Tag: multiplication of fraction

Questions Related to multiplication of fraction

The daily consumption of milk of a family is $\displaystyle 3\frac{1}{4}$ litres. The quantity of milk consumed by the family during the month of September 2003 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. 90 lit

  2. $\displaystyle 100\frac{1}{2}$ lit

  3. $\displaystyle 97\frac{1}{2}$ lit

  4. none

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Correct Option: C
Explanation:

Per day consumption $=3\cfrac14$liters.

There are $30$ days in the month of September.
So, Consumption in september $=30\times 3\cfrac14=30\times \cfrac {13}{4}=97\cfrac12$liters.
Option C is correct.

Consider the following statements : 
A. The product of an integer and a rational number can never be a natural number 
B. The quotient of division of an integer by a rational number can never be an integer
Which of the statements given above is/are correct ?

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

  1. A only

  2. B only

  3. Both A and B

  4. Neither A nor B

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Correct Option: D
Explanation:

Let integer = 4 and Rational number = $\displaystyle \frac{2}{1} $
Then product = $\displaystyle 4\times\frac{2}{1}=8 $ (a natural number)
and Quotient = $\displaystyle 4\div \frac{2}{1}=4\times \frac{1}{2}=2 $ (an integer)

What would be the reciprocal of the sum of the reciprocal of the numbers $\displaystyle \frac{3}{5}$ and $\displaystyle \frac{7}{3}$?

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

  1. $\displaystyle \frac{1}{42}$

  2. $\displaystyle \frac{21}{44}$

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

  4. $\displaystyle \frac{36}{55}$

Show answer
Correct Option: B
Explanation:

Sum of the reciprocals of $\displaystyle \dfrac{3}{5}$ and $\dfrac{7}{3}$
$\displaystyle =\frac{5}{3}+\frac{3}{7}=\frac{35+9}{21}=\frac{44}{21}$
$\displaystyle \therefore $ Required number $\displaystyle =\frac{21}{44} $

Reciprocal of $\displaystyle \frac {7}{5}$ 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. $1\displaystyle \frac {2}{5}$

  2. $\displaystyle \frac {5}{7}$

  3. $5\displaystyle \frac {2}{3}$

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

Show answer
Correct Option: B
Explanation:

We know that the reciprocal of any number $n$ is $\dfrac {1}{n}$. When we multiply a number by its reciprocal, we get $1$ as the answer. For example: $n\times \dfrac { 1 }{ n } =1$ 


Therefore, the reciprocal of  the given fraction $\dfrac {7}{5}$ is as follows:

$\dfrac { 1 }{ \dfrac { 7 }{ 5 }  } =\dfrac { 5 }{ 7 } \quad \quad \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ \dfrac { 1 }{ x }  } =\dfrac { x }{ 1 }  \right}$ 

Hence, the reciprocal of $\dfrac {7}{5}$ is $\dfrac {5}{7}$.

Reciprocal of $\displaystyle \frac{6}{3}$ 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. -$\displaystyle \frac{6}{3}$

  2. -$\displaystyle \frac{3}{6}$

  3. $\displaystyle \frac{3}{6}$

  4. $36$

Show answer
Correct Option: C
Explanation:

The reciprocal of a number is $1$ divided by that number. For example, the reciprocal of $a$ is $\dfrac {1}{a}$


Now, we find the reciprocal of $\dfrac {6}{3}$ as follows:

$\dfrac { 1 }{ \dfrac { 6 }{ 3 }  } =\dfrac { 3 }{ 6 } \quad \quad \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ \dfrac { 1 }{ x }  } =\dfrac { x }{ 1 }  \right}$ 

Hence, the reciprocal of $\dfrac {6}{3}$ is $\dfrac {3}{6}$

Reciprocal of $2 \displaystyle \frac{1}{3}$ 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. $\displaystyle \frac{7}{3}$

  2. $-\displaystyle \frac{7}{3}$

  3. $-\displaystyle \frac{3}{7}$

  4. $\displaystyle \frac{3}{7}$

Show answer
Correct Option: D
Explanation:

We first rewrite the given mixed fraction $2\dfrac { 1 }{ 3 }$ as $\dfrac {7}{3}$. 


We know that the reciprocal of a number is $1$ divided by that number. For example, the reciprocal of $a$ is $\dfrac {1}{a}$
 

Now, we find the reciprocal of $\dfrac {7}{3}$ as follows:

$\dfrac { 1 }{ \dfrac { 7 }{ 3 }  } =\dfrac { 3 }{ 7 } \quad \quad \quad \quad \quad \quad \quad \left\{ \because \quad \dfrac { 1 }{ \dfrac { 1 }{ x }  } =\dfrac { x }{ 1 }  \right\}$ 

Hence, the reciprocal of $2\dfrac { 1 }{ 3 }$ is $\dfrac {3}{7}$

Reciprocal of $3$ 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. $-3$

  2. $-\displaystyle \frac{1}{3}$

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

  4. None of these

Show answer
Correct Option: C
Explanation:

The reciprocal of a number is $1$ divided by that number. For example, the reciprocal of $a$ is $\dfrac {1}{a}$


Hence, the reciprocal of $3$ is $\dfrac {1}{3}$

Ravi had $\displaystyle \frac {5}{6}$ of a cake. He ate $\displaystyle \frac {2}{3}$ of it. What part of the cake did he eat?

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

  1. $\displaystyle \frac {5}{9}$

  2. $\displaystyle \frac {10}{12}$

  3. $\displaystyle \frac {10}{6}$

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

Show answer
Correct Option: A
Explanation:

It is given that Ravi had $\dfrac {5}{6}$ of a cake and from that piece of cake he ate $\dfrac {2}{3}$rd of it which means that:


$\dfrac { 5 }{ 6 } \times \dfrac { 2 }{ 3 } \ =\dfrac { 5 }{ 3 } \times \dfrac { 1 }{ 3 } \ =\dfrac { 5 }{ 9 }$

Hence, Ravi ate $\dfrac {5}{9}$th part of the cake.

The product of a fractional number and its multiplicative inverse 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. $0$

  2. $1$

  3. number itself

  4. none

Show answer
Correct Option: B
Explanation:

If the product of two numbers is $1$, then each number is known as multiplicative inverse or the reciprocal of one another. To find the multiplicative inverse of a proper or improper fraction, interchange the numerator and denominator. For example, the multiplicative inverse of the fraction $\dfrac {5}{18}$ is $\dfrac {18}{5}$.


Now, the product of the fractional number $\dfrac {5}{18}$ and its multiplicative inverse $\dfrac {18}{5}$ is as follows:

$\dfrac { 5 }{ 18 } \times \dfrac { 18 }{ 5 } =1$

Hence, the product of a fractional number and its multiplicative inverse is $1$.

The reciprocal of the fraction $\displaystyle  \frac { 5 }{ 11 }$ 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. $\displaystyle \frac { 11 }{ 5 }$

  2. $\displaystyle \frac { 5 }{ 11 }$

  3. $\displaystyle \frac { 1 }{ 5 }$

  4. $\displaystyle \frac { 1 }{ 11 }$

Show answer
Correct Option: A
Explanation:

the reciprocal of 5/11 is 11/5..