Evaluate
\frac{34}{7}\approx 4.857142857
Factor
\frac{2 \cdot 17}{7} = 4\frac{6}{7} = 4.857142857142857
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)170}\\\end{array}
Use the 1^{st} digit 1 from dividend 170
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)170}\\\end{array}
Since 1 is less than 35, use the next digit 7 from dividend 170 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)170}\\\end{array}
Use the 2^{nd} digit 7 from dividend 170
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)170}\\\end{array}
Since 17 is less than 35, use the next digit 0 from dividend 170 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)170}\\\end{array}
Use the 3^{rd} digit 0 from dividend 170
\begin{array}{l}\phantom{35)}004\phantom{6}\\35\overline{)170}\\\phantom{35)}\underline{\phantom{}140\phantom{}}\\\phantom{35)9}30\\\end{array}
Find closest multiple of 35 to 170. We see that 4 \times 35 = 140 is the nearest. Now subtract 140 from 170 to get reminder 30. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }30
Since 30 is less than 35, stop the division. The reminder is 30. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}