Brüche vereinfachen

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From users who are members of Lineare Algebra 1 :

Ulrich Görtz

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Ready to use

4 years, 5 months ago

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Ulrich Görtz 4 years, 5 months ago

Published this.

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Ulrich Görtz 4 years, 5 months ago

Gave some feedback: Ready to use

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Ulrich Görtz 4 years, 5 months ago

Gave some feedback: Needs to be tested

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Ulrich Görtz 4 years, 6 months ago

Gave some feedback: Has some problems

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Ulrich Görtz 4 years, 6 months ago

Gave some feedback: Ready to use

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Ulrich Görtz 4 years, 6 months ago

Created this as a copy of Simplifying fractions.

Name	Status	Author	Last Modified
Simplifying fractions	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
W2a: Simplifying fractions	Ready to use	Timur Zaripov	17/06/2022 09:37
Brüche vereinfachen	Ready to use	Ulrich Görtz	30/09/2024 19:41

There are 7 other versions that do you not have access to.

Question statement

Schreiben Sie die folgenden Ausdrücke als gekürzte Brüche.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
b	integer	1
g	integer	7
f	integer	3
s1	integer	-1
s	integer	-1
test	integer	11
result	rational	21/11
a2	integer	-2
b2	integer	1
c2	integer	9
d2	integer	7
e2	integer	20
ee	integer	4
f2	integer	3
g2	integer	3
num2	integer	-1020
den2	integer	729
result2	rational	-340/243
a3	integer	-3
b3	integer	6
c3	integer	-2
d3	integer	3
e3	integer	5
f3	integer	1
g3	integer	3
num3	integer	180
den3	integer	-28
result3	rational	-45/7

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..7)

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`

→ Used by:

g
s1
test

Advice
"Part a)" - prompt

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

$\simplify{{g} / ({a} + {s1} * ({b * g} / {f}))}$
Ergebnis: Unnamed gap

Das Ergebnis muss in der Form a/b mit ganzen Zahlen a und b angegeben werden (keine Dezimalzahlen, keine Klammern, ...).

Advice

(a) Es gilt

$\simplify[std, timesDot]{{g} / ({a} + {s1} * ({b * g} / {f}))} = \simplify[std, timesDot]{{g} / (({a} * {f} + {s1} * {b * g}) / {f})} =\simplify[std, timesDot]{{g} / (({a * f + s1 * b * g}) / {f})}= \simplify[std, timesDot]{({f}*{g}) / ({a * f + s1 * b * g})} = \simplify[std]{({g * f} / {(a * f + s1 * b * g)})}$
Wir benutzen dabei, dass durch den Bruch

$\frac{a}{b}$ zu teilen, dasselbe ist, wie mit dem Kehrbruch

$\frac{b}{a}$ zu multiplizieren.
Das Ergebnis ist gekürzt, d.h. Zähler und Nenner haben keinen gemeinsamen Teiler.

(b) Es gilt

$\simplify[std, timesDot]{ ({a2} + {b2}/{c2})/({d2}/{e2} + {f2}/{g2}) } = \simplify[std]{ {a2*c2+b2}/{c2}} / \simplify[std]{({d2*g2+e2*f2}/{e2*g2}) } = \simplify[std]{{a2*c2+b2}/{c2}} \cdot \simplify[std]{ {e2*g2}/{d2*g2+e2*f2} }= \simplify[std]{ {(a2*c2+b2)*e2*g2}/{c2*(d2*g2+e2*f2)} }$

$\simplify[std]{ ({b3}/{c3} + {a3})/({d3}/{e3} + {f3}/{g3}) } = \simplify[std, timesDot]{ {a3*c3+b3}/{c3}} / \simplify[std, timesDot]{({d3*g3+e3*f3}/{e3*g3}) } = \simplify[std]{{a3*c3+b3}/{c3}} \cdot \simplify[std]{ {e3*g3}/{d3*g3+e3*f3} }= \simplify[std]{ {(a3*c3+b3)*e3*g3}/{c3*(d3*g3+e3*f3)} }$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Bruchrechnung by Ulrich Görtz in Lineare Algebra 1.
Bruchrechnung by Ulrich Görtz in Mathe für WiWi.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 6 months ago

Ulrich Görtz 4 years, 6 months ago

Ulrich Görtz 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Brüche vereinfachen

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 6 months ago

Ulrich Görtz 4 years, 6 months ago

Ulrich Görtz 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`