Evaluate
\frac{115}{102}\approx 1.12745098
Factor
\frac{5 \cdot 23}{2 \cdot 3 \cdot 17} = 1\frac{13}{102} = 1.1274509803921569
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\begin{array}{l}\phantom{102)}\phantom{1}\\102\overline{)115}\\\end{array}
Use the 1^{st} digit 1 from dividend 115
\begin{array}{l}\phantom{102)}0\phantom{2}\\102\overline{)115}\\\end{array}
Since 1 is less than 102, use the next digit 1 from dividend 115 and add 0 to the quotient
\begin{array}{l}\phantom{102)}0\phantom{3}\\102\overline{)115}\\\end{array}
Use the 2^{nd} digit 1 from dividend 115
\begin{array}{l}\phantom{102)}00\phantom{4}\\102\overline{)115}\\\end{array}
Since 11 is less than 102, use the next digit 5 from dividend 115 and add 0 to the quotient
\begin{array}{l}\phantom{102)}00\phantom{5}\\102\overline{)115}\\\end{array}
Use the 3^{rd} digit 5 from dividend 115
\begin{array}{l}\phantom{102)}001\phantom{6}\\102\overline{)115}\\\phantom{102)}\underline{\phantom{}102\phantom{}}\\\phantom{102)9}13\\\end{array}
Find closest multiple of 102 to 115. We see that 1 \times 102 = 102 is the nearest. Now subtract 102 from 115 to get reminder 13. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }13
Since 13 is less than 102, stop the division. The reminder is 13. 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}