Evaluate
\frac{985}{159}\approx 6.194968553
Factor
\frac{5 \cdot 197}{3 \cdot 53} = 6\frac{31}{159} = 6.19496855345912
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\begin{array}{l}\phantom{159)}\phantom{1}\\159\overline{)985}\\\end{array}
Use the 1^{st} digit 9 from dividend 985
\begin{array}{l}\phantom{159)}0\phantom{2}\\159\overline{)985}\\\end{array}
Since 9 is less than 159, use the next digit 8 from dividend 985 and add 0 to the quotient
\begin{array}{l}\phantom{159)}0\phantom{3}\\159\overline{)985}\\\end{array}
Use the 2^{nd} digit 8 from dividend 985
\begin{array}{l}\phantom{159)}00\phantom{4}\\159\overline{)985}\\\end{array}
Since 98 is less than 159, use the next digit 5 from dividend 985 and add 0 to the quotient
\begin{array}{l}\phantom{159)}00\phantom{5}\\159\overline{)985}\\\end{array}
Use the 3^{rd} digit 5 from dividend 985
\begin{array}{l}\phantom{159)}006\phantom{6}\\159\overline{)985}\\\phantom{159)}\underline{\phantom{}954\phantom{}}\\\phantom{159)9}31\\\end{array}
Find closest multiple of 159 to 985. We see that 6 \times 159 = 954 is the nearest. Now subtract 954 from 985 to get reminder 31. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }31
Since 31 is less than 159, stop the division. The reminder is 31. 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}