Evaluate
\frac{115}{3}\approx 38.333333333
Factor
\frac{5 \cdot 23}{3} = 38\frac{1}{3} = 38.333333333333336
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)575}\\\end{array}
Use the 1^{st} digit 5 from dividend 575
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)575}\\\end{array}
Since 5 is less than 15, use the next digit 7 from dividend 575 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)575}\\\end{array}
Use the 2^{nd} digit 7 from dividend 575
\begin{array}{l}\phantom{15)}03\phantom{4}\\15\overline{)575}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)}12\\\end{array}
Find closest multiple of 15 to 57. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 57 to get reminder 12. Add 3 to quotient.
\begin{array}{l}\phantom{15)}03\phantom{5}\\15\overline{)575}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)}125\\\end{array}
Use the 3^{rd} digit 5 from dividend 575
\begin{array}{l}\phantom{15)}038\phantom{6}\\15\overline{)575}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)}125\\\phantom{15)}\underline{\phantom{}120\phantom{}}\\\phantom{15)99}5\\\end{array}
Find closest multiple of 15 to 125. We see that 8 \times 15 = 120 is the nearest. Now subtract 120 from 125 to get reminder 5. Add 8 to quotient.
\text{Quotient: }38 \text{Reminder: }5
Since 5 is less than 15, stop the division. The reminder is 5. The topmost line 038 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 38.
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}