Converting between Mixed Numbers and Improper Fractions

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Chris Graham	said	Should not be used	7 years, 7 months ago
Lauren Richards	said	Needs to be tested	7 years, 8 months ago
Christian Lawson-Perfect	said	Has some problems	7 years, 8 months ago
Elliott Fletcher	said	Has some problems	7 years, 9 months ago

History

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Chris Graham commented 7 years, 7 months ago

I've changed the status to "should not be used", as this has been split into separate questions.

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Chris Graham 7