Ian's copy of Using BODMAS to evaluate arithmetic expressions

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Ian Loasby

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Ian Loasby 6 years, 10 months ago

Created this as a copy of Using BODMAS to evaluate arithmetic expressions.

Name	Status	Author	Last Modified
Using BODMAS to evaluate arithmetic expressions	Ready to use	Stanislav Duris	20/11/2019 14:44
Ian's copy of Using BODMAS to evaluate arithmetic expressions	draft	Ian Loasby	21/06/2018 11:30
Musa's copy of Using BODMAS	draft	Musa Mammadov	01/08/2022 08:18
Musa's copy of Using BODMAS - 3 Questions	draft	Musa Mammadov	27/06/2023 01:45
Musa's copy of 3 Using BODMAS	draft	Musa Mammadov	27/06/2023 01:47
BIDMAS practise 1	draft	Merryn Horrocks	03/01/2023 06:13
BIDMAS practise 2	draft	Merryn Horrocks	26/10/2021 09:10
BIDMAS practise 3	draft	Merryn Horrocks	26/10/2021 09:11
BIDMAS practise 4	draft	Merryn Horrocks	26/10/2021 09:11
BIDMAS practise 5	draft	Merryn Horrocks	26/10/2021 09:11

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Question statement

Wrong order of solving operations can often lead to incorrect answers. Therefore, the order in which we carry out a calculation is important.

BODMAS is a mnemonic which tells us the correct order in which operations should be carried out:

Brackets ⇒ Ordinals ⇒ Division/Multiplication ⇒ Addition/Subtraction

Apply BODMAS and try to solve these calculations.

Give any introductory information the student needs.

			Name	Type	Generated Value

int	integer	5
sint	integer	2
eint	integer	3
oint	integer	7
pint	integer	1
bint	integer	33

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Value

xxxxxxxxxx
 
random(2..10 except sint)

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Random integer from 2 to 10.

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

← Depends on:

sint

→ Used by:

eint
oint

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$\var{int*int} ÷ \var{int} \times \var{int} =$ $?$

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{int*int}

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1

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Advice

The correct order of carrying out operations can be remembered by the mnemonic BODMAS:

Brackets ⇒ Ordinals ⇒ Division/Multiplication ⇒ Addition/Subtraction

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.

Note that brackets have the highest priority, but when we evaluate them, we still need to follow BODMAS inside them.

Sometimes, an alternative acronym BIDMAS (Brackets, Indices, ...) is also used.

Division and multiplication have the same priority, so we just work from left to right. $\var{int*int} ÷ \var{int} = \var{int}$ and hence

$\begin{align} \var{int*int} ÷ \var{int} \times \var{int} &= \var{int} \times \var{int} \\&= \var{int*int} \text{.} \end{align}$

Similarly, $\var{eint*2} ÷ \var{eint/2} = 4$ and hence

$\begin{align} \var{eint*2} ÷ \var{eint/2} \times \var{eint} &= 4 \times \var{eint} \\&= \var{4*eint}\text{.} \end{align}$

Applying BODMAS, multiplication has a priority over addition. $\var{sint + 2} \times \var{sint} = \var{(sint + 2)*sint}$ and hence

$\begin{align} \var{sint} + \var{sint + 2} \times \var{sint} &= \var{sint} + \var{(sint + 2)*sint} \\&= \var{sint + (sint + 2)*sint}\text{.} \end{align}$

Applying BODMAS, multiplication and division have priority over addition and subtraction. $1 \times 0 = 0$ and $\var{bint}\div\var{bint} = 1$ so

$\begin{align} \var{bint - 15} - 1 \times 0 + \var{bint}\div\var{bint} &= \var{bint - 15} - 0 + 1 \\&= \var{bint - 14}\text{.} \end{align}$

Roots can be considered as powers, while fractions can be considered as a bracket divided by a bracket.

$\displaystyle \text{Numerator is considered as a bracket } (\var{oint}^2+ \sqrt{\var{eint*eint}}) \text{ and the denominator as } (3 \times 2 - 2 \times 2)\text{.}$

Before we evaluate numerator, we calculate powers:

$\begin{align} \sqrt{\var{eint*eint}} &= \var{eint} \text{,} \\\var{oint}^2 &= \var{oint*oint} \text{.} \end{align}$

Before we evaluate denominator we calculate multiplications:

$\begin{align} 3 \times 2 &= 6 \text{ and } \\ 2 \times 2 &= 4\text{.} \end{align}$

Performing addition/subtraction as the last step in evaluating numerator/denominator we get:

$\begin{align} (\var{oint}^2+ \sqrt{\var{eint*eint}}) &= \var{oint*oint} + \var{eint} \\&= \var{oint*oint + eint} \\\text{and} \\(3 \times 2 - 2 \times 2) &= 6 - 4 \\&= 2 \end{align}$

So the fraction

$\begin{align} \displaystyle \frac{(\var{oint}^2+ \var{eint})}{(3 \times 2 - 2 \times 2)} &= \frac{\var{(oint*oint + eint)}}{2}\text{.} \end{align}$

Evaluating the final bracket we get:

$(10 - 2) = 8\text{.}$

As we evaluated all brackets, we can continue with:

$\displaystyle \frac{\var{oint}^2+ \sqrt{\var{eint*eint}}}{3 \times 2 - 2 \times 2} + (10 - 2) \div \var{pint} = \frac{\var{(oint*oint + eint)}}{2} + 8 \div \var{pint}$

Now, division has a priority over addition so since $\frac{\var{(oint*oint + eint)}}{2} = \var{(oint*oint + eint)/2}$ and $8 \div \var{pint} = \var{8/pint}$ :

$\begin{align} \frac{\var{(oint*oint + eint)}}{2} + 8 \div \var{pint} &= \var{(oint*oint + eint)/2} + \var{8/pint} \\&= \var{(oint*oint + eint)/2 + 8/pint}\text{.} \end{align}$

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This question is used in the following exam:

NUMBAS first by Ian Loasby in Ian's workspace.

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Ian's copy of Using BODMAS to evaluate arithmetic expressions

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Ian Loasby 6 years, 10 months ago

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Ian's copy of Using BODMAS to evaluate arithmetic expressions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

Comment

Checkpoint description

Ian Loasby 6 years, 10 months ago

Error in variable testing condition

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Generated value: integer

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Generated value: `integer`