Evaluate
\frac{41}{35}\approx 1.171428571
Factor
\frac{41}{5 \cdot 7} = 1\frac{6}{35} = 1.1714285714285715
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)82}\\\end{array}
Use the 1^{st} digit 8 from dividend 82
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)82}\\\end{array}
Since 8 is less than 70, use the next digit 2 from dividend 82 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)82}\\\end{array}
Use the 2^{nd} digit 2 from dividend 82
\begin{array}{l}\phantom{70)}01\phantom{4}\\70\overline{)82}\\\phantom{70)}\underline{\phantom{}70\phantom{}}\\\phantom{70)}12\\\end{array}
Find closest multiple of 70 to 82. We see that 1 \times 70 = 70 is the nearest. Now subtract 70 from 82 to get reminder 12. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }12
Since 12 is less than 70, stop the division. The reminder is 12. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}