Evaluate
\frac{40}{7}\approx 5.714285714
Factor
\frac{2 ^ {3} \cdot 5}{7} = 5\frac{5}{7} = 5.714285714285714
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\begin{array}{l}\phantom{28)}\phantom{1}\\28\overline{)160}\\\end{array}
Use the 1^{st} digit 1 from dividend 160
\begin{array}{l}\phantom{28)}0\phantom{2}\\28\overline{)160}\\\end{array}
Since 1 is less than 28, use the next digit 6 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{28)}0\phantom{3}\\28\overline{)160}\\\end{array}
Use the 2^{nd} digit 6 from dividend 160
\begin{array}{l}\phantom{28)}00\phantom{4}\\28\overline{)160}\\\end{array}
Since 16 is less than 28, use the next digit 0 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{28)}00\phantom{5}\\28\overline{)160}\\\end{array}
Use the 3^{rd} digit 0 from dividend 160
\begin{array}{l}\phantom{28)}005\phantom{6}\\28\overline{)160}\\\phantom{28)}\underline{\phantom{}140\phantom{}}\\\phantom{28)9}20\\\end{array}
Find closest multiple of 28 to 160. We see that 5 \times 28 = 140 is the nearest. Now subtract 140 from 160 to get reminder 20. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }20
Since 20 is less than 28, stop the division. The reminder is 20. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}