Evaluate
\frac{263}{15}\approx 17.533333333
Factor
\frac{263}{3 \cdot 5} = 17\frac{8}{15} = 17.533333333333335
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)789}\\\end{array}
Use the 1^{st} digit 7 from dividend 789
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)789}\\\end{array}
Since 7 is less than 45, use the next digit 8 from dividend 789 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)789}\\\end{array}
Use the 2^{nd} digit 8 from dividend 789
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)789}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)}33\\\end{array}
Find closest multiple of 45 to 78. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 78 to get reminder 33. Add 1 to quotient.
\begin{array}{l}\phantom{45)}01\phantom{5}\\45\overline{)789}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)}339\\\end{array}
Use the 3^{rd} digit 9 from dividend 789
\begin{array}{l}\phantom{45)}017\phantom{6}\\45\overline{)789}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)}339\\\phantom{45)}\underline{\phantom{}315\phantom{}}\\\phantom{45)9}24\\\end{array}
Find closest multiple of 45 to 339. We see that 7 \times 45 = 315 is the nearest. Now subtract 315 from 339 to get reminder 24. Add 7 to quotient.
\text{Quotient: }17 \text{Reminder: }24
Since 24 is less than 45, stop the division. The reminder is 24. The topmost line 017 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 17.
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}