Tag: multiplication and division of integers

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Questions Related to multiplication and division of integers

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

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

  1. Positive

  2. Negative

  3. 0

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

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

  1. $+1$
  2. $+288$
  3. $0$
  4. $+8$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $+8$.

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

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

  1. $+1$
  2. $0$
  3. $-1$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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, $(-1)^{11}=-1$

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

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. $\displaystyle\frac{-3}{10}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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
$\Rightarrow x  = \dfrac{-7}{10}$