 
Theorem: $0×a=0$ for any integer $a.$

So option B is the correct answer.

$\displaystyle (-8)\times (-2)\times (+3)\times (-4) = $ 

  1. $+192$

  2. $-192$

  3. $+28$

  4. $-4$


Correct Option: B
Explanation:

$\displaystyle (-8)\times (-2)\times (+3)\times (-4)
= +16\times  -12
= -192 $

Sixth power of (-2) is

  1. $-64$

  2. $+32$

  3. $+64$

  4. $-16$


Correct Option: C
Explanation:

$\displaystyle ({ -2 })^{ 6 }=\quad -2\times -2\times -2\times -2\times -2\times -2
= +64 $

$Factor \times Factor$ is equal to  ____ .

  1. difference

  2. multiple

  3. sum

  4. None of these


Correct Option: B
Explanation:

$×$ sign between any $2$ numbers results in the product of those numbers or the multiple. 


So, option B is the correct answer.

Value of $\displaystyle { 2 }^{ 2 }{ \times (-3) }^{ 2 }{ \times 2 }^{ 2 }{ \times (-4) }^{ 2 } $ is

  1. $2034$

  2. $2403$

  3. $2304$

  4. None of these


Correct Option: C
Explanation:

$\displaystyle { 2 }^{ 2 }{ \times (-3) }^{ 2 }{ \times 2 }^{ 2 }{ \times (-4) }^{ 2 }\ =4\times +9\times 4\times 16\ =2304$ 

$8 - [ 12 - ({ - 2 \times - 4 (4 of -4 ) }) ] $=

  1. $-132$

  2. $132$

  3. $0$

  4. None of these


Correct Option: A
Explanation:

$8 - [ 12 - ({ - 2 \times  - 4 (4 of -4 )) } ] $
$= 8 - [12 - ({ - 2 \times -4 \times  -16})]$
$= 8 - [12 - ({ - 128 })]$
$= 8 - [12 +128]$
$=8 -140$
$= -132$

Observe the given multiplies of 37
$\displaystyle 37\times 3$ = 111
$\displaystyle 37\times 6$ = 222
$\displaystyle 37\times 9$ = 333
$\displaystyle 37\times 12$ = 444
-----------------------------------------------
-----------------------------------------------
Find the product of $\displaystyle 37\times 27$ ?

  1. 999

  2. Greatest 3 digit number

  3. Either A or B

  4. Smallest 3-digit number


Correct Option: C
Explanation:

$\displaystyle 37\times 3=37\times \left ( 3\times 1 \right )=111$
$\displaystyle 37\times 6=37\times \left ( 3\times 2\right )=222$
$\displaystyle 37\times 9=37\times \left ( 3\times 3\right )=333$
------------------------------------------
------------------------------------------
$\displaystyle 37\times 27=37\times \left ( 3\times 9 \right )=999$

The value of $555 \displaystyle \times   193 - 555 \displaystyle \times  93$ is

  1. $555,931$

  2. $1,210,321$

  3. $53,912$

  4. $55,500$


Correct Option: D
Explanation:

Solving the given expression,
$555$  $\displaystyle \times  $ $193 - 555$ $\displaystyle \times  $ $93$
$= 555 \displaystyle \times    (193 - 93)$
$= 555 \displaystyle \times   100 = 55500$

(-32) $\displaystyle \div  $ (-4)

  1. +8

  2. -18

  3. +18

  4. -8


Correct Option: A
Explanation:

$\dfrac{-32}{-4}$ = 8 

Solve $-132\div11$

  1. $+101$

  2. $-101$

  3. $+11$

  4. $-12$


Correct Option: D
Explanation:

We can write $-132÷11$ as $-132×\dfrac 1{11}$

Or, $\dfrac{-132}{11} =(-12)$

So option D is the correct answer.

