Evaluate
\frac{107}{13}\approx 8.230769231
Factor
\frac{107}{13} = 8\frac{3}{13} = 8.23076923076923
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)107}\\\end{array}
Use the 1^{st} digit 1 from dividend 107
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)107}\\\end{array}
Since 1 is less than 13, use the next digit 0 from dividend 107 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)107}\\\end{array}
Use the 2^{nd} digit 0 from dividend 107
\begin{array}{l}\phantom{13)}00\phantom{4}\\13\overline{)107}\\\end{array}
Since 10 is less than 13, use the next digit 7 from dividend 107 and add 0 to the quotient
\begin{array}{l}\phantom{13)}00\phantom{5}\\13\overline{)107}\\\end{array}
Use the 3^{rd} digit 7 from dividend 107
\begin{array}{l}\phantom{13)}008\phantom{6}\\13\overline{)107}\\\phantom{13)}\underline{\phantom{}104\phantom{}}\\\phantom{13)99}3\\\end{array}
Find closest multiple of 13 to 107. We see that 8 \times 13 = 104 is the nearest. Now subtract 104 from 107 to get reminder 3. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }3
Since 3 is less than 13, stop the division. The reminder is 3. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
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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}