Algebra V: algebraic fractions (reasoning)

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heike hoffmann 6 years, 4 months ago

Created this as a copy of Algebra V: algebraic fractions (reasoning).

Name	Status	Author	Last Modified
Equivalent Fractions	Ready to use	Rob Cade	17/06/2016 12:18
Gapfills in fractions	draft	Christian Lawson-Perfect	05/05/2021 14:17
Fractions: equivalent	Ready to use	Ben Brawn	26/08/2024 05:43
Algebraic fractions: simplifying/cancelling	Ready to use	Ben Brawn	06/02/2025 00:42
Algebra V: algebraic fractions (reasoning)	Ready to use	Luke Park	17/08/2016 17:19
Francis 's copy of Algebra V: algebraic fractions (simplification)	draft	Francis Duah	12/08/2016 14:48
Algebra V: algebraic fractions (simplification)	Ready to use	Nasir Firoz Khan	17/08/2016 17:31
Anthony's copy of Equivalent Fractions	draft	Anthony Brown	14/09/2016 20:17
Anthony's copy of Gapfills in fractions	draft	Anthony Brown	16/09/2016 00:01
Add two fractions with the same denominator	draft	Anthony Brown	27/08/2021 12:36
Add two fractions with the same denominator (some negative numbers).	draft	Anthony Brown	05/07/2017 23:14
Subtract two fractions with the same denominator	draft	Anthony Brown	05/07/2017 23:22
Subtract two fractions with the same denominator (some negative numbers).	draft	Anthony Brown	05/07/2017 23:21
Add two fractions with different denominators	draft	Anthony Brown	05/07/2017 23:08
Add two fractions with different denominators (some negative numbers)	draft	Anthony Brown	05/07/2017 23:13
Subtract two fractions with different denominators	draft	Anthony Brown	05/07/2017 23:03
Subtract two fractions with different denominators (some negative numbers)	draft	Anthony Brown	05/07/2017 23:00
Multiply two fractions	draft	Anthony Brown	11/07/2017 19:13
Multiply two fractions (some negative numbers)	draft	Anthony Brown	11/07/2017 19:14
Divide two fractions	draft	Anthony Brown	05/07/2017 20:59
Divide two fractions (some negative numbers)	draft	Anthony Brown	05/07/2017 20:58
Calculating powers (a^(-1))	draft	Anthony Brown	05/07/2017 17:01
Calculating powers ((-a)^(-b))	draft	Anthony Brown	05/07/2017 17:04
Calculating powers (-a^(-b))	draft	Anthony Brown	05/07/2017 16:17
Calculating powers (1^(-b))	draft	Anthony Brown	05/07/2017 17:00
Calculating powers (-a^(-a))	draft	Anthony Brown	05/07/2017 17:00
Calculating powers (-a^(-1))	draft	Anthony Brown	05/07/2017 13:14
Calculating powers (a^(-1))	draft	Anthony Brown	05/07/2017 13:13
Algebra V: algebraic fractions (reasoning)	draft	steve kilgallon	09/11/2016 19:00
Vicky's copy of Gapfills in fractions	draft	Vicky Hall	14/06/2017 14:46
gap in breuk	draft	Johan Maertens	10/07/2017 13:34
Calculating powers (a^(-b))	draft	Anthony Brown	11/07/2017 16:29
Add two fractions with the same denominator	draft	Anthony Brown	12/08/2017 13:03
Add two fractions with the same denominator (some negative numbers).	draft	Anthony Brown	12/08/2017 13:04
Subtract two fractions with the same denominator	draft	Anthony Brown	12/08/2017 13:05
Subtract two fractions with the same denominator (some negative numbers).	draft	Anthony Brown	12/08/2017 13:05
Add two fractions with different denominators	draft	Anthony Brown	12/08/2017 13:06
Add two fractions with different denominators (some negative numbers)	draft	Anthony Brown	12/08/2017 13:07
Subtract two fractions with different denominators	draft	Anthony Brown	12/08/2017 13:07
Subtract two fractions with different denominators (some negative numbers)	draft	Anthony Brown	12/08/2017 13:08
Multiply two fractions	draft	Anthony Brown	12/08/2017 14:42
Multiply two fractions (some negative numbers)	draft	Anthony Brown	12/08/2017 14:43
Divide two fractions	draft	Anthony Brown	12/08/2017 14:44
Divide two fractions (some negative numbers)	draft	Anthony Brown	12/08/2017 14:45
Calculating powers (a^(-1))	draft	Anthony Brown	12/08/2017 19:18
Calculating powers (-a^(-1))	draft	Anthony Brown	12/08/2017 19:19
Calculating powers (a^(-b))	draft	Anthony Brown	12/08/2017 19:20
Calculating powers (-a^(-b))	draft	Anthony Brown	12/08/2017 19:20
Calculating powers (-a^(-a))	draft	Anthony Brown	12/08/2017 19:21
Calculating powers (1^(-b))	draft	Anthony Brown	12/08/2017 19:22
Calculating powers ((-a)^(-b))	draft	Anthony Brown	12/08/2017 19:22
copy of fractions question	draft	Lovkush Agarwal	08/09/2017 14:33
Hannah's copy of Equivalent Fractions	draft	Hannah Bartholomew	14/09/2017 12:02
Johan's copy of Gapfills in fractions	draft	Johan Maertens	23/01/2018 16:01
Ida's copy of Algebraic fractions: simplifying/cancelling	draft	Ida Landgärds	13/04/2018 09:16
Algebra V: algebraic fractions (reasoning)	draft	heike hoffmann	14/11/2018 20:43
Algebraic fractions: simplifying/cancelling	Ready to use	heike hoffmann	14/11/2018 20:53
Terry's copy of Algebraic fractions: simplifying/cancelling	draft	Terry Young	03/04/2019 17:35
Complex Numbers; Division 01 (Rect')	Ready to use	Michael Proudman	08/02/2022 15:21
Merryn's copy of Fractions: equivalent	Ready to use	Merryn Horrocks	07/03/2024 01:07

