Multiplying and dividing integers - class-VI

$3 \times -1=-3$

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 

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 $

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

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 $

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 $

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

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

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

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 $

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

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

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 $

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

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

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

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:

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

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

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

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

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

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

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

-6 $\times$ -2 = + 12

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

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

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

$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,$5.\overline { 63 }\times 11$
$=>\frac{558}{99}\times 11$
$=>62$

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

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

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

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

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

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

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

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

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

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

$\dfrac{-32}{-4}$ = 8 

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

Negative

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,

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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.

Since the temperature is $4$ times as cold.

Let the other integer is $x$.

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

The given statement is false.

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}$

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

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

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

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

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

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

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

78*(-1)=-78

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

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 = $(-5)\times 60 =-300\ m$ 

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

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

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

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

$687\times687-313\times313$