Evaluate
\frac{115}{89}\approx 1.292134831
Factor
\frac{5 \cdot 23}{89} = 1\frac{26}{89} = 1.2921348314606742
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\begin{array}{l}\phantom{267)}\phantom{1}\\267\overline{)345}\\\end{array}
Use the 1^{st} digit 3 from dividend 345
\begin{array}{l}\phantom{267)}0\phantom{2}\\267\overline{)345}\\\end{array}
Since 3 is less than 267, use the next digit 4 from dividend 345 and add 0 to the quotient
\begin{array}{l}\phantom{267)}0\phantom{3}\\267\overline{)345}\\\end{array}
Use the 2^{nd} digit 4 from dividend 345
\begin{array}{l}\phantom{267)}00\phantom{4}\\267\overline{)345}\\\end{array}
Since 34 is less than 267, use the next digit 5 from dividend 345 and add 0 to the quotient
\begin{array}{l}\phantom{267)}00\phantom{5}\\267\overline{)345}\\\end{array}
Use the 3^{rd} digit 5 from dividend 345
\begin{array}{l}\phantom{267)}001\phantom{6}\\267\overline{)345}\\\phantom{267)}\underline{\phantom{}267\phantom{}}\\\phantom{267)9}78\\\end{array}
Find closest multiple of 267 to 345. We see that 1 \times 267 = 267 is the nearest. Now subtract 267 from 345 to get reminder 78. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }78
Since 78 is less than 267, stop the division. The reminder is 78. 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}