Evaluate
154
Factor
2\times 7\times 11
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)3388}\\\end{array}
Use the 1^{st} digit 3 from dividend 3388
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)3388}\\\end{array}
Since 3 is less than 22, use the next digit 3 from dividend 3388 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)3388}\\\end{array}
Use the 2^{nd} digit 3 from dividend 3388
\begin{array}{l}\phantom{22)}01\phantom{4}\\22\overline{)3388}\\\phantom{22)}\underline{\phantom{}22\phantom{99}}\\\phantom{22)}11\\\end{array}
Find closest multiple of 22 to 33. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 33 to get reminder 11. Add 1 to quotient.
\begin{array}{l}\phantom{22)}01\phantom{5}\\22\overline{)3388}\\\phantom{22)}\underline{\phantom{}22\phantom{99}}\\\phantom{22)}118\\\end{array}
Use the 3^{rd} digit 8 from dividend 3388
\begin{array}{l}\phantom{22)}015\phantom{6}\\22\overline{)3388}\\\phantom{22)}\underline{\phantom{}22\phantom{99}}\\\phantom{22)}118\\\phantom{22)}\underline{\phantom{}110\phantom{9}}\\\phantom{22)99}8\\\end{array}
Find closest multiple of 22 to 118. We see that 5 \times 22 = 110 is the nearest. Now subtract 110 from 118 to get reminder 8. Add 5 to quotient.
\begin{array}{l}\phantom{22)}015\phantom{7}\\22\overline{)3388}\\\phantom{22)}\underline{\phantom{}22\phantom{99}}\\\phantom{22)}118\\\phantom{22)}\underline{\phantom{}110\phantom{9}}\\\phantom{22)99}88\\\end{array}
Use the 4^{th} digit 8 from dividend 3388
\begin{array}{l}\phantom{22)}0154\phantom{8}\\22\overline{)3388}\\\phantom{22)}\underline{\phantom{}22\phantom{99}}\\\phantom{22)}118\\\phantom{22)}\underline{\phantom{}110\phantom{9}}\\\phantom{22)99}88\\\phantom{22)}\underline{\phantom{99}88\phantom{}}\\\phantom{22)9999}0\\\end{array}
Find closest multiple of 22 to 88. We see that 4 \times 22 = 88 is the nearest. Now subtract 88 from 88 to get reminder 0. Add 4 to quotient.
\text{Quotient: }154 \text{Reminder: }0
Since 0 is less than 22, stop the division. The reminder is 0. The topmost line 0154 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 154.
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}