Evaluate
\frac{35}{6}\approx 5.833333333
Factor
\frac{5 \cdot 7}{2 \cdot 3} = 5\frac{5}{6} = 5.833333333333333
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\begin{array}{l}\phantom{48)}\phantom{1}\\48\overline{)280}\\\end{array}
Use the 1^{st} digit 2 from dividend 280
\begin{array}{l}\phantom{48)}0\phantom{2}\\48\overline{)280}\\\end{array}
Since 2 is less than 48, use the next digit 8 from dividend 280 and add 0 to the quotient
\begin{array}{l}\phantom{48)}0\phantom{3}\\48\overline{)280}\\\end{array}
Use the 2^{nd} digit 8 from dividend 280
\begin{array}{l}\phantom{48)}00\phantom{4}\\48\overline{)280}\\\end{array}
Since 28 is less than 48, use the next digit 0 from dividend 280 and add 0 to the quotient
\begin{array}{l}\phantom{48)}00\phantom{5}\\48\overline{)280}\\\end{array}
Use the 3^{rd} digit 0 from dividend 280
\begin{array}{l}\phantom{48)}005\phantom{6}\\48\overline{)280}\\\phantom{48)}\underline{\phantom{}240\phantom{}}\\\phantom{48)9}40\\\end{array}
Find closest multiple of 48 to 280. We see that 5 \times 48 = 240 is the nearest. Now subtract 240 from 280 to get reminder 40. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }40
Since 40 is less than 48, stop the division. The reminder is 40. 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}