Using BODMAS to evaluate arithmetic expressions

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Christian Lawson-Perfect	said	Ready to use	7 years, 9 months ago
Stanislav Duris	said	Needs to be tested	7 years, 9 months ago
Vicky Hall	said	Has some problems	7 years, 9 months ago
Chris Graham	said	Has some problems	7 years, 9 months ago

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Stanislav Duris 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 9 months ago

Saved a checkpoint:

This looks good! I changed a few words to sound more natural in English.

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Stanislav Duris 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Vicky Hall 7 years, 9 months ago

Gave some feedback: Has some problems

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Vicky Hall commented 7 years, 9 months ago

In the 'show steps' sections for the final part, you say 'we give roots and fractions the same priority as brackets'. This is not true. Explain to the student that a root is another way of writing a power, so that comes under the Order part of BODMAS,while a fraction means the numerator divided by the denominator, so that follows the Division part of BODMAS.

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Stanislav Duris 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Stanislav Duris commented 7 years, 9 months ago

I've made suggested adjustments. Previously, there was a step explaining BODMAS in part e) but this was probably too late in the question. I've moved this summary to the statement.

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Chris Graham 7 years, 9 months ago

Gave some feedback: Has some problems

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Chris Graham commented 7 years, 9 months ago

The statement begins "Apply BODMAS..." What if the student has never seen this acronym. I think I would begin with a short summary, or at least add this as a step, so that they can seek help.

You don't need the horizontal lines in the advice. There;s nothing particularly wrong with them aesthetically, however they're inconsistent with other questions.

Try to punctuate equations in the advice as discussed yesterday.

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Stanislav Duris 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Stanislav Duris 7 years, 9 months ago

Created this.

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	4
sint	integer	5
eint	integer	3
oint	integer	7
pint	integer	1
bint	integer	35

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10 except sint)

JME function reference

Description

Random integer from 2 to 10.

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

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

sint

→ Used by:

eint
oint

This variable doesn't seem to be used anywhere.

Parts

Part a) Choose one from a list
Part b) Choose one from a list
Part c) Choose one from a list
Part d) Choose one from a list
Part e) Gap-fill
1. Gap Number entry
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1. Step Information only

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Ask the student a question, and give any hints about how they should answer this part.

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

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{int*int}

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{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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Using BODMAS to evaluate arithmetic expressions

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Taxonomy: mathcentre

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Taxonomy: Context

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Stanislav Duris 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Vicky Hall 7 years, 9 months ago

Vicky Hall commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris commented 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

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Generated value: `integer`

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Using BODMAS to evaluate arithmetic expressions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Stanislav Duris 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Vicky Hall 7 years, 9 months ago

Vicky Hall commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris commented 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Choose one from a list

Advanced settings

Generated value: `integer`