Evaluate
\frac{4705}{38}\approx 123.815789474
Factor
\frac{5 \cdot 941}{2 \cdot 19} = 123\frac{31}{38} = 123.8157894736842
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\begin{array}{l}\phantom{38)}\phantom{1}\\38\overline{)4705}\\\end{array}
Use the 1^{st} digit 4 from dividend 4705
\begin{array}{l}\phantom{38)}0\phantom{2}\\38\overline{)4705}\\\end{array}
Since 4 is less than 38, use the next digit 7 from dividend 4705 and add 0 to the quotient
\begin{array}{l}\phantom{38)}0\phantom{3}\\38\overline{)4705}\\\end{array}
Use the 2^{nd} digit 7 from dividend 4705
\begin{array}{l}\phantom{38)}01\phantom{4}\\38\overline{)4705}\\\phantom{38)}\underline{\phantom{}38\phantom{99}}\\\phantom{38)9}9\\\end{array}
Find closest multiple of 38 to 47. We see that 1 \times 38 = 38 is the nearest. Now subtract 38 from 47 to get reminder 9. Add 1 to quotient.
\begin{array}{l}\phantom{38)}01\phantom{5}\\38\overline{)4705}\\\phantom{38)}\underline{\phantom{}38\phantom{99}}\\\phantom{38)9}90\\\end{array}
Use the 3^{rd} digit 0 from dividend 4705
\begin{array}{l}\phantom{38)}012\phantom{6}\\38\overline{)4705}\\\phantom{38)}\underline{\phantom{}38\phantom{99}}\\\phantom{38)9}90\\\phantom{38)}\underline{\phantom{9}76\phantom{9}}\\\phantom{38)9}14\\\end{array}
Find closest multiple of 38 to 90. We see that 2 \times 38 = 76 is the nearest. Now subtract 76 from 90 to get reminder 14. Add 2 to quotient.
\begin{array}{l}\phantom{38)}012\phantom{7}\\38\overline{)4705}\\\phantom{38)}\underline{\phantom{}38\phantom{99}}\\\phantom{38)9}90\\\phantom{38)}\underline{\phantom{9}76\phantom{9}}\\\phantom{38)9}145\\\end{array}
Use the 4^{th} digit 5 from dividend 4705
\begin{array}{l}\phantom{38)}0123\phantom{8}\\38\overline{)4705}\\\phantom{38)}\underline{\phantom{}38\phantom{99}}\\\phantom{38)9}90\\\phantom{38)}\underline{\phantom{9}76\phantom{9}}\\\phantom{38)9}145\\\phantom{38)}\underline{\phantom{9}114\phantom{}}\\\phantom{38)99}31\\\end{array}
Find closest multiple of 38 to 145. We see that 3 \times 38 = 114 is the nearest. Now subtract 114 from 145 to get reminder 31. Add 3 to quotient.
\text{Quotient: }123 \text{Reminder: }31
Since 31 is less than 38, stop the division. The reminder is 31. The topmost line 0123 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 123.
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}