Evaluate
\frac{189}{107}\approx 1.76635514
Factor
\frac{3 ^ {3} \cdot 7}{107} = 1\frac{82}{107} = 1.766355140186916
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\begin{array}{l}\phantom{107)}\phantom{1}\\107\overline{)189}\\\end{array}
Use the 1^{st} digit 1 from dividend 189
\begin{array}{l}\phantom{107)}0\phantom{2}\\107\overline{)189}\\\end{array}
Since 1 is less than 107, use the next digit 8 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{107)}0\phantom{3}\\107\overline{)189}\\\end{array}
Use the 2^{nd} digit 8 from dividend 189
\begin{array}{l}\phantom{107)}00\phantom{4}\\107\overline{)189}\\\end{array}
Since 18 is less than 107, use the next digit 9 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{107)}00\phantom{5}\\107\overline{)189}\\\end{array}
Use the 3^{rd} digit 9 from dividend 189
\begin{array}{l}\phantom{107)}001\phantom{6}\\107\overline{)189}\\\phantom{107)}\underline{\phantom{}107\phantom{}}\\\phantom{107)9}82\\\end{array}
Find closest multiple of 107 to 189. We see that 1 \times 107 = 107 is the nearest. Now subtract 107 from 189 to get reminder 82. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }82
Since 82 is less than 107, stop the division. The reminder is 82. 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}