Product of two integers with unlike signs is

  1. negative

  2. 0

  3. positive

  4. none


Correct Option: A
Explanation:

Negative

Solve ($-144\displaystyle \div  16$) 

  1. $+9$

  2. $+11$

  3. $-9$

  4. $-11$


Correct Option: C
Explanation:

When you divide a negative number by a positive number then the quotient is negative. When you divide a positive number by a negative number then the quotient is also negative. So, in this case,

-144/16 = -9
So option C is the correct answer.

If the dividend and divisor have unlike signs then the quotient will be _____

  1. positive

  2. negative

  3. zero

  4. none


Correct Option: B
Explanation:

If the dividend and divisor have unlike signs then the quotient will be Negative.


Division of Integers is similar to the division of whole numbers (both positive) except the sign of the quotient needs to be determined.

If both the dividend and divisor are positive, the quotient will be positive.
(+16) ÷ (+4) = +4

If both the dividend and divisor are negative, the quotient will be positive.
(-16) ÷ (-4) = +4

If only one of the dividend or divisor is negative, the quotient will be negative.
(+16) ÷ (-4) = -4     or      (-16) ÷ (+4) = -4

In other words, if the signs are the same the quotient will be positive, if they are different, the quotient will be negative
Hence Option B

-112 $\displaystyle \times $ _____ = +112

  1. +1

  2. 0

  3. -1

  4. +112


Correct Option: C
Explanation:

-112 $\displaystyle \times $ (-1) = +112

Evaluate $-12\displaystyle \times 21$ 

  1. $-2412$

  2. $-242$

  3. $-252$

  4. $+252$


Correct Option: C
Explanation:

The product of a negative and a positive number is always a negative number.


$-12×21= (-252)$


So option C is the correct answer.

Evaluate $(-6)$ $\displaystyle \times $ $(-2) $

  1. $-8$

  2. $+8$

  3. $-12$

  4. $+12$


Correct Option: D
Explanation:

The product of two negative numbers is always a positive number.


So, $-6×(-2)= +12$


So option D is the correct answer.

If ${ B }^{ 3 }A< 0$ and $A> 0$, which of the following must be negative?

  1. $AB$

  2. ${ B }^{ 2 }A$

  3. ${B}^{4}$

  4. $\cfrac { A }{ { B }^{ 2 } } $

  5. $-\cfrac { B }{ A } $


Correct Option: A
Explanation:

If $A$ is positive ${B}^{3}$ must be negative. Therefore, $B$ must be negative. If $A$ is positive and $B$ is negative, the product $AB$ must be negative.

Evaluate:$144\div-12$

  1. $12$

  2. $-12$

  3. $1$

  4. $2$


Correct Option: B
Explanation:
The positive integer $144$ can be divided by a negative integer $-12$ as follows:

$144\div -12=-\dfrac { 144 }{ 12 } =-12$

Hence, $144\div -12=-12$

Evaluate:$-456\div12$

  1. $38$

  2. $-38$

  3. $1$

  4. $2$


Correct Option: B
Explanation:
The negative integer $-456$ can be divided by a positive integer $12$ as follows:

$-456\div 12=-\dfrac { 456 }{ 12 } =-38$

Hence, $-456\div 12=-38$

Simplify to its nearest integer.
$1624.12\times 3.891=?$

  1. $6100$

  2. $6203$

  3. $6032$

  4. $6320$

  5. $6230$


Correct Option: D
Explanation:

$1624.13\times 3.8912=6319.81\approx 6320$
Hence option D is the correct answer.

State the following statement as True or False.
Multiplication and Division of two negative numbers is always a negative number.

  1. True

  2. False


Correct Option: B
Explanation:

Multiplication and Division of two negative numbers is always a positive number.

Find the value of $x$ in this equation : $\dfrac{392}{x}=-196$.

  1. $2$

  2. $4$

  3. $-2$

  4. $-4$


Correct Option: C
Explanation:

$x=-\dfrac{392}{196}=-2$

Simplify the following :-
$(-441)\div(21)$=?

  1. $21$

  2. $-21$

  3. $20$

  4. $-20$


Correct Option: B
Explanation:

$\dfrac{-441}{21}=-21$

Hence option $B$ is correct.

