Evaluate
\frac{107}{60}\approx 1.783333333
Factor
\frac{107}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{47}{60} = 1.7833333333333334
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)107}\\\end{array}
Use the 1^{st} digit 1 from dividend 107
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)107}\\\end{array}
Since 1 is less than 60, use the next digit 0 from dividend 107 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)107}\\\end{array}
Use the 2^{nd} digit 0 from dividend 107
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)107}\\\end{array}
Since 10 is less than 60, use the next digit 7 from dividend 107 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)107}\\\end{array}
Use the 3^{rd} digit 7 from dividend 107
\begin{array}{l}\phantom{60)}001\phantom{6}\\60\overline{)107}\\\phantom{60)}\underline{\phantom{9}60\phantom{}}\\\phantom{60)9}47\\\end{array}
Find closest multiple of 60 to 107. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 107 to get reminder 47. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }47
Since 47 is less than 60, stop the division. The reminder is 47. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}