Question

How do you find the value of \[5.8 \div 1.2?\]

Answer 1

Hint: Given is a division based problem of two decimal numbers. Both are having one decimal digit. We will first remove the decimal by multiplying the numerator and denominator by 10. Then we will simplify the division by regular process of division. That is dividend 58 by 12. Where dividend is 58 and divisor is 12.

Complete step-by-step answer:
Given that \[5.8 \div 1.2\]
First we will multiply both the numbers by 10 to remove the decimal.
\[5.8 \times 10 \div 1.2 \times 10\]
Now the division will be
\[58 \div 12\]
This is our regular division.
\[12\mathop{\left){\vphantom{1\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, 4}\]
Now the remainder is 10 and quotient is 4.
We will again divide the remainder taking the decimal as quotient
\[12\mathop{\left){\vphantom{1\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
    \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
    \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {4.}}\]
Now we will find the next number in a table of 12 that is either less than or equal to 100.
\[12\mathop{\left){\vphantom{1\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
   - 96 \\
  \bar 0\bar 0\bar 4 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
   - 96 \\
  \bar 0\bar 0\bar 4 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {4.8}}\]
Now again remainder is 4 we will repeat the process above
\[12\mathop{\left){\vphantom{1\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
   - 96 \\
  \bar 0\bar 0\bar 4\bar 0 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
   - 96 \\
  \bar 0\bar 0\bar 4\bar 0 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {4.8}}\]
Now again we will add zero to the remainder
\[12\mathop{\left){\vphantom{1\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
   - 96 \\
  \bar 0\bar 0\bar 4\bar 0 \\
   - 036 \\
  \bar 0\bar 0\bar 0\bar 4 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  58 \\
   - 48 \\
  \bar 1\bar 0\bar 0 \\
   - 96 \\
  \bar 0\bar 0\bar 4\bar 0 \\
   - 036 \\
  \bar 0\bar 0\bar 0\bar 4 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {4.83}}\]
This is a repeated remainder. So we will stop here. This is our answer.
So, the correct answer is “4.83”.

Note: Note that we can solve this by simplifying the given division by considering it as a fraction. We will find the HCF and then divide them.
\[\dfrac{{58}}{{12}}\]
Their HCF is 2.
\[\dfrac{{58 \div 2}}{{12 \div 2}} = \dfrac{{29}}{6}\]
Now since 6 and 29 have no HCF except 1 we will directly perform the division.
\[\dfrac{{29}}{6} = 4.83\]
Both have the same answer, only the methods are different.