Evaluate
\frac{445}{39}\approx 11.41025641
Factor
\frac{5 \cdot 89}{3 \cdot 13} = 11\frac{16}{39} = 11.41025641025641
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\begin{array}{l}\phantom{78)}\phantom{1}\\78\overline{)890}\\\end{array}
Use the 1^{st} digit 8 from dividend 890
\begin{array}{l}\phantom{78)}0\phantom{2}\\78\overline{)890}\\\end{array}
Since 8 is less than 78, use the next digit 9 from dividend 890 and add 0 to the quotient
\begin{array}{l}\phantom{78)}0\phantom{3}\\78\overline{)890}\\\end{array}
Use the 2^{nd} digit 9 from dividend 890
\begin{array}{l}\phantom{78)}01\phantom{4}\\78\overline{)890}\\\phantom{78)}\underline{\phantom{}78\phantom{9}}\\\phantom{78)}11\\\end{array}
Find closest multiple of 78 to 89. We see that 1 \times 78 = 78 is the nearest. Now subtract 78 from 89 to get reminder 11. Add 1 to quotient.
\begin{array}{l}\phantom{78)}01\phantom{5}\\78\overline{)890}\\\phantom{78)}\underline{\phantom{}78\phantom{9}}\\\phantom{78)}110\\\end{array}
Use the 3^{rd} digit 0 from dividend 890
\begin{array}{l}\phantom{78)}011\phantom{6}\\78\overline{)890}\\\phantom{78)}\underline{\phantom{}78\phantom{9}}\\\phantom{78)}110\\\phantom{78)}\underline{\phantom{9}78\phantom{}}\\\phantom{78)9}32\\\end{array}
Find closest multiple of 78 to 110. We see that 1 \times 78 = 78 is the nearest. Now subtract 78 from 110 to get reminder 32. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }32
Since 32 is less than 78, stop the division. The reminder is 32. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}