Simplify the following :-
$\dfrac{39\times(-42)}{(-13)}$= ?

  1. $-126$

  2. $14$

  3. $-14$

  4. $126$


Correct Option: D
Explanation:

Lets simplift $\dfrac{39\times (-42)}{-13}$ as 

$=\dfrac{3\times (-42)}{-1}$
$=126$

What is the value of $x$ in the following equation?
$-319\div  x =-11$.

  1. $39$

  2. $-29$

  3. $29$

  4. $-39$


Correct Option: C
Explanation:

We need to find $x$ in $-319\div x=-11$
$\dfrac{-319}{x}=-11\ \Rightarrow x=\dfrac{-319}{-11}=29$

State the following statement is True or False
Multiplication and Division of two negative numbers is always a negative number

  1. True

  2. False


Correct Option: B
Explanation:

Multiplication and Division of two negative numbers is always a positive number.

$-32\times x= 160$, $-23\times y= -115$
What is the value of $x\div y$?

  1. $-1$

  2. $1$

  3. $-5$

  4. $5$


Correct Option: A
Explanation:
Given, $-32\times x=160, -23\times y=-115$
We have $x=\dfrac{160}{-32}$

and $ y=\dfrac{-115}{-23}=\dfrac{115}{23}$

Thus $\dfrac{x}{y}=\dfrac{160\times 23}{-32\times 115}=-\dfrac{32\times23}{32\times 23}=-1$

State the following statement is True or False
Multiplication of one negative number and one positive number results into negative number

  1. True

  2. False


Correct Option: A
Explanation:

$(-)\times (+)=(-)\Rightarrow $   Multiplication of one negative number and one positive number results into negative number

State the following statement is True or False
The value of $-32\times -13= -416$

  1. True

  2. False


Correct Option: B
Explanation:

The value of $-32\times -13$ is $416$.

Multiplication of two negative numbers results into a positive number.

Which of the following statements is true?

  1. The product of a positive and a negative integer is negative

  2. The product of a negative and a positive integer may be zero

  3. For all non-zero integers a and b, $a\times b$ is always greater than either a or b

  4. None of these


Correct Option: A
Explanation:

a) The product of a positive and a negative integer is negative = True

b) The product of a negative and a positive integer may be zero = False
c) For all non-zero integers $a$ and $b$, $a\times b$ is always greater than either $a$ or $b$ = False
Hence option A is correct answer.

The sign of the product of two unlike integers is __________.

  1. Positive

  2. Negative

  3. Positive or negative

  4. Cannot be determined


Correct Option: B
Explanation:

The sign of the product of two unlike integers i.e.positive integer and negative integer is always negative.
Hence the correct answer is option B.

What will be the sign of the product if we together multiply $199$ negative integers and $10$ positive integers?

  1. Negative

  2. Positive

  3. Can't say

  4. Data is insufficient


Correct Option: A
Explanation:

Multiplication of $2$ negative integer result into positive integer.

 
If we multiply $199$ negative integer, then the result will be negative integer

Now if we multiply $10$ positive numbers with $199$ negative integers 

we will get a negative integer because multiplication of negative and positive 
integer will always result in negative integer.

Hence option A is correct.

Which of the following statement is CORRECT?

  1. The product of a positive and a negative integer is always negative.

  2. The addition of a negative and a positive integer is always zero.

  3. For all non-zero integers a and b, a X b is always greater than either a or b.

  4. None of these


Correct Option: A
Explanation:

In option (A)       $-x\times x=-x^{2}$ which is always negative. option is correct.

In option (B)        $ -x+y$ not equals to $0$ it zero only when $x=y$  option is incorrect.
In option (C)         let $a=-3$ and $b=4$ then $a\times b=-3\times 4=-12$  which is less than both a and b. hence this option is also incorrect.
hence only option $A$ is correct.

The product of each negative integer with $-1$ is always ______.

  1. Positive

  2. Negative

  3. $0$

  4. Not defined


Correct Option: A
Explanation:

When we multiply negative integer with $-1$ because we get a positive quantity when we multiply two negative quantities we get a positive quantity. 

