Evaluate
\frac{45}{7}\approx 6.428571429
Factor
\frac{3 ^ {2} \cdot 5}{7} = 6\frac{3}{7} = 6.428571428571429
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)450}\\\end{array}
Use the 1^{st} digit 4 from dividend 450
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)450}\\\end{array}
Since 4 is less than 70, use the next digit 5 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)450}\\\end{array}
Use the 2^{nd} digit 5 from dividend 450
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)450}\\\end{array}
Since 45 is less than 70, use the next digit 0 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)450}\\\end{array}
Use the 3^{rd} digit 0 from dividend 450
\begin{array}{l}\phantom{70)}006\phantom{6}\\70\overline{)450}\\\phantom{70)}\underline{\phantom{}420\phantom{}}\\\phantom{70)9}30\\\end{array}
Find closest multiple of 70 to 450. We see that 6 \times 70 = 420 is the nearest. Now subtract 420 from 450 to get reminder 30. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }30
Since 30 is less than 70, stop the division. The reminder is 30. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}