Evaluate
\frac{133}{101}\approx 1.316831683
Factor
\frac{7 \cdot 19}{101} = 1\frac{32}{101} = 1.316831683168317
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\begin{array}{l}\phantom{101)}\phantom{1}\\101\overline{)133}\\\end{array}
Use the 1^{st} digit 1 from dividend 133
\begin{array}{l}\phantom{101)}0\phantom{2}\\101\overline{)133}\\\end{array}
Since 1 is less than 101, use the next digit 3 from dividend 133 and add 0 to the quotient
\begin{array}{l}\phantom{101)}0\phantom{3}\\101\overline{)133}\\\end{array}
Use the 2^{nd} digit 3 from dividend 133
\begin{array}{l}\phantom{101)}00\phantom{4}\\101\overline{)133}\\\end{array}
Since 13 is less than 101, use the next digit 3 from dividend 133 and add 0 to the quotient
\begin{array}{l}\phantom{101)}00\phantom{5}\\101\overline{)133}\\\end{array}
Use the 3^{rd} digit 3 from dividend 133
\begin{array}{l}\phantom{101)}001\phantom{6}\\101\overline{)133}\\\phantom{101)}\underline{\phantom{}101\phantom{}}\\\phantom{101)9}32\\\end{array}
Find closest multiple of 101 to 133. We see that 1 \times 101 = 101 is the nearest. Now subtract 101 from 133 to get reminder 32. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }32
Since 32 is less than 101, stop the division. The reminder is 32. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
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{ 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}