Evaluate
\frac{89}{25}=3.56
Factor
\frac{89}{5 ^ {2}} = 3\frac{14}{25} = 3.56
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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)445}\\\end{array}
Use the 1^{st} digit 4 from dividend 445
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)445}\\\end{array}
Since 4 is less than 125, use the next digit 4 from dividend 445 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)445}\\\end{array}
Use the 2^{nd} digit 4 from dividend 445
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)445}\\\end{array}
Since 44 is less than 125, use the next digit 5 from dividend 445 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)445}\\\end{array}
Use the 3^{rd} digit 5 from dividend 445
\begin{array}{l}\phantom{125)}003\phantom{6}\\125\overline{)445}\\\phantom{125)}\underline{\phantom{}375\phantom{}}\\\phantom{125)9}70\\\end{array}
Find closest multiple of 125 to 445. We see that 3 \times 125 = 375 is the nearest. Now subtract 375 from 445 to get reminder 70. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }70
Since 70 is less than 125, stop the division. The reminder is 70. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}