Evaluate
\frac{127}{97}\approx 1.309278351
Factor
\frac{127}{97} = 1\frac{30}{97} = 1.309278350515464
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\begin{array}{l}\phantom{97)}\phantom{1}\\97\overline{)127}\\\end{array}
Use the 1^{st} digit 1 from dividend 127
\begin{array}{l}\phantom{97)}0\phantom{2}\\97\overline{)127}\\\end{array}
Since 1 is less than 97, use the next digit 2 from dividend 127 and add 0 to the quotient
\begin{array}{l}\phantom{97)}0\phantom{3}\\97\overline{)127}\\\end{array}
Use the 2^{nd} digit 2 from dividend 127
\begin{array}{l}\phantom{97)}00\phantom{4}\\97\overline{)127}\\\end{array}
Since 12 is less than 97, use the next digit 7 from dividend 127 and add 0 to the quotient
\begin{array}{l}\phantom{97)}00\phantom{5}\\97\overline{)127}\\\end{array}
Use the 3^{rd} digit 7 from dividend 127
\begin{array}{l}\phantom{97)}001\phantom{6}\\97\overline{)127}\\\phantom{97)}\underline{\phantom{9}97\phantom{}}\\\phantom{97)9}30\\\end{array}
Find closest multiple of 97 to 127. We see that 1 \times 97 = 97 is the nearest. Now subtract 97 from 127 to get reminder 30. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }30
Since 30 is less than 97, stop the division. The reminder is 30. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
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Linear equation
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Matrix
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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
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Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}