Evaluate
\frac{37}{7}\approx 5.285714286
Factor
\frac{37}{7} = 5\frac{2}{7} = 5.285714285714286
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)111}\\\end{array}
Use the 1^{st} digit 1 from dividend 111
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)111}\\\end{array}
Since 1 is less than 21, use the next digit 1 from dividend 111 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)111}\\\end{array}
Use the 2^{nd} digit 1 from dividend 111
\begin{array}{l}\phantom{21)}00\phantom{4}\\21\overline{)111}\\\end{array}
Since 11 is less than 21, use the next digit 1 from dividend 111 and add 0 to the quotient
\begin{array}{l}\phantom{21)}00\phantom{5}\\21\overline{)111}\\\end{array}
Use the 3^{rd} digit 1 from dividend 111
\begin{array}{l}\phantom{21)}005\phantom{6}\\21\overline{)111}\\\phantom{21)}\underline{\phantom{}105\phantom{}}\\\phantom{21)99}6\\\end{array}
Find closest multiple of 21 to 111. We see that 5 \times 21 = 105 is the nearest. Now subtract 105 from 111 to get reminder 6. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }6
Since 6 is less than 21, stop the division. The reminder is 6. 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}