Evaluate
\frac{107}{23}\approx 4.652173913
Factor
\frac{107}{23} = 4\frac{15}{23} = 4.6521739130434785
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)107}\\\end{array}
Use the 1^{st} digit 1 from dividend 107
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)107}\\\end{array}
Since 1 is less than 23, use the next digit 0 from dividend 107 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)107}\\\end{array}
Use the 2^{nd} digit 0 from dividend 107
\begin{array}{l}\phantom{23)}00\phantom{4}\\23\overline{)107}\\\end{array}
Since 10 is less than 23, use the next digit 7 from dividend 107 and add 0 to the quotient
\begin{array}{l}\phantom{23)}00\phantom{5}\\23\overline{)107}\\\end{array}
Use the 3^{rd} digit 7 from dividend 107
\begin{array}{l}\phantom{23)}004\phantom{6}\\23\overline{)107}\\\phantom{23)}\underline{\phantom{9}92\phantom{}}\\\phantom{23)9}15\\\end{array}
Find closest multiple of 23 to 107. We see that 4 \times 23 = 92 is the nearest. Now subtract 92 from 107 to get reminder 15. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }15
Since 15 is less than 23, stop the division. The reminder is 15. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}