Evaluate
47
Factor
47
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)705}\\\end{array}
Use the 1^{st} digit 7 from dividend 705
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)705}\\\end{array}
Since 7 is less than 15, use the next digit 0 from dividend 705 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)705}\\\end{array}
Use the 2^{nd} digit 0 from dividend 705
\begin{array}{l}\phantom{15)}04\phantom{4}\\15\overline{)705}\\\phantom{15)}\underline{\phantom{}60\phantom{9}}\\\phantom{15)}10\\\end{array}
Find closest multiple of 15 to 70. We see that 4 \times 15 = 60 is the nearest. Now subtract 60 from 70 to get reminder 10. Add 4 to quotient.
\begin{array}{l}\phantom{15)}04\phantom{5}\\15\overline{)705}\\\phantom{15)}\underline{\phantom{}60\phantom{9}}\\\phantom{15)}105\\\end{array}
Use the 3^{rd} digit 5 from dividend 705
\begin{array}{l}\phantom{15)}047\phantom{6}\\15\overline{)705}\\\phantom{15)}\underline{\phantom{}60\phantom{9}}\\\phantom{15)}105\\\phantom{15)}\underline{\phantom{}105\phantom{}}\\\phantom{15)999}0\\\end{array}
Find closest multiple of 15 to 105. We see that 7 \times 15 = 105 is the nearest. Now subtract 105 from 105 to get reminder 0. Add 7 to quotient.
\text{Quotient: }47 \text{Reminder: }0
Since 0 is less than 15, stop the division. The reminder is 0. The topmost line 047 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 47.
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}