Evaluate
\frac{99}{50}=1.98
Factor
\frac{3 ^ {2} \cdot 11}{2 \cdot 5 ^ {2}} = 1\frac{49}{50} = 1.98
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\begin{array}{l}\phantom{42000)}\phantom{1}\\42000\overline{)83160}\\\end{array}
Use the 1^{st} digit 8 from dividend 83160
\begin{array}{l}\phantom{42000)}0\phantom{2}\\42000\overline{)83160}\\\end{array}
Since 8 is less than 42000, use the next digit 3 from dividend 83160 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}0\phantom{3}\\42000\overline{)83160}\\\end{array}
Use the 2^{nd} digit 3 from dividend 83160
\begin{array}{l}\phantom{42000)}00\phantom{4}\\42000\overline{)83160}\\\end{array}
Since 83 is less than 42000, use the next digit 1 from dividend 83160 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}00\phantom{5}\\42000\overline{)83160}\\\end{array}
Use the 3^{rd} digit 1 from dividend 83160
\begin{array}{l}\phantom{42000)}000\phantom{6}\\42000\overline{)83160}\\\end{array}
Since 831 is less than 42000, use the next digit 6 from dividend 83160 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}000\phantom{7}\\42000\overline{)83160}\\\end{array}
Use the 4^{th} digit 6 from dividend 83160
\begin{array}{l}\phantom{42000)}0000\phantom{8}\\42000\overline{)83160}\\\end{array}
Since 8316 is less than 42000, use the next digit 0 from dividend 83160 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}0000\phantom{9}\\42000\overline{)83160}\\\end{array}
Use the 5^{th} digit 0 from dividend 83160
\begin{array}{l}\phantom{42000)}00001\phantom{10}\\42000\overline{)83160}\\\phantom{42000)}\underline{\phantom{}42000\phantom{}}\\\phantom{42000)}41160\\\end{array}
Find closest multiple of 42000 to 83160. We see that 1 \times 42000 = 42000 is the nearest. Now subtract 42000 from 83160 to get reminder 41160. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }41160
Since 41160 is less than 42000, stop the division. The reminder is 41160. The topmost line 00001 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}