Order of calculations

The order of calculation is uniquely determined. Therefore, it is usually not possible to change it according to what would be easiest for the calculation. The order of calculations is determined as follows:[br][br][color=#0000ff]1. Perform calculations inside brackets. [/color] [br][color=#0000ff]2. Perform multiplication and division from left to right in given order.[/color][br][color=#0000ff]3. Addition and subtraction from left to right in given order.[/color][br][br][br][color=#0000ff]Example 1[/color]. [br][br][math] \begin{array}{lcl}[br]&&1+[4\cdot (2+3)-6]/2\\[br]\text{Calculate the inner part of parentheses: }&=&1+[4\cdot 5-6]/2 \\[br]\text{Lasketaan hakasulkeiden sisällä oleva kertolasku: }&=&1+[20-6]/2\\[br]\text{Calculate the multiplication inside square brackets: }&=&1+14/2\\[br]\text{Calculate division: }&=&1+7\\[br]\text{Calculate addision: }&=&8[br]\end{array}[/math][br] [br]  [br][color=#0000ff]Example 2. [/color] Consider the following tasks. Figures and calculations are all in the same order, but brackets change the order of calculations. In this case, the results are completely different.[br][br] [math] \begin{eqnarray} a)[br]&&8\cdot 5-56:8+4\\[br]&=&40-7+4\\[br]&=&37\\[br]\end{eqnarray}[/math][br][br][math] \begin{eqnarray}b)[br]&&8\cdot 5-(56:8+4)\\[br]&=&40-(7+4)\\[br]&=&40-11\\[br]&=&29\\[br]\end{eqnarray}[/math][br][br][math] \begin{eqnarray} c)[br]&&8\cdot (5-56:8+4)\\[br]&=&8\cdot (5-7+4)\\[br]&=&8\cdot 2\\[br]&=&16\\[br]\end{eqnarray}[/math][br][br][math] \begin{eqnarray}d)[br]&&8\cdot 5-56:(8+4)\\[br]&=&40-56:12\\[br]&=&40-\frac{56}{12}\\[br]&=&40-\frac{14}{3}\\[br]&=&\frac{120}{3}-\frac{14}{3}\\[br]&=&\frac{106}{3}\\[br]&=&35\frac{1}{3}[br]\end{eqnarray}[/math]

Information: Order of calculations