Evaluate
\frac{10}{3}\approx 3.333333333
Factor
\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)140}\\\end{array}
Use the 1^{st} digit 1 from dividend 140
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)140}\\\end{array}
Since 1 is less than 42, use the next digit 4 from dividend 140 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)140}\\\end{array}
Use the 2^{nd} digit 4 from dividend 140
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)140}\\\end{array}
Since 14 is less than 42, use the next digit 0 from dividend 140 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)140}\\\end{array}
Use the 3^{rd} digit 0 from dividend 140
\begin{array}{l}\phantom{42)}003\phantom{6}\\42\overline{)140}\\\phantom{42)}\underline{\phantom{}126\phantom{}}\\\phantom{42)9}14\\\end{array}
Find closest multiple of 42 to 140. We see that 3 \times 42 = 126 is the nearest. Now subtract 126 from 140 to get reminder 14. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }14
Since 14 is less than 42, stop the division. The reminder is 14. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}