Evaluate
\frac{680}{9}\approx 75.555555556
Factor
\frac{2 ^ {3} \cdot 5 \cdot 17}{3 ^ {2}} = 75\frac{5}{9} = 75.55555555555556
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)1360}\\\end{array}
Use the 1^{st} digit 1 from dividend 1360
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)1360}\\\end{array}
Since 1 is less than 18, use the next digit 3 from dividend 1360 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)1360}\\\end{array}
Use the 2^{nd} digit 3 from dividend 1360
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)1360}\\\end{array}
Since 13 is less than 18, use the next digit 6 from dividend 1360 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)1360}\\\end{array}
Use the 3^{rd} digit 6 from dividend 1360
\begin{array}{l}\phantom{18)}007\phantom{6}\\18\overline{)1360}\\\phantom{18)}\underline{\phantom{}126\phantom{9}}\\\phantom{18)9}10\\\end{array}
Find closest multiple of 18 to 136. We see that 7 \times 18 = 126 is the nearest. Now subtract 126 from 136 to get reminder 10. Add 7 to quotient.
\begin{array}{l}\phantom{18)}007\phantom{7}\\18\overline{)1360}\\\phantom{18)}\underline{\phantom{}126\phantom{9}}\\\phantom{18)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 1360
\begin{array}{l}\phantom{18)}0075\phantom{8}\\18\overline{)1360}\\\phantom{18)}\underline{\phantom{}126\phantom{9}}\\\phantom{18)9}100\\\phantom{18)}\underline{\phantom{99}90\phantom{}}\\\phantom{18)99}10\\\end{array}
Find closest multiple of 18 to 100. We see that 5 \times 18 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 5 to quotient.
\text{Quotient: }75 \text{Reminder: }10
Since 10 is less than 18, stop the division. The reminder is 10. The topmost line 0075 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 75.
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}