Evaluate
\frac{55}{6}\approx 9.166666667
Factor
\frac{5 \cdot 11}{2 \cdot 3} = 9\frac{1}{6} = 9.166666666666666
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)385}\\\end{array}
Use the 1^{st} digit 3 from dividend 385
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)385}\\\end{array}
Since 3 is less than 42, use the next digit 8 from dividend 385 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)385}\\\end{array}
Use the 2^{nd} digit 8 from dividend 385
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)385}\\\end{array}
Since 38 is less than 42, use the next digit 5 from dividend 385 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)385}\\\end{array}
Use the 3^{rd} digit 5 from dividend 385
\begin{array}{l}\phantom{42)}009\phantom{6}\\42\overline{)385}\\\phantom{42)}\underline{\phantom{}378\phantom{}}\\\phantom{42)99}7\\\end{array}
Find closest multiple of 42 to 385. We see that 9 \times 42 = 378 is the nearest. Now subtract 378 from 385 to get reminder 7. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }7
Since 7 is less than 42, stop the division. The reminder is 7. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}