Evaluate
\frac{142}{3}\approx 47.333333333
Factor
\frac{2 \cdot 71}{3} = 47\frac{1}{3} = 47.333333333333336
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)568}\\\end{array}
Use the 1^{st} digit 5 from dividend 568
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)568}\\\end{array}
Since 5 is less than 12, use the next digit 6 from dividend 568 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)568}\\\end{array}
Use the 2^{nd} digit 6 from dividend 568
\begin{array}{l}\phantom{12)}04\phantom{4}\\12\overline{)568}\\\phantom{12)}\underline{\phantom{}48\phantom{9}}\\\phantom{12)9}8\\\end{array}
Find closest multiple of 12 to 56. We see that 4 \times 12 = 48 is the nearest. Now subtract 48 from 56 to get reminder 8. Add 4 to quotient.
\begin{array}{l}\phantom{12)}04\phantom{5}\\12\overline{)568}\\\phantom{12)}\underline{\phantom{}48\phantom{9}}\\\phantom{12)9}88\\\end{array}
Use the 3^{rd} digit 8 from dividend 568
\begin{array}{l}\phantom{12)}047\phantom{6}\\12\overline{)568}\\\phantom{12)}\underline{\phantom{}48\phantom{9}}\\\phantom{12)9}88\\\phantom{12)}\underline{\phantom{9}84\phantom{}}\\\phantom{12)99}4\\\end{array}
Find closest multiple of 12 to 88. We see that 7 \times 12 = 84 is the nearest. Now subtract 84 from 88 to get reminder 4. Add 7 to quotient.
\text{Quotient: }47 \text{Reminder: }4
Since 4 is less than 12, stop the division. The reminder is 4. The topmost line 047 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 47.
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}