Evaluate
\frac{103}{60}\approx 1.716666667
Factor
\frac{103}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{43}{60} = 1.7166666666666666
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)103}\\\end{array}
Use the 1^{st} digit 1 from dividend 103
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)103}\\\end{array}
Since 1 is less than 60, use the next digit 0 from dividend 103 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)103}\\\end{array}
Use the 2^{nd} digit 0 from dividend 103
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)103}\\\end{array}
Since 10 is less than 60, use the next digit 3 from dividend 103 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)103}\\\end{array}
Use the 3^{rd} digit 3 from dividend 103
\begin{array}{l}\phantom{60)}001\phantom{6}\\60\overline{)103}\\\phantom{60)}\underline{\phantom{9}60\phantom{}}\\\phantom{60)9}43\\\end{array}
Find closest multiple of 60 to 103. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 103 to get reminder 43. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }43
Since 43 is less than 60, stop the division. The reminder is 43. 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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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
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