Evaluate
\frac{40}{7}\approx 5.714285714
Factor
\frac{2 ^ {3} \cdot 5}{7} = 5\frac{5}{7} = 5.714285714285714
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)400}\\\end{array}
Since 4 is less than 70, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)400}\\\end{array}
Since 40 is less than 70, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)400}\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{70)}005\phantom{6}\\70\overline{)400}\\\phantom{70)}\underline{\phantom{}350\phantom{}}\\\phantom{70)9}50\\\end{array}
Find closest multiple of 70 to 400. We see that 5 \times 70 = 350 is the nearest. Now subtract 350 from 400 to get reminder 50. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }50
Since 50 is less than 70, stop the division. The reminder is 50. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}