Evaluate
\frac{2309}{98}\approx 23.56122449
Factor
\frac{2309}{2 \cdot 7 ^ {2}} = 23\frac{55}{98} = 23.56122448979592
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\begin{array}{l}\phantom{98)}\phantom{1}\\98\overline{)2309}\\\end{array}
Use the 1^{st} digit 2 from dividend 2309
\begin{array}{l}\phantom{98)}0\phantom{2}\\98\overline{)2309}\\\end{array}
Since 2 is less than 98, use the next digit 3 from dividend 2309 and add 0 to the quotient
\begin{array}{l}\phantom{98)}0\phantom{3}\\98\overline{)2309}\\\end{array}
Use the 2^{nd} digit 3 from dividend 2309
\begin{array}{l}\phantom{98)}00\phantom{4}\\98\overline{)2309}\\\end{array}
Since 23 is less than 98, use the next digit 0 from dividend 2309 and add 0 to the quotient
\begin{array}{l}\phantom{98)}00\phantom{5}\\98\overline{)2309}\\\end{array}
Use the 3^{rd} digit 0 from dividend 2309
\begin{array}{l}\phantom{98)}002\phantom{6}\\98\overline{)2309}\\\phantom{98)}\underline{\phantom{}196\phantom{9}}\\\phantom{98)9}34\\\end{array}
Find closest multiple of 98 to 230. We see that 2 \times 98 = 196 is the nearest. Now subtract 196 from 230 to get reminder 34. Add 2 to quotient.
\begin{array}{l}\phantom{98)}002\phantom{7}\\98\overline{)2309}\\\phantom{98)}\underline{\phantom{}196\phantom{9}}\\\phantom{98)9}349\\\end{array}
Use the 4^{th} digit 9 from dividend 2309
\begin{array}{l}\phantom{98)}0023\phantom{8}\\98\overline{)2309}\\\phantom{98)}\underline{\phantom{}196\phantom{9}}\\\phantom{98)9}349\\\phantom{98)}\underline{\phantom{9}294\phantom{}}\\\phantom{98)99}55\\\end{array}
Find closest multiple of 98 to 349. We see that 3 \times 98 = 294 is the nearest. Now subtract 294 from 349 to get reminder 55. Add 3 to quotient.
\text{Quotient: }23 \text{Reminder: }55
Since 55 is less than 98, stop the division. The reminder is 55. The topmost line 0023 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 23.
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}