A teacher assigns $5$ points for a correct answer, and $-2$ points for an incorrect answer, and $0$ points for leaving the questioned unanswered. What is the score for a student who had $22$ correct
answers, $15$ incorrect answers, and $7$ unanswered questions? 

  1. $60$

  2. $75$

  3. $80$

  4. $93$


Correct Option: C
Explanation:

Since, the teacher assigns 5 points for a correct answer, and −2 points for an correct answer, and 0 points for leaving the questioned unanswered.

So,the student gets $(22\times 5) +(15\times -2)+ (7\times 0)  = 80$

The temperature at Bar Harbor, Maine, was $-3^{o}$ F. It then dropped during the night to
be $4$ times as cold. What was the temperature then?

  1. $12^{o}$ F

  2. $-12^{o}$ F

  3. $16^{o}$ F

  4. $-16^{o}$ F


Correct Option: B
Explanation:

Since the temperature is $4$ times as cold.

$\therefore $  Temperature then was $4\times -3= -12^o $ F

The square of any natural number cannot be in the form of 

  1. $5z$, where $z$ is a positive integer

  2. $5z+1$, where $z$ is a positive integer

  3. $5z+3$, where $z$ is a positive integer

  4. $5z+4$, where $z$ is a positive integer

  5. $None\ of\ these$


Correct Option: A

 If the product of two integers is $72$ and one of them is $-9$, then the other integer is.

  1. $-8$

  2. $8$

  3. $81$

  4. $63$


Correct Option: A
Explanation:

Let the other integer is $x$.

Then according to the problem,
$x\times (-9)=72$
or, $x=-\dfrac{72}{9}=-8$.

State whether the statement is true/false.

The product of a positive and a negative integer is negative.

  1. True

  2. False


Correct Option: A
Explanation:

$(+ve\,integer)\times(-ve\,integer)=(-ve\,integer)$

Which of the following statements are true?
Of the two integers, if one is negative, then their product must be positive.

  1. True

  2. False


Correct Option: A
Explanation:

The given statement is false.

As consider $2,-3$, both are integers and one is positive and the other is negative.
Now their product is $2\times (-3)=-6$ which is not positive.

Evaluate $\displaystyle\ \frac {5\times (-144)\times (-27)}{(-15)\times(18)\times(-16)}$

  1. $\dfrac {9}{4}$

  2. $\dfrac {9}{8}$

  3. $\dfrac {9}{2}$

  4. $\dfrac {-9}{2}$


Correct Option: C
Explanation:

As there are $ 2 $ negative numbers in the numerator and $ 2 $ in the denominator, the answer will be positive.

Canceling out the common factors and simplifying we get

$ \dfrac { 5\times (-144)\times (-27) }{ -(15)\times 18 \times (-16) } =\dfrac{9 \times 27}{3 \times 18} =\dfrac{9}{2}$

Solve: ${(-12)\times (-3) \times 4\times (-6) =}$ ?

  1. $-144$

  2. $-908$

  3. $+864$

  4. $-864$


Correct Option: D
Explanation:

$(−12)×(−3)×4×(−6)=(36)\times 4\times (-6)\ =144\times (-6)\ =-864$

$(-12) \times (+21) =$

  1. $-2412$

  2. $-242$

  3. $-252$

  4. $+252$


Correct Option: C
Explanation:
We know that the product of two integers with unlike signs is always negative.

We are given the two unlike integers, one with positive sign and one with negative sign that is $-12$ and $+21$ then the product of these integers is:

$(-12)\times (+21)=-(12\times 21)=-252$ which is a negative integer.

Hence, $(-12)\times (+21)=-252$.

If the dividend and divisor have like signs then the quotient will be .......... .

  1. positive

  2. negative

  3. zero

  4. none


Correct Option: A
Explanation:
If both the dividend and divisor are positive, the quotient will be positive. For example:

$(+16)\div (+4) = +4$

If both the dividend and divisor are negative, the quotient will be positive. For example:

$(-16)\div (-4) = +4$

If only one of the dividend or divisor is negative, the quotient will be negative. For example:

$(-16)\div (+4) = -4$     or     $(+16)\div (-4) = -4$

Therefore, we conclude that if the signs are the same/like, the quotient will be positive, if they are different/unlike, the quotient will be negative.

