Evaluate
\frac{345}{2}=172.5
Factor
\frac{3 \cdot 5 \cdot 23}{2} = 172\frac{1}{2} = 172.5
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)17250}\\\end{array}
Use the 1^{st} digit 1 from dividend 17250
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)17250}\\\end{array}
Since 1 is less than 100, use the next digit 7 from dividend 17250 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)17250}\\\end{array}
Use the 2^{nd} digit 7 from dividend 17250
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)17250}\\\end{array}
Since 17 is less than 100, use the next digit 2 from dividend 17250 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)17250}\\\end{array}
Use the 3^{rd} digit 2 from dividend 17250
\begin{array}{l}\phantom{100)}001\phantom{6}\\100\overline{)17250}\\\phantom{100)}\underline{\phantom{}100\phantom{99}}\\\phantom{100)9}72\\\end{array}
Find closest multiple of 100 to 172. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 172 to get reminder 72. Add 1 to quotient.
\begin{array}{l}\phantom{100)}001\phantom{7}\\100\overline{)17250}\\\phantom{100)}\underline{\phantom{}100\phantom{99}}\\\phantom{100)9}725\\\end{array}
Use the 4^{th} digit 5 from dividend 17250
\begin{array}{l}\phantom{100)}0017\phantom{8}\\100\overline{)17250}\\\phantom{100)}\underline{\phantom{}100\phantom{99}}\\\phantom{100)9}725\\\phantom{100)}\underline{\phantom{9}700\phantom{9}}\\\phantom{100)99}25\\\end{array}
Find closest multiple of 100 to 725. We see that 7 \times 100 = 700 is the nearest. Now subtract 700 from 725 to get reminder 25. Add 7 to quotient.
\begin{array}{l}\phantom{100)}0017\phantom{9}\\100\overline{)17250}\\\phantom{100)}\underline{\phantom{}100\phantom{99}}\\\phantom{100)9}725\\\phantom{100)}\underline{\phantom{9}700\phantom{9}}\\\phantom{100)99}250\\\end{array}
Use the 5^{th} digit 0 from dividend 17250
\begin{array}{l}\phantom{100)}00172\phantom{10}\\100\overline{)17250}\\\phantom{100)}\underline{\phantom{}100\phantom{99}}\\\phantom{100)9}725\\\phantom{100)}\underline{\phantom{9}700\phantom{9}}\\\phantom{100)99}250\\\phantom{100)}\underline{\phantom{99}200\phantom{}}\\\phantom{100)999}50\\\end{array}
Find closest multiple of 100 to 250. We see that 2 \times 100 = 200 is the nearest. Now subtract 200 from 250 to get reminder 50. Add 2 to quotient.
\text{Quotient: }172 \text{Reminder: }50
Since 50 is less than 100, stop the division. The reminder is 50. The topmost line 00172 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 172.
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}