Manipulation of formula 2

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Frank Doheny

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Frank Doheny

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7 years, 4 months ago

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Frank Doheny 7 years, 4 months ago

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Frank Doheny 8 years, 4 months ago

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Frank Doheny 8 years, 6 months ago

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Name	Status	Author	Last Modified
Manipulation of formula 2	Ready to use	Frank Doheny	24/11/2017 08:16
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Maria's copy of Manipulation of formula 2	draft	Maria Aneiros	25/05/2019 07:25

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Question statement

Rearrange the following expression to make V the subject:

$\frac{\var{a}V+1}{\var{b}R+3}=\frac{\var{c}V+5}{\var{d}R+7}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	14
b	integer	10
c	integer	4
d	integer	14

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A random number between and (inclusive) with step size

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Generated value: `integer`

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Parts

Gap-fill
1. Gap Mathematical expression
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Express your answer as a fraction:

$V =$ Unnamed gap

Advice

When one fraction equals another fraction we can clear both fractions by cross-multiplying:

$(\var{a}V+1)*(\var{d}R+7)=(\var{b}R+3)*(\var{c}V+5)$

$\simplify{{a}*{d}}VR+\simplify{7*{a}}V+\var{d}R+7=\simplify{{b}*{c}}VR+\simplify{5*{b}}R+\simplify{3*{c}}V+15$

Gathering all the terms involving $V$ to the left hand side and moving all other terms to the right hand side gives

$\simplify{{a}*{d}-{b}*{c}}VR+\simplify{7*{a}-3*{c}}V=\simplify{5*{b}-{d}}R+8$

Factoring $V$ out on the left hand side

$V(\simplify{{a}*{d}-{b}*{c}}R+\simplify{7*{a}-3*{c}})=\simplify{5*{b}-{d}}R+8$

Thus

$V=\frac{\simplify{5*{b}-{d}}R+8}{\simplify{{a}*{d}-{b}*{c}}R+\simplify{7*{a}-3*{c}}}$

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Frank Doheny 7 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Manipulation of formula 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`