Hence, if the dividend and divisor have like signs then the quotient will be positive.

Sign of the product of 231 negative integer and 9 positive integer is

  1. Negative

  2. Positive

  3. 0

  4. None of these


Correct Option: A
Explanation:
We know that the product of two integers with unlike signs (two integers, one with positive sign and one with negative sign) is always negative.

The given two integers are $-231$ and $+9$ and the product of these integers is:

$(-231)\times (+9)=-(231\times 9)=-2079$ which is a negative integer.

Hence, sign of the product of the given integers is negative.

One integer is greater than the other by $+4$. If one number is $-16$ then the other is_____.

  1. $+12$

  2. $0$

  3. $-1$

  4. $-12$


Correct Option: D
Explanation:

Let the two integers be $x$ and $y$. One of the integer is given, that is $-16$. So let $y=-16$


Also, it is given that one integer is greater than the other by $+4$. Therefore, we have:

$x-y=+4\ \Rightarrow x-(-16)=4\ \Rightarrow x+16=4\ \Rightarrow x=4-16\ \Rightarrow x=-12$

Hence, the other integer is $-12$.

The product of each positive integer with $-1$ is always ______.

  1. Positive

  2. Negative

  3. 0

  4. None of these


Correct Option: B
Explanation:

Let us take a positive integer $+2$ and multiply it with the given negative integer $-1$.


We know that the  product of two integers with unlike signs is always negative.

Therefore, the product of the integers with unlike signs $+2$ and $-1$ is:

$(+2)\times (-1)=-(2\times 1)=-2$ which is a negative integer.

Hence, the positive integer whose product with $-1$ is always negative.

Product of two integers is $-48$. If one of the integers is $-6$ then the other is

  1. $+1$

  2. $+288$

  3. $0$

  4. $+8$


Correct Option: D
Explanation:

Let the other integer be $x$. One of the integer is given that is $-6$.


Also, it is given that the product of the two integers is $-48$. Therefore, we have:

$x\times (-6)=-48\ \Rightarrow -6x=-48\ \Rightarrow 6x=48\ \Rightarrow x=\dfrac { 48 }{ 6 } \ \Rightarrow x=8$

Hence, the other integer is $+8$.

$(-1)^{11}$ value is

  1. $+1$

  2. $0$

  3. $-1$

  4. none of these


Correct Option: C
Explanation:

We know that if the power $n$ of any negative integer $x$ is even then the resulting integer will always be positive and if the power $n$ of any negative integer $x$ is odd then the resulting integer will always be negative. For example, if the negative integer is $x=-2$, then


Odd power:
$(-2)^3=-2\times -2\times -2=-8$ which is a negative integer.

Even power:

$(-2)^2=-2\times -2=4$ which is a positive integer.

Similarly, $(-1)^{11}=-1$ because $-1$ is a negative integer and $11$ is an odd number, so the result will be a negative integer.

Hence, $(-1)^{11}=-1$

$\displaystyle -84\times \quad ......= +84 $

  1. 0

  2. +1

  3. +84

  4. -1


Correct Option: D
Explanation:

(-84)(-1)=(+84)

remember
(-)(-)=+

$\displaystyle (148)\div (-4)\quad =$

  1. +37

  2. -37

  3. -38

  4. None of these


Correct Option: B
Explanation:

$(148)\div(-4)=-148\div4=-37$

$\displaystyle 78\times \quad ....... = -78 $

  1. 1

  2. 178

  3. 0

  4. -1


Correct Option: D
Explanation:

78*(-1)=-78

hence option D is correct

$\displaystyle (-8)\times (-4) =$

  1. -8

  2. -32

  3. -4

  4. +32


Correct Option: D
Explanation:

$(-8)\times(-4)=8\times4=32$

Suppose we represent the distance above the ground by a positive integer and that below the ground by a negative integer, then answer the following:
An elevator descends into a mine shaft at the rate of $5$meters per minute. What will be its position after one hour? 

