Tag: division of integers and its properties

Questions Related to division of integers and its properties

What is the number to be multiplied by $(-7)^{-1}$ so as to get $10^{-1}$ as the product?

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

  1. $\displaystyle\frac{-7}{10}$

  2. $\displaystyle\frac{7}{10}$

  3. $\displaystyle\frac{9}{10}$

  4. $\displaystyle\frac{-3}{10}$

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Correct Option: A
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
$\Rightarrow x  = \dfrac{-7}{10}$


Simplify: $(-4)\times 63 = x \times 21$.

Find the value of $x$.

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

  1. $-21$

  2. $12$

  3. $21$

  4. $-12$

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Correct Option: D
Explanation:

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

Simplify: $\dfrac{(-33)\times(96)}{(11)\times(-24)}$.

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

  1. $-14$

  2. $12$

  3. $10$

  4. $-12$

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Correct Option: B
Explanation:

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

Given $-51\times x= 204$ and $-33\times y= -297$, then find the value of $-x\times y$.

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

  1. $-36$

  2. $33$

  3. $36$

  4. $-33$

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Correct Option: C
Explanation:
Given, $-51\times x=204$ and $-33\times y=-297$
Therefore, $x=-\dfrac{204}{51}=-4$
and $ y=\dfrac{-297}{-33}=9$
Thus $-x\times y=-(-4)\times9=36$

$-42\times x= 336$, $-28\times y= -84$
What is the value of $x$ and $y$ respectively?

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

  1. $8$ and $3$

  2. $-8$ and $3$

  3. $8$ and $-3$

  4. $-8$ and $-3$

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Correct Option: B
Explanation:
Given, $-42\times x=336$ and $-28\times y=-84$

Thus $x=\dfrac{336}{-42}=-8$

and $ y=\dfrac{-84}{-28}=3$

Product of two unlike integers 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. $1$

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Correct Option: B
Explanation:
Product of a positive integer and negative integer=$(+)\times (-) $=Negative
Product of a negative integer and positive integer=$(-)\times (+) $=Negative

Without actual multiplication, then value of $687 \times 687 - 313 \times 313$

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

  1. $3,50,004$

  2. $3,74,000$

  3. $5,74,000$

  4. $2,74,000$

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Correct Option: B
Explanation:

$687\times687-313\times313$


$=(687)^2-(313)^2$

Using identity $(a+b)(a-b)=a²-b²$

$= (687+313)(687-313)$

$=1000\times374$

$= 3,74,000$

$\therefore \text{option B is correct}.$