There are 115 other versions that do you not have access to.

Question statement

In the following questions, fill in the gaps by simplifying algebraic fractions:
NOTE: To write powers like- $x^2$ , write x^2 and so on

Give any introductory information the student needs.

			Name	Type	Generated Value

amult	integer	-3
ar	integer	9
a	integer	-27
br	integer	-7
b	integer	21
cr	integer	11
c	integer	-33
dr	integer	10
d	integer	-30
f	integer	2

			Name	Type	Generated Value

			g	integer	11
			h	integer	8

			Name	Type	Generated Value

primes	list	[ 7, 17 ]
j	integer	7
k	integer	17
l	integer	14

			Name	Type	Generated Value

			m	integer	6
			n	integer	16

			Name	Type	Generated Value

integer

			Name	Type	Generated Value

common	integer	4
list	list	[ 11, 6, 4, 9 ]
q	integer	44
r	integer	24
s	integer	16
t	integer	36

			Name	Type	Generated Value

			name	list	Nested 2×2 list
			x		Definition of variable `x` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random([-10,-5,-3,-2,-1,2,3,5,10])

JME function reference

Description

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`

-3

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only
Part c) Choose several from a list
1. Step Information only
Part d) Choose several from a list
1. Step Information only
Part e) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only
Part f) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only
Part g) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
  Add
1. Step Information only

Gap-fill

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

{Name[0][0]} has written $\displaystyle{\simplify{({a}x+{b})/({c}y+{d})}}$ in the equivalent form $\displaystyle{\simplify{({ar}x+{br})/({cr}y+{dr})}}$ .

What has {Name[0][0]} done to the first fraction in order to get the second? {Name[0][1]} has divided the top and bottom by Unnamed gap .

Advice

Algebraic fractions involve various rules and some important tips are:

1.If we multiply or divide the top and bottom of a fraction by a number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.

2.When you have a fraction, say $\displaystyle{\frac{1+2a+3b}{5+x}}$ , it represents the result of dividing everything on top by everything on the bottom, that is

$\frac{1+2a+3b}{5+x}=\frac{1}{5+x}+\frac{2a}{5+x}+\frac{3b}{5+x}$

3. Whenever we have such a 'fraction on a fraction' we want to rewrite the fraction to it is just one fraction. We can do this by multiplying by the denominator of the smaller/inner fraction.

For more information, check out this video-

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry
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Choose several from a list
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Choose several from a list
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Gap-fill
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Mathematical expression
Mathematical expression		Hasn't run yet
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Gap-fill
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Mathematical expression
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Information only

This question is used in the following exam:

Basics Algebra by Max S in Max's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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heike hoffmann 6 years, 4 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Algebra V: algebraic fractions (reasoning)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

heike hoffmann 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`