Algebra V: algebraic fractions (simplification)

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Nasir Firoz Khan

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Nasir Firoz Khan

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8 years, 7 months ago

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Nasir Firoz Khan 8 years, 7 months ago

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Nasir Firoz Khan 8 years, 7 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, simplify the given algebraic fractions by using operations on fractions and basic BODMAS:

Give any introductory information the student needs.

			Name	Type	Generated Value

amult	integer	-10
ar	integer	7
a	integer	-70
br	integer	3
b	integer	-30
cr	integer	-9
c	integer	90
dr	integer	-12
d	integer	120
f	integer	11

			Name	Type	Generated Value

			g	integer	9
			h	integer	11

			Name	Type	Generated Value

primes	list	[ 13, 5 ]
j	integer	13
k	integer	5
l	integer	26

			Name	Type	Generated Value

			m	integer	22
			n	integer	19

			Name	Type	Generated Value

integer

			Name	Type	Generated Value

common	integer	4
list	list	[ 9, 3, 7, 5 ]
q	integer	36
r	integer	12
s	integer	28
t	integer	20

			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`

-10

→ Used by:

"Part a)" → "Unnamed gap" - Minimum accepted value
"Part a)" → "Unnamed gap" - Maximum accepted value

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.

Check this video for further guidance:

Give a worked solution to the whole question.

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

This question is used in the following exams:

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Algebra V: algebraic fractions (simplification)

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Nasir Firoz Khan 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 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 (simplification)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Nasir Firoz Khan 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`