Question

If the value of \[5 \div 3\dfrac{4}{7} = k.\] Find $5k$.

Answer 1

Hint: First of convert the \[3\dfrac{4}{7}\] fractional number by using this formula:
\[a\dfrac{b}{c} = \dfrac{{ac + b}}{c}\]
Because we cannot divide a mixed fraction by any number directly, so we convert it into a proper fraction. Then find the value of k.
After that multiply on both-side 5 So, we get the value of 5k.
* A mixed fraction is of the form \[a\dfrac{b}{c}\] which can be converted into a proper fraction using the formula. \[a\dfrac{b}{c} = \dfrac{{ac + b}}{c}\]

Complete step-by-step answer:
From the question
\[5 \div 3\dfrac{4}{7} = k.\]
In above equation converting the \[3\dfrac{4}{7}\]fractional number by using this formula \[a\dfrac{b}{c} = \dfrac{{ac + b}}{c}\]
Substitute a=3, b=4, c=7
$\Rightarrow$ \[5 \div \dfrac{{(7 \times 3) + 4}}{7} = k.\]
On simplifying the above equation,
$\Rightarrow$ \[5 \div \dfrac{{21 + 4}}{7} = k.\]
Adding the values in the numerator
$\Rightarrow$ \[5 \div \dfrac{{25}}{7} = k.\]
On further simplification,
$\Rightarrow$ \[k = \dfrac{{35}}{{25}}\]
Then take common $5$ from denominator and numerator and cancel both so we get the value of $k$.
Now we know if we have the value of a single unit then to find the value of multiple units we multiply the number of units to the value of a single unit.
Here value of single unit is \[\dfrac{7}{5}\] and number of units are $5$, therefore,
Multiplying both side of the equation by 5 we get,
\[5k = 7\]

$\therefore$The value of 5k is 7.

Note:
To convert any \[a\dfrac{b}{c}\]number into fractional number formula for this is:
\[a\dfrac{b}{c} = \dfrac{{ac + b}}{c}\].
If this type of number is given then convert first into a fractional number so you can easily do the question otherwise get an error in the answer.
Another approach for this question is to directly find the value of 5k.
\[5 \div 3\dfrac{4}{7} = k.\]
In above equation converting the \[3\dfrac{4}{7}\]fractional number by using this formula \[a\dfrac{b}{c} = \dfrac{{ac + b}}{c}\]
\[5 \div \dfrac{{(7 \times 3) + 4}}{7} = k.\]
\[5 \div \dfrac{{21 + 4}}{7} = k.\]
\[5 \div \dfrac{{25}}{7} = k.\]
Then multiply on both-side 5 we get,
\[5k = \dfrac{{7 \times 5 \times 5}}{{25}}\]
\[5k = 7\]
After solving this we get the value of $5k$
\[5k = 7\]