Evaluate
34
Factor
2\times 17
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)1020}\\\end{array}
Use the 1^{st} digit 1 from dividend 1020
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)1020}\\\end{array}
Since 1 is less than 30, use the next digit 0 from dividend 1020 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)1020}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1020
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)1020}\\\end{array}
Since 10 is less than 30, use the next digit 2 from dividend 1020 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)1020}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1020
\begin{array}{l}\phantom{30)}003\phantom{6}\\30\overline{)1020}\\\phantom{30)}\underline{\phantom{9}90\phantom{9}}\\\phantom{30)9}12\\\end{array}
Find closest multiple of 30 to 102. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 102 to get reminder 12. Add 3 to quotient.
\begin{array}{l}\phantom{30)}003\phantom{7}\\30\overline{)1020}\\\phantom{30)}\underline{\phantom{9}90\phantom{9}}\\\phantom{30)9}120\\\end{array}
Use the 4^{th} digit 0 from dividend 1020
\begin{array}{l}\phantom{30)}0034\phantom{8}\\30\overline{)1020}\\\phantom{30)}\underline{\phantom{9}90\phantom{9}}\\\phantom{30)9}120\\\phantom{30)}\underline{\phantom{9}120\phantom{}}\\\phantom{30)9999}0\\\end{array}
Find closest multiple of 30 to 120. We see that 4 \times 30 = 120 is the nearest. Now subtract 120 from 120 to get reminder 0. Add 4 to quotient.
\text{Quotient: }34 \text{Reminder: }0
Since 0 is less than 30, stop the division. The reminder is 0. The topmost line 0034 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 34.
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}