Evaluate
\frac{78}{35}\approx 2.228571429
Factor
\frac{2 \cdot 3 \cdot 13}{5 \cdot 7} = 2\frac{8}{35} = 2.2285714285714286
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)156}\\\end{array}
Use the 1^{st} digit 1 from dividend 156
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)156}\\\end{array}
Since 1 is less than 70, use the next digit 5 from dividend 156 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)156}\\\end{array}
Use the 2^{nd} digit 5 from dividend 156
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)156}\\\end{array}
Since 15 is less than 70, use the next digit 6 from dividend 156 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)156}\\\end{array}
Use the 3^{rd} digit 6 from dividend 156
\begin{array}{l}\phantom{70)}002\phantom{6}\\70\overline{)156}\\\phantom{70)}\underline{\phantom{}140\phantom{}}\\\phantom{70)9}16\\\end{array}
Find closest multiple of 70 to 156. We see that 2 \times 70 = 140 is the nearest. Now subtract 140 from 156 to get reminder 16. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }16
Since 16 is less than 70, stop the division. The reminder is 16. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}