Evaluate
\frac{33}{31}\approx 1.064516129
Factor
\frac{3 \cdot 11}{31} = 1\frac{2}{31} = 1.064516129032258
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\begin{array}{l}\phantom{155)}\phantom{1}\\155\overline{)165}\\\end{array}
Use the 1^{st} digit 1 from dividend 165
\begin{array}{l}\phantom{155)}0\phantom{2}\\155\overline{)165}\\\end{array}
Since 1 is less than 155, use the next digit 6 from dividend 165 and add 0 to the quotient
\begin{array}{l}\phantom{155)}0\phantom{3}\\155\overline{)165}\\\end{array}
Use the 2^{nd} digit 6 from dividend 165
\begin{array}{l}\phantom{155)}00\phantom{4}\\155\overline{)165}\\\end{array}
Since 16 is less than 155, use the next digit 5 from dividend 165 and add 0 to the quotient
\begin{array}{l}\phantom{155)}00\phantom{5}\\155\overline{)165}\\\end{array}
Use the 3^{rd} digit 5 from dividend 165
\begin{array}{l}\phantom{155)}001\phantom{6}\\155\overline{)165}\\\phantom{155)}\underline{\phantom{}155\phantom{}}\\\phantom{155)9}10\\\end{array}
Find closest multiple of 155 to 165. We see that 1 \times 155 = 155 is the nearest. Now subtract 155 from 165 to get reminder 10. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }10
Since 10 is less than 155, stop the division. The reminder is 10. 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}