Tag: parts and whole

Questions Related to parts and whole

If $\large{1\frac{2}{7}}$ of $\large{\frac{56}{63}}$ is simplified. Then the answer is

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\large{\frac{8}{7}}$

  2. $\large{1\frac{1}{7}}$

  3. $\large{\frac{8}{5}}$

  4. $\large{1\frac{3}{5}}$

Show answer
Correct Option: A,B
Explanation:

$\large{1\frac{2}{7}}$ of $\large{\frac{56}{63}}$
$=\large{\frac{9}{7}} \times \large{\frac{56}{63}}$
$=\large{\frac{8}{7}}$ or $\large{1\frac{1}{7}}$.

If $\dfrac {3}{4}$ of $\dfrac {1}{2}$ of a number is $60$ then the number is:

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $160$

  2. $400$

  3. $500$

  4. $700$

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Correct Option: A
Explanation:
let the number be $x$

now $\dfrac 34$ of $\dfrac 12$ of x is $60$

$\Rightarrow \dfrac { 3 }{ 4 } (\dfrac { 1 }{ 2 } (x))=60\\ \Rightarrow \dfrac { 3x }{ 8 } =60\\ \Rightarrow x=\dfrac { 60\times 8 }{ 3 } =160$ 

$\dfrac{\dfrac { 540 }{ 11 } \times 7}{343\dfrac { 7 }{ 11 }}$ 

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. 1

  2. 2

  3. 3

  4. 4

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Correct Option: A
Explanation:

$\begin{array}{l} In\, \, L.H.S \ No.=\frac { { 540\times 7 } }{ { 11 } } \times \frac { { 11 } }{ { \left( { 343\times 11+7 } \right)  } }  \ \frac { { 540\times 7 } }{ { 7\left( { { 7^{ 2 } }\times 11+1 } \right)  } }  \ No.=\frac { { 540 } }{ { 539+1 } } =1 \end{array}$

Whole number is 1.

The value of the expression $\sqrt {34-24\sqrt 2}\times (4+3\sqrt 2)$ is

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $-2$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: B
Explanation:

$\sqrt {34-24\sqrt 2}\times (4+3\sqrt 2)$


$=\sqrt {34-24\sqrt 2}\sqrt {(4+3\sqrt 2)^2}$

$=\sqrt {(34-24\sqrt 2)(16+18+24\sqrt 2)}$

$=\sqrt {(34-24\sqrt 2)(34+24\sqrt 2)}$

$=\sqrt {(34)^2(24\sqrt 2)^2}$

$=\sqrt {1156-1152}=\sqrt 4=2$

The product of two-fifths of a number and $80\%$ of another number is what percent of the product of the numbers

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $20\%$

  2. $24\%$

  3. $28\%$

  4. $32\%$

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Correct Option: D

A certain number of men went to a hotel. Each man spent as many rupees as one-fourth of the men. If the total bill paid was Rs $20449$, then how many men visited in the hotel ?

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $286$

  2. $284$

  3. $281$

  4. $283$

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Correct Option: A
Explanation:

Let the number of men visiting hotel be $x$


Money spent by one man $=\dfrac{1}{4}x$

Total bill $=20449$

$x\times \dfrac{1}{4}x=20449$

$x^2=81796$

$x=286\,men$.


Multiply $\dfrac{6}{13}$ by the reciprocal of $\dfrac{-7}{16}$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\dfrac{-95}{91}$

  2. $\dfrac{-96}{91}$

  3. $\dfrac{96}{91}$

  4. None of these

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Correct Option: B
Explanation:
Reciprocal of $\dfrac{-7}{16}$ is $\dfrac{-16}{7}$

Now $\dfrac{6}{13}\times$ Reciprocal of $\dfrac{-7}{16}$

$=\dfrac{6}{13}\times\dfrac{-16}{7}$

$=\dfrac{6\times -16}{13\times 7}=\dfrac{-96}{91}$

If one-third of one-fourth of a number is $15$, then three-tenth of that number is:

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $75$

  2. $22$

  3. $18$

  4. $66$

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Correct Option: C

Two-Third of a number and $\displaystyle \frac{25}{216}$ of its reciprocal are equal. What is the number?

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\displaystyle \frac{25}{144}$

  2. $\displaystyle \frac{5}{12}$

  3. $\displaystyle \frac{144}{25}$

  4. $\displaystyle \frac{12}{5}$

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Correct Option: B
Explanation:

Let the number be x Given $\displaystyle \frac{2}{3}x=\frac{25}{216}\times\frac{1}{x}$
$\displaystyle\Rightarrow x^{2}=\frac{25}{216 _{72}}\times\frac{3^{1}}{2}=\frac{25}{144}$
$\displaystyle\Rightarrow x=\sqrt{\frac{25}{144}}=\frac{5}{12}$

$\displaystyle \left ( 999\frac{999}{1000}\times 7 \right )$ is equal to 

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\displaystyle 6993\frac{7}{1000}$

  2. $\displaystyle 7000\frac{7}{1000}$

  3. $\displaystyle 6633\frac{7}{1000}$

  4. $\displaystyle 6999\frac{993}{1000}$

Show answer
Correct Option: D
Explanation:

Given expression $\displaystyle =\left ( 999+\frac{999}{1000} \right )\times7$
$\displaystyle=1000-1+1-\frac{1}{1000}\times7$
$\displaystyle=\left ( 1000-\frac{1}{1000} \right )\times7=7000-\frac{7}{1000}$
$\displaystyle=6999+1-\frac{7}{1000}=6999+\frac{993}{1000}$
$\displaystyle=6999\frac{993}{1000}$