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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

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

  1. $\displaystyle \frac{3}{16}$
  2. $\displaystyle \frac{9}{16}$
  3. $\displaystyle \frac{1}{16}$
  4. $\displaystyle \frac{7}{16}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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

  1. 0

  2. -1

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\frac{(0.9+0.1)\left [ (0.9)^{2}-0.9\times 0.1+(0.1)^{2} \right ]}{(0.9)^{2}-0.9\times 0.1+(0.1)^{2}}=(0.9+0.1)=1$
Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

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

  1. 2

  2. 0

  3. -1

  4. 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$y^{4}\div y ofy^{3}\div y^{2}\times y^{5}\div y^{3}$
=$y^{4}\div y\times y^{3}\div y^{2}\times y^{2}$
=$\frac{y^{4}}{y^{4}}\times \frac{y^{4}}{y^{4}}=1\times 1=1$
Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

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

  1. $2034$
  2. $2403$
  3. $2304$

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

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