Evaluate
\frac{40}{31}\approx 1.290322581
Factor
\frac{2 ^ {3} \cdot 5}{31} = 1\frac{9}{31} = 1.2903225806451613
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\begin{array}{l}\phantom{310)}\phantom{1}\\310\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{310)}0\phantom{2}\\310\overline{)400}\\\end{array}
Since 4 is less than 310, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{310)}0\phantom{3}\\310\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{310)}00\phantom{4}\\310\overline{)400}\\\end{array}
Since 40 is less than 310, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{310)}00\phantom{5}\\310\overline{)400}\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{310)}001\phantom{6}\\310\overline{)400}\\\phantom{310)}\underline{\phantom{}310\phantom{}}\\\phantom{310)9}90\\\end{array}
Find closest multiple of 310 to 400. We see that 1 \times 310 = 310 is the nearest. Now subtract 310 from 400 to get reminder 90. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }90
Since 90 is less than 310, stop the division. The reminder is 90. 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}