Evaluate
\frac{4975}{3}\approx 1658.333333333
Factor
\frac{5 ^ {2} \cdot 199}{3} = 1658\frac{1}{3} = 1658.3333333333333
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)19900}\\\end{array}
Use the 1^{st} digit 1 from dividend 19900
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)19900}\\\end{array}
Since 1 is less than 12, use the next digit 9 from dividend 19900 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)19900}\\\end{array}
Use the 2^{nd} digit 9 from dividend 19900
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}7\\\end{array}
Find closest multiple of 12 to 19. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 19 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{12)}01\phantom{5}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}79\\\end{array}
Use the 3^{rd} digit 9 from dividend 19900
\begin{array}{l}\phantom{12)}016\phantom{6}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}79\\\phantom{12)}\underline{\phantom{9}72\phantom{99}}\\\phantom{12)99}7\\\end{array}
Find closest multiple of 12 to 79. We see that 6 \times 12 = 72 is the nearest. Now subtract 72 from 79 to get reminder 7. Add 6 to quotient.
\begin{array}{l}\phantom{12)}016\phantom{7}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}79\\\phantom{12)}\underline{\phantom{9}72\phantom{99}}\\\phantom{12)99}70\\\end{array}
Use the 4^{th} digit 0 from dividend 19900
\begin{array}{l}\phantom{12)}0165\phantom{8}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}79\\\phantom{12)}\underline{\phantom{9}72\phantom{99}}\\\phantom{12)99}70\\\phantom{12)}\underline{\phantom{99}60\phantom{9}}\\\phantom{12)99}10\\\end{array}
Find closest multiple of 12 to 70. We see that 5 \times 12 = 60 is the nearest. Now subtract 60 from 70 to get reminder 10. Add 5 to quotient.
\begin{array}{l}\phantom{12)}0165\phantom{9}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}79\\\phantom{12)}\underline{\phantom{9}72\phantom{99}}\\\phantom{12)99}70\\\phantom{12)}\underline{\phantom{99}60\phantom{9}}\\\phantom{12)99}100\\\end{array}
Use the 5^{th} digit 0 from dividend 19900
\begin{array}{l}\phantom{12)}01658\phantom{10}\\12\overline{)19900}\\\phantom{12)}\underline{\phantom{}12\phantom{999}}\\\phantom{12)9}79\\\phantom{12)}\underline{\phantom{9}72\phantom{99}}\\\phantom{12)99}70\\\phantom{12)}\underline{\phantom{99}60\phantom{9}}\\\phantom{12)99}100\\\phantom{12)}\underline{\phantom{999}96\phantom{}}\\\phantom{12)9999}4\\\end{array}
Find closest multiple of 12 to 100. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 100 to get reminder 4. Add 8 to quotient.
\text{Quotient: }1658 \text{Reminder: }4
Since 4 is less than 12, stop the division. The reminder is 4. The topmost line 01658 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1658.
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}