Evaluate
\frac{15}{7}\approx 2.142857143
Factor
\frac{3 \cdot 5}{7} = 2\frac{1}{7} = 2.142857142857143
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\begin{array}{l}\phantom{28)}\phantom{1}\\28\overline{)60}\\\end{array}
Use the 1^{st} digit 6 from dividend 60
\begin{array}{l}\phantom{28)}0\phantom{2}\\28\overline{)60}\\\end{array}
Since 6 is less than 28, use the next digit 0 from dividend 60 and add 0 to the quotient
\begin{array}{l}\phantom{28)}0\phantom{3}\\28\overline{)60}\\\end{array}
Use the 2^{nd} digit 0 from dividend 60
\begin{array}{l}\phantom{28)}02\phantom{4}\\28\overline{)60}\\\phantom{28)}\underline{\phantom{}56\phantom{}}\\\phantom{28)9}4\\\end{array}
Find closest multiple of 28 to 60. We see that 2 \times 28 = 56 is the nearest. Now subtract 56 from 60 to get reminder 4. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }4
Since 4 is less than 28, stop the division. The reminder is 4. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}