Tag: multiplication and division of integers

Questions Related to multiplication and division of integers

The product of two factors with unlike signs is ...........

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

  1. positive

  2. negative

  3. cannot be determined

  4. none of these

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Correct Option: B
Explanation:

Let 2 and -3 be the two factors.
Clearly, $2\times-3=-6$, which is negative.
Hence, Option B is correct.

The value of $\displaystyle \frac{1\div\frac{2}{3}\times \frac{3}{4} }{1\div \frac{2}{3}\times \frac{3}{4}}$ on simplification is

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

  1. $\displaystyle \frac{3}{16}$

  2. $\displaystyle \frac{9}{16}$

  3. $\displaystyle \frac{1}{16}$

  4. $\displaystyle \frac{7}{16}$

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Correct Option: B
Explanation:

$\frac{1\div \frac{2}{3}\times \frac{3}{4}}{1+\div \frac{2}{3}of\frac{4}{3}}$

$\frac{1\div \frac{2}{3}\times \frac{3}{4}}{1\div \frac{2}{3}\times \frac{4}{3}}$
$\frac{1\times \frac{1}{2}}{1\times \frac{8}{9}}$
$\Rightarrow \frac{1\times 2}{1\times \frac{8}{9}}$
$\Rightarrow \frac{\frac{1}{2}}{\frac{8}{9}} =\frac{9}{16}$

The value of $\displaystyle \frac{0.9\times 0.9\times 0.9+0.1\times 0.1\times 0.1}{0.9\times 0.9-0.9\times 0.1+0.1\times 0.1}$ on simplification is

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

  1. 0

  2. -1

  3. 2

  4. 1

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Correct Option: D
Explanation:
$\frac{0.9\times 0.9\times 0.9+0.1\times 0.1\times 0.1}{0.9\times 0.9-0.9\times 0.1+0.1\times 0.1}$
=$\frac{(0.9)^{3}+(0.1)^{3}}{(0.9)^{2}-0.9\times 0.1+(0.1)^{2}}$
We know that$ a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$
Then $\frac{(0.9+0.1)\left [ (0.9)^{2}-0.9\times 0.1+(0.1)^{2} \right ]}{(0.9)^{2}-0.9\times 0.1+(0.1)^{2}}=(0.9+0.1)=1$

The simplified value of $\displaystyle y^{4}\div y$ of $\displaystyle y^{3}\div y^{2}\times y^{5}\div y^{3}$ is

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

  1. 2

  2. 0

  3. -1

  4. 1

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Correct Option: D
Explanation:
$y^{4}\div y ofy^{3}\div y^{2}\times y^{5}\div y^{3}$
=$y^{4}\div y\times y^{3}\div y^{2}\times y^{2}$
=$\frac{y^{4}}{y^{4}}\times \frac{y^{4}}{y^{4}}=1\times 1=1$

The product of any number and "0" 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. number itself

  4. none of these

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Correct Option: B
Explanation:
The product of any number and zero is zero. 
Theorem: $0×a=0$ for any integer $a.$

So option B is the correct answer.

$\displaystyle (-8)\times (-2)\times (+3)\times (-4) = $ 

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

  1. $+192$

  2. $-192$

  3. $+28$

  4. $-4$

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Correct Option: B
Explanation:

$\displaystyle (-8)\times (-2)\times (+3)\times (-4)
= +16\times  -12
= -192 $

Sixth power of (-2) is

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

  1. $-64$

  2. $+32$

  3. $+64$

  4. $-16$

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Correct Option: C
Explanation:

$\displaystyle ({ -2 })^{ 6 }=\quad -2\times -2\times -2\times -2\times -2\times -2
= +64 $

$Factor \times Factor$ is equal to  ____ .

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

  1. difference

  2. multiple

  3. sum

  4. None of these

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Correct Option: B
Explanation:

$×$ sign between any $2$ numbers results in the product of those numbers or the multiple. 


So, option B is the correct answer.

Value of $\displaystyle { 2 }^{ 2 }{ \times (-3) }^{ 2 }{ \times 2 }^{ 2 }{ \times (-4) }^{ 2 } $ is

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

  1. $2034$

  2. $2403$

  3. $2304$

  4. None of these

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Correct Option: C
Explanation:

$\displaystyle { 2 }^{ 2 }{ \times (-3) }^{ 2 }{ \times 2 }^{ 2 }{ \times (-4) }^{ 2 }\ =4\times +9\times 4\times 16\ =2304$ 

$8 - [ 12 - ({ - 2 \times - 4 (4 of -4 ) }) ] $=

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

  1. $-132$

  2. $132$

  3. $0$

  4. None of these

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Correct Option: A
Explanation:

$8 - [ 12 - ({ - 2 \times  - 4 (4 of -4 )) } ] $
$= 8 - [12 - ({ - 2 \times -4 \times  -16})]$
$= 8 - [12 - ({ - 128 })]$
$= 8 - [12 +128]$
$=8 -140$
$= -132$