Evaluate
\frac{977}{172}\approx 5.680232558
Factor
\frac{977}{2 ^ {2} \cdot 43} = 5\frac{117}{172} = 5.680232558139535
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\begin{array}{l}\phantom{172)}\phantom{1}\\172\overline{)977}\\\end{array}
Use the 1^{st} digit 9 from dividend 977
\begin{array}{l}\phantom{172)}0\phantom{2}\\172\overline{)977}\\\end{array}
Since 9 is less than 172, use the next digit 7 from dividend 977 and add 0 to the quotient
\begin{array}{l}\phantom{172)}0\phantom{3}\\172\overline{)977}\\\end{array}
Use the 2^{nd} digit 7 from dividend 977
\begin{array}{l}\phantom{172)}00\phantom{4}\\172\overline{)977}\\\end{array}
Since 97 is less than 172, use the next digit 7 from dividend 977 and add 0 to the quotient
\begin{array}{l}\phantom{172)}00\phantom{5}\\172\overline{)977}\\\end{array}
Use the 3^{rd} digit 7 from dividend 977
\begin{array}{l}\phantom{172)}005\phantom{6}\\172\overline{)977}\\\phantom{172)}\underline{\phantom{}860\phantom{}}\\\phantom{172)}117\\\end{array}
Find closest multiple of 172 to 977. We see that 5 \times 172 = 860 is the nearest. Now subtract 860 from 977 to get reminder 117. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }117
Since 117 is less than 172, stop the division. The reminder is 117. 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}