Tag: division of integers and its properties

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

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

  1. $-18$
  2. $18$
  3. $16$
  4. $-16$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $

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

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

  1. negative

  2. positive

  3. 0

  4. none
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

Product of two integers with unlike signs is

  1. Negative

  2. 0

  3. Positive

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

Product of two integers with like signs is

  1. Negative

  2. Positive

  3. 0

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

$(+132) $ $\div$ $ (-12)$

  1. $+ 101$
  2. $-101$
  3. $+ 11$
  4. $-11$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

  1. -144

  2. -908

  3. +864

  4. -864
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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


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