Question

What is the value of $80.88 \div 8.425$ ?

Answer 1

Hint: Here we are going to convert the decimal number into fraction and then divide by the common factors of numerator and the denominator if possible.

Complete step-by-step solution:
Given $80.88 \div 8.425$ to make this as a fraction and write like this $\dfrac{{80.88}}{{8.425}}$
Both denominator and numerator are the decimal numbers. To make them as a fraction, we are multiplying $1000$ to both numerator and denominator.
That is $\dfrac{{80.88}}{{8.425}} = \dfrac{{80.88 \times 1000}}{{8.425 \times 1000}}$--------------(1)
On simplifying it we get,
$ \Rightarrow \dfrac{{80880}}{{8425}}$ --------------------------(2)
Now finding the factors of both numerator and also the denominator, let start with numerator term,
\[\begin{array}{*{20}{c}}
  {2\left| \!{\underline {\,
  {80880} \,}} \right. } \\
  {2\left| \!{\underline {\,
  {40440} \,}} \right. } \\
  {2\left| \!{\underline {\,
  {20220} \,}} \right. } \\
  {3\left| \!{\underline {\,
  {10110} \,}} \right. } \\
  {5\left| \!{\underline {\,
  {3370} \,}} \right. } \\
  {2\left| \!{\underline {\,
  {674} \,}} \right. } \\
  {\underline {\,\,337} }
\end{array}\]
Now the factors of $80880 = 2 \times 2 \times 2 \times 3 \times 5 \times 2 \times 337$---------(3)
Now for the denominator term using same similar method,
$\begin{array}{*{20}{c}}
  {5\left| \!{\underline {\,
  {8425} \,}} \right. } \\
  {5\left| \!{\underline {\,
  {1685} \,}} \right. } \\
  {\underline {337} }
\end{array}$
Now the factors of $8425 = 5 \times 5 \times 337$---------(4)
Substitute the equation (3) and (4) in equation (2) we get,
$ \Rightarrow \dfrac{{80880}}{{8425}} = \dfrac{{2 \times 2 \times 2 \times 3 \times 5 \times 2 \times 337}}{{5 \times 5 \times 337}}$
On simplifying the above fraction we get,
$ \Rightarrow \dfrac{{80880}}{{8425}} = \dfrac{{2 \times 2 \times 2 \times 3 \times 2}}{5}$
On simplifying it we get,
$ \Rightarrow \dfrac{{80880}}{{8425}} = \dfrac{{240}}{{25}} = \dfrac{{48}}{5}$
Dividing the above term , we get,
\[\begin{array}{*{20}{c}}
  {\,\,\,\,\,9.6} \\
  {5)\overline {480} } \\
  {\underline {\,\,480} } \\
  {\underline {\,\,\,0} }
\end{array}\]
Now getting the exact answer for this division $\dfrac{{80.88}}{{8.425}} = 9.6$
The final answer is $9.6$.

Note: We know that when the number obtained by dividing by the denominator is the decimal form of the fraction. There can be two situations in converting fractions to decimals. When division stops after a certain number of steps as the remainder becomes zero. When division continues as there is a remainder after every step.
To divide a decimal by another decimal, we can move the decimal point in the divisor to the right until it is the whole number. And move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number. Then divide the new dividend by the new divisor.