Evaluate
\frac{575}{42}\approx 13.69047619
Factor
\frac{5 ^ {2} \cdot 23}{2 \cdot 3 \cdot 7} = 13\frac{29}{42} = 13.69047619047619
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)575}\\\end{array}
Use the 1^{st} digit 5 from dividend 575
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)575}\\\end{array}
Since 5 is less than 42, use the next digit 7 from dividend 575 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)575}\\\end{array}
Use the 2^{nd} digit 7 from dividend 575
\begin{array}{l}\phantom{42)}01\phantom{4}\\42\overline{)575}\\\phantom{42)}\underline{\phantom{}42\phantom{9}}\\\phantom{42)}15\\\end{array}
Find closest multiple of 42 to 57. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 57 to get reminder 15. Add 1 to quotient.
\begin{array}{l}\phantom{42)}01\phantom{5}\\42\overline{)575}\\\phantom{42)}\underline{\phantom{}42\phantom{9}}\\\phantom{42)}155\\\end{array}
Use the 3^{rd} digit 5 from dividend 575
\begin{array}{l}\phantom{42)}013\phantom{6}\\42\overline{)575}\\\phantom{42)}\underline{\phantom{}42\phantom{9}}\\\phantom{42)}155\\\phantom{42)}\underline{\phantom{}126\phantom{}}\\\phantom{42)9}29\\\end{array}
Find closest multiple of 42 to 155. We see that 3 \times 42 = 126 is the nearest. Now subtract 126 from 155 to get reminder 29. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }29
Since 29 is less than 42, stop the division. The reminder is 29. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}