Evaluate
\frac{11}{2}=5.5
Factor
\frac{11}{2} = 5\frac{1}{2} = 5.5
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)385}\\\end{array}
Use the 1^{st} digit 3 from dividend 385
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)385}\\\end{array}
Since 3 is less than 70, use the next digit 8 from dividend 385 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)385}\\\end{array}
Use the 2^{nd} digit 8 from dividend 385
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)385}\\\end{array}
Since 38 is less than 70, use the next digit 5 from dividend 385 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)385}\\\end{array}
Use the 3^{rd} digit 5 from dividend 385
\begin{array}{l}\phantom{70)}005\phantom{6}\\70\overline{)385}\\\phantom{70)}\underline{\phantom{}350\phantom{}}\\\phantom{70)9}35\\\end{array}
Find closest multiple of 70 to 385. We see that 5 \times 70 = 350 is the nearest. Now subtract 350 from 385 to get reminder 35. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }35
Since 35 is less than 70, stop the division. The reminder is 35. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}