  1. $250$

  2. $300$

  3. $100$

  4. $50$


Correct Option: B
Explanation:

Since, the elevator going down, so the distance covered by it will be represented by a negative integer.
Change in position of elevator in one minute = $-5 m$.
Position of the elevator after $60$ minutes = $(-5)\times 60 =-300\ m$ 

i.e. $ 300\ m$ below ground level.

$\displaystyle (-24)\times (-2)\times (-2)\times 0\times (-4) =$

  1. $+384$

  2. $-384$

  3. $0$

  4. None of these


Correct Option: C
Explanation:

$\displaystyle (-24)\times (-2)\times (-2)\times 0\times (-4)
= +48\times 0\times -4
=0\times -4
=0 $

Integer used to represent $30$ km towards the right:

  1. $30$ km left

  2. $-30$ km

  3. $+30$ km

  4. $0$


Correct Option: C
Explanation:

The integer used to represent $30$ km towards the west is $ +30 $ km

Hence, the answer is $+30$ km.

What is the number to be multiplied by $(-7)^{-1}$ so as to get $10^{-1}$ as the product?

  1. $\displaystyle\frac{-7}{10}$

  2. $\displaystyle\frac{7}{10}$

  3. $\displaystyle\frac{9}{10}$

  4. $\displaystyle\frac{-3}{10}$


Correct Option: A
Explanation:
let the number be $ x$
According to the question:
$\Rightarrow(-7)^{-1} x = 10 ^{-1}$
$\Rightarrow\dfrac{1}{-7^{1}}x = \dfrac{1}{10}$
Applying cross multiplication
$\Rightarrow x  = \dfrac{-7}{10}$


Simplify: $(-4)\times 63 = x \times 21$.

Find the value of $x$.

  1. $-21$

  2. $12$

  3. $21$

  4. $-12$


Correct Option: D
Explanation:

$X=\dfrac{(-4)\times63}{21}=-12$

Simplify: $\dfrac{(-33)\times(96)}{(11)\times(-24)}$.

  1. $-14$

  2. $12$

  3. $10$

  4. $-12$


Correct Option: B
Explanation:

$\dfrac{-33\times 96}{11\times -24}=(-3)\times (-4)=12$

Given $-51\times x= 204$ and $-33\times y= -297$, then find the value of $-x\times y$.

  1. $-36$

  2. $33$

  3. $36$

  4. $-33$


Correct Option: C
Explanation:
Given, $-51\times x=204$ and $-33\times y=-297$
Therefore, $x=-\dfrac{204}{51}=-4$
and $ y=\dfrac{-297}{-33}=9$
Thus $-x\times y=-(-4)\times9=36$

$-42\times x= 336$, $-28\times y= -84$
What is the value of $x$ and $y$ respectively?

  1. $8$ and $3$

  2. $-8$ and $3$

  3. $8$ and $-3$

  4. $-8$ and $-3$


Correct Option: B
Explanation:
Given, $-42\times x=336$ and $-28\times y=-84$

Thus $x=\dfrac{336}{-42}=-8$

and $ y=\dfrac{-84}{-28}=3$

Product of two unlike integers is always:

  1. Positive

  2. Negative

  3. $0$

  4. $1$


Correct Option: B
Explanation:
Product of a positive integer and negative integer=$(+)\times (-) $=Negative
Product of a negative integer and positive integer=$(-)\times (+) $=Negative

Without actual multiplication, then value of $687 \times 687 - 313 \times 313$

  1. $3,50,004$

  2. $3,74,000$

  3. $5,74,000$

  4. $2,74,000$


Correct Option: B
Explanation:

$687\times687-313\times313$


$=(687)^2-(313)^2$

Using identity $(a+b)(a-b)=a²-b²$

$= (687+313)(687-313)$

$=1000\times374$

$= 3,74,000$

$\therefore \text{option B is correct}.$

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