Evaluate
\frac{345}{98}\approx 3.520408163
Factor
\frac{3 \cdot 5 \cdot 23}{2 \cdot 7 ^ {2}} = 3\frac{51}{98} = 3.520408163265306
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\begin{array}{l}\phantom{98)}\phantom{1}\\98\overline{)345}\\\end{array}
Use the 1^{st} digit 3 from dividend 345
\begin{array}{l}\phantom{98)}0\phantom{2}\\98\overline{)345}\\\end{array}
Since 3 is less than 98, use the next digit 4 from dividend 345 and add 0 to the quotient
\begin{array}{l}\phantom{98)}0\phantom{3}\\98\overline{)345}\\\end{array}
Use the 2^{nd} digit 4 from dividend 345
\begin{array}{l}\phantom{98)}00\phantom{4}\\98\overline{)345}\\\end{array}
Since 34 is less than 98, use the next digit 5 from dividend 345 and add 0 to the quotient
\begin{array}{l}\phantom{98)}00\phantom{5}\\98\overline{)345}\\\end{array}
Use the 3^{rd} digit 5 from dividend 345
\begin{array}{l}\phantom{98)}003\phantom{6}\\98\overline{)345}\\\phantom{98)}\underline{\phantom{}294\phantom{}}\\\phantom{98)9}51\\\end{array}
Find closest multiple of 98 to 345. We see that 3 \times 98 = 294 is the nearest. Now subtract 294 from 345 to get reminder 51. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }51
Since 51 is less than 98, stop the division. The reminder is 51. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}