Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Wrong order of solving operations can often lead to incorrect answers. Therefore, the order in which we carry out a calculation is important.
\nBODMAS is a mnemonic which tells us the correct order in which operations should be carried out:
\n\n\nBrackets ⇒ Ordinals ⇒ Division/Multiplication ⇒ Addition/Subtraction
\n
Apply BODMAS and try to solve these calculations.
", "advice": "The correct order of carrying out operations can be remembered by the mnemonic BODMAS:
\n\n\nBrackets ⇒ Ordinals ⇒ Division/Multiplication ⇒ Addition/Subtraction
\n
It is important to notice that division and multiplication have the same priority - division does not have a priority over multiplication. Similarly, adition and subtraction also have the same priority. When the order is unclear, we work from left to right.
\nNote that brackets have the highest priority, but when we evaluate them, we still need to follow BODMAS inside them.
\nSometimes, an alternative acronym BIDMAS (Brackets, Indices, ...) is also used.
\na)
\nDivision and multiplication have the same priority, so we just work from left to right. $\\var{int*int} ÷ \\var{int} = \\var{int}$ and hence
\n\\[\\begin{align} \\var{int*int} ÷ \\var{int} \\times \\var{int} &= \\var{int} \\times \\var{int} \\\\&= \\var{int*int} \\text{.} \\end{align}\\]
\n\nb)
\nSimilarly, $\\var{eint*2} ÷ \\var{eint/2} = 4 $ and hence
\n\\[\\begin{align} \\var{eint*2} ÷ \\var{eint/2} \\times \\var{eint} &= 4 \\times \\var{eint} \\\\&= \\var{4*eint}\\text{.} \\end{align}\\]
\n\nc)
\nApplying BODMAS, multiplication has a priority over addition. $\\var{sint + 2} \\times \\var{sint} = \\var{(sint + 2)*sint}$ and hence
\n\\[\\begin{align} \\var{sint} + \\var{sint + 2} \\times \\var{sint} &= \\var{sint} + \\var{(sint + 2)*sint} \\\\&= \\var{sint + (sint + 2)*sint}\\text{.} \\end{align}\\]
\n\nd)
\nApplying BODMAS, multiplication and division have priority over addition and subtraction. $1 \\times 0 = 0$ and $\\var{bint}\\div\\var{bint} = 1$ so
\n\\[\\begin{align} \\var{bint - 15} - 1 \\times 0 + \\var{bint}\\div\\var{bint} &= \\var{bint - 15} - 0 + 1 \\\\&= \\var{bint - 14}\\text{.} \\end{align}\\]
\n\ne)
\nRoots can be considered as powers, while fractions can be considered as a bracket divided by a bracket.
\n\\[\\displaystyle \\text{Numerator is considered as a bracket } (\\var{oint}^2+ \\sqrt{\\var{eint*eint}}) \\text{ and the denominator as } (3 \\times 2 - 2 \\times 2)\\text{.}\\]
\nBefore we evaluate numerator, we calculate powers:
\n\\[\\begin{align} \\sqrt{\\var{eint*eint}} &= \\var{eint} \\text{,}
\\\\\\var{oint}^2 &= \\var{oint*oint} \\text{.} \\end{align}\\]
Before we evaluate denominator we calculate multiplications:
\n\\[\\begin{align} 3 \\times 2 &= 6 \\text{ and } \\\\ 2 \\times 2 &= 4\\text{.} \\end{align}\\]
\nPerforming addition/subtraction as the last step in evaluating numerator/denominator we get:
\n\\[ \\begin{align} (\\var{oint}^2+ \\sqrt{\\var{eint*eint}}) &= \\var{oint*oint} + \\var{eint}
\\\\&= \\var{oint*oint + eint}
\\\\\\text{and}
\\\\(3 \\times 2 - 2 \\times 2) &= 6 - 4
\\\\&= 2 \\end{align} \\]
So the fraction
\n\\[\\begin{align} \\displaystyle \\frac{(\\var{oint}^2+ \\var{eint})}{(3 \\times 2 - 2 \\times 2)} &= \\frac{\\var{(oint*oint + eint)}}{2}\\text{.} \\end{align}\\]
\nEvaluating the final bracket we get:
\n\\[(10 - 2) = 8\\text{.}\\]
\nAs we evaluated all brackets, we can continue with:
\n\\[\\displaystyle \\frac{\\var{oint}^2+ \\sqrt{\\var{eint*eint}}}{3 \\times 2 - 2 \\times 2} + (10 - 2) \\div \\var{pint} = \\frac{\\var{(oint*oint + eint)}}{2} + 8 \\div \\var{pint} \\]
\nNow, division has a priority over addition so since $\\frac{\\var{(oint*oint + eint)}}{2} = \\var{(oint*oint + eint)/2}$ and $8 \\div \\var{pint} = \\var{8/pint}$:
\n\\[\\begin{align} \\frac{\\var{(oint*oint + eint)}}{2} + 8 \\div \\var{pint} &= \\var{(oint*oint + eint)/2} + \\var{8/pint} \\\\&= \\var{(oint*oint + eint)/2 + 8/pint}\\text{.} \\end{align}\\]
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