Evaluate
\frac{80}{7}\approx 11.428571429
Factor
\frac{2 ^ {4} \cdot 5}{7} = 11\frac{3}{7} = 11.428571428571429
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\begin{array}{l}\phantom{28)}\phantom{1}\\28\overline{)320}\\\end{array}
Use the 1^{st} digit 3 from dividend 320
\begin{array}{l}\phantom{28)}0\phantom{2}\\28\overline{)320}\\\end{array}
Since 3 is less than 28, use the next digit 2 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{28)}0\phantom{3}\\28\overline{)320}\\\end{array}
Use the 2^{nd} digit 2 from dividend 320
\begin{array}{l}\phantom{28)}01\phantom{4}\\28\overline{)320}\\\phantom{28)}\underline{\phantom{}28\phantom{9}}\\\phantom{28)9}4\\\end{array}
Find closest multiple of 28 to 32. We see that 1 \times 28 = 28 is the nearest. Now subtract 28 from 32 to get reminder 4. Add 1 to quotient.
\begin{array}{l}\phantom{28)}01\phantom{5}\\28\overline{)320}\\\phantom{28)}\underline{\phantom{}28\phantom{9}}\\\phantom{28)9}40\\\end{array}
Use the 3^{rd} digit 0 from dividend 320
\begin{array}{l}\phantom{28)}011\phantom{6}\\28\overline{)320}\\\phantom{28)}\underline{\phantom{}28\phantom{9}}\\\phantom{28)9}40\\\phantom{28)}\underline{\phantom{9}28\phantom{}}\\\phantom{28)9}12\\\end{array}
Find closest multiple of 28 to 40. We see that 1 \times 28 = 28 is the nearest. Now subtract 28 from 40 to get reminder 12. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }12
Since 12 is less than 28, stop the division. The reminder is 12. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}