Tag: division of integers and its properties

Questions Related to division of integers and its properties

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

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

  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. $None\ of\ these$

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Correct Option: A

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

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

  1. $-8$

  2. $8$

  3. $81$

  4. $63$

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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.

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

  1. True

  2. False

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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.

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

  1. True

  2. False

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

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

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

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

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

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

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

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

  1. $-144$

  2. $-908$

  3. $+864$

  4. $-864$

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Correct Option: D
Explanation:

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

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

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

  1. $-2412$

  2. $-242$

  3. $-252$

  4. $+252$

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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 .......... .

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

  1. positive

  2. negative

  3. zero

  4. none

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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

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

  1. Negative

  2. Positive

  3. 0

  4. None of these

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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_____.

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

  1. $+12$

  2. $0$

  3. $-1$

  4. $-12$

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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 $-12$.