Evaluate
\frac{89}{46}\approx 1.934782609
Factor
\frac{89}{2 \cdot 23} = 1\frac{43}{46} = 1.934782608695652
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\begin{array}{l}\phantom{138)}\phantom{1}\\138\overline{)267}\\\end{array}
Use the 1^{st} digit 2 from dividend 267
\begin{array}{l}\phantom{138)}0\phantom{2}\\138\overline{)267}\\\end{array}
Since 2 is less than 138, use the next digit 6 from dividend 267 and add 0 to the quotient
\begin{array}{l}\phantom{138)}0\phantom{3}\\138\overline{)267}\\\end{array}
Use the 2^{nd} digit 6 from dividend 267
\begin{array}{l}\phantom{138)}00\phantom{4}\\138\overline{)267}\\\end{array}
Since 26 is less than 138, use the next digit 7 from dividend 267 and add 0 to the quotient
\begin{array}{l}\phantom{138)}00\phantom{5}\\138\overline{)267}\\\end{array}
Use the 3^{rd} digit 7 from dividend 267
\begin{array}{l}\phantom{138)}001\phantom{6}\\138\overline{)267}\\\phantom{138)}\underline{\phantom{}138\phantom{}}\\\phantom{138)}129\\\end{array}
Find closest multiple of 138 to 267. We see that 1 \times 138 = 138 is the nearest. Now subtract 138 from 267 to get reminder 129. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }129
Since 129 is less than 138, stop the division. The reminder is 129. 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}