Evaluate
\frac{699}{197}\approx 3.54822335
Factor
\frac{3 \cdot 233}{197} = 3\frac{108}{197} = 3.548223350253807
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\begin{array}{l}\phantom{197)}\phantom{1}\\197\overline{)699}\\\end{array}
Use the 1^{st} digit 6 from dividend 699
\begin{array}{l}\phantom{197)}0\phantom{2}\\197\overline{)699}\\\end{array}
Since 6 is less than 197, use the next digit 9 from dividend 699 and add 0 to the quotient
\begin{array}{l}\phantom{197)}0\phantom{3}\\197\overline{)699}\\\end{array}
Use the 2^{nd} digit 9 from dividend 699
\begin{array}{l}\phantom{197)}00\phantom{4}\\197\overline{)699}\\\end{array}
Since 69 is less than 197, use the next digit 9 from dividend 699 and add 0 to the quotient
\begin{array}{l}\phantom{197)}00\phantom{5}\\197\overline{)699}\\\end{array}
Use the 3^{rd} digit 9 from dividend 699
\begin{array}{l}\phantom{197)}003\phantom{6}\\197\overline{)699}\\\phantom{197)}\underline{\phantom{}591\phantom{}}\\\phantom{197)}108\\\end{array}
Find closest multiple of 197 to 699. We see that 3 \times 197 = 591 is the nearest. Now subtract 591 from 699 to get reminder 108. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }108
Since 108 is less than 197, stop the division. The reminder is 108. 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}