Evaluate
\frac{640}{91}\approx 7.032967033
Factor
\frac{2 ^ {7} \cdot 5}{7 \cdot 13} = 7\frac{3}{91} = 7.032967032967033
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\begin{array}{l}\phantom{91)}\phantom{1}\\91\overline{)640}\\\end{array}
Use the 1^{st} digit 6 from dividend 640
\begin{array}{l}\phantom{91)}0\phantom{2}\\91\overline{)640}\\\end{array}
Since 6 is less than 91, use the next digit 4 from dividend 640 and add 0 to the quotient
\begin{array}{l}\phantom{91)}0\phantom{3}\\91\overline{)640}\\\end{array}
Use the 2^{nd} digit 4 from dividend 640
\begin{array}{l}\phantom{91)}00\phantom{4}\\91\overline{)640}\\\end{array}
Since 64 is less than 91, use the next digit 0 from dividend 640 and add 0 to the quotient
\begin{array}{l}\phantom{91)}00\phantom{5}\\91\overline{)640}\\\end{array}
Use the 3^{rd} digit 0 from dividend 640
\begin{array}{l}\phantom{91)}007\phantom{6}\\91\overline{)640}\\\phantom{91)}\underline{\phantom{}637\phantom{}}\\\phantom{91)99}3\\\end{array}
Find closest multiple of 91 to 640. We see that 7 \times 91 = 637 is the nearest. Now subtract 637 from 640 to get reminder 3. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }3
Since 3 is less than 91, stop the division. The reminder is 3. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}