Evaluate
\frac{398}{49}\approx 8.12244898
Factor
\frac{2 \cdot 199}{7 ^ {2}} = 8\frac{6}{49} = 8.122448979591837
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\begin{array}{l}\phantom{49)}\phantom{1}\\49\overline{)398}\\\end{array}
Use the 1^{st} digit 3 from dividend 398
\begin{array}{l}\phantom{49)}0\phantom{2}\\49\overline{)398}\\\end{array}
Since 3 is less than 49, use the next digit 9 from dividend 398 and add 0 to the quotient
\begin{array}{l}\phantom{49)}0\phantom{3}\\49\overline{)398}\\\end{array}
Use the 2^{nd} digit 9 from dividend 398
\begin{array}{l}\phantom{49)}00\phantom{4}\\49\overline{)398}\\\end{array}
Since 39 is less than 49, use the next digit 8 from dividend 398 and add 0 to the quotient
\begin{array}{l}\phantom{49)}00\phantom{5}\\49\overline{)398}\\\end{array}
Use the 3^{rd} digit 8 from dividend 398
\begin{array}{l}\phantom{49)}008\phantom{6}\\49\overline{)398}\\\phantom{49)}\underline{\phantom{}392\phantom{}}\\\phantom{49)99}6\\\end{array}
Find closest multiple of 49 to 398. We see that 8 \times 49 = 392 is the nearest. Now subtract 392 from 398 to get reminder 6. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }6
Since 6 is less than 49, stop the division. The reminder is 6. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}