Evaluate
\frac{141}{113}\approx 1.247787611
Factor
\frac{3 \cdot 47}{113} = 1\frac{28}{113} = 1.247787610619469
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\begin{array}{l}\phantom{113)}\phantom{1}\\113\overline{)141}\\\end{array}
Use the 1^{st} digit 1 from dividend 141
\begin{array}{l}\phantom{113)}0\phantom{2}\\113\overline{)141}\\\end{array}
Since 1 is less than 113, use the next digit 4 from dividend 141 and add 0 to the quotient
\begin{array}{l}\phantom{113)}0\phantom{3}\\113\overline{)141}\\\end{array}
Use the 2^{nd} digit 4 from dividend 141
\begin{array}{l}\phantom{113)}00\phantom{4}\\113\overline{)141}\\\end{array}
Since 14 is less than 113, use the next digit 1 from dividend 141 and add 0 to the quotient
\begin{array}{l}\phantom{113)}00\phantom{5}\\113\overline{)141}\\\end{array}
Use the 3^{rd} digit 1 from dividend 141
\begin{array}{l}\phantom{113)}001\phantom{6}\\113\overline{)141}\\\phantom{113)}\underline{\phantom{}113\phantom{}}\\\phantom{113)9}28\\\end{array}
Find closest multiple of 113 to 141. We see that 1 \times 113 = 113 is the nearest. Now subtract 113 from 141 to get reminder 28. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }28
Since 28 is less than 113, stop the division. The reminder is 28. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}