Evaluate
189
Factor
3^{3}\times 7
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)8505}\\\end{array}
Use the 1^{st} digit 8 from dividend 8505
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)8505}\\\end{array}
Since 8 is less than 45, use the next digit 5 from dividend 8505 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)8505}\\\end{array}
Use the 2^{nd} digit 5 from dividend 8505
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)8505}\\\phantom{45)}\underline{\phantom{}45\phantom{99}}\\\phantom{45)}40\\\end{array}
Find closest multiple of 45 to 85. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 85 to get reminder 40. Add 1 to quotient.
\begin{array}{l}\phantom{45)}01\phantom{5}\\45\overline{)8505}\\\phantom{45)}\underline{\phantom{}45\phantom{99}}\\\phantom{45)}400\\\end{array}
Use the 3^{rd} digit 0 from dividend 8505
\begin{array}{l}\phantom{45)}018\phantom{6}\\45\overline{)8505}\\\phantom{45)}\underline{\phantom{}45\phantom{99}}\\\phantom{45)}400\\\phantom{45)}\underline{\phantom{}360\phantom{9}}\\\phantom{45)9}40\\\end{array}
Find closest multiple of 45 to 400. We see that 8 \times 45 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 8 to quotient.
\begin{array}{l}\phantom{45)}018\phantom{7}\\45\overline{)8505}\\\phantom{45)}\underline{\phantom{}45\phantom{99}}\\\phantom{45)}400\\\phantom{45)}\underline{\phantom{}360\phantom{9}}\\\phantom{45)9}405\\\end{array}
Use the 4^{th} digit 5 from dividend 8505
\begin{array}{l}\phantom{45)}0189\phantom{8}\\45\overline{)8505}\\\phantom{45)}\underline{\phantom{}45\phantom{99}}\\\phantom{45)}400\\\phantom{45)}\underline{\phantom{}360\phantom{9}}\\\phantom{45)9}405\\\phantom{45)}\underline{\phantom{9}405\phantom{}}\\\phantom{45)9999}0\\\end{array}
Find closest multiple of 45 to 405. We see that 9 \times 45 = 405 is the nearest. Now subtract 405 from 405 to get reminder 0. Add 9 to quotient.
\text{Quotient: }189 \text{Reminder: }0
Since 0 is less than 45, stop the division. The reminder is 0. The topmost line 0189 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 189.
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}