Tag: division of integers and its properties

Questions Related to division of integers and its properties

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

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. Positive

  2. Negative

  3. 0

  4. None of these

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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

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $+1$

  2. $+288$

  3. $0$

  4. $+8$

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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

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $+1$

  2. $0$

  3. $-1$

  4. none of these

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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 $

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. 0

  2. +1

  3. +84

  4. -1

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Correct Option: D
Explanation:

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

remember
(-)(-)=+

$\displaystyle (148)\div (-4)\quad =$

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. +37

  2. -37

  3. -38

  4. None of these

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Correct Option: B
Explanation:

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

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

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. 1

  2. 178

  3. 0

  4. -1

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Correct Option: D
Explanation:

78*(-1)=-78

hence option D is correct

$\displaystyle (-8)\times (-4) =$

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. -8

  2. -32

  3. -4

  4. +32

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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? 

maths the integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $250$

  2. $300$

  3. $100$

  4. $50$

Show answer
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.

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

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $+384$

  2. $-384$

  3. $0$

  4. None of these

Show answer
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:

maths the integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $30$ km left

  2. $-30$ km

  3. $+30$ km

  4. $0$

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Correct Option: C
Explanation:

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

Hence, the answer is $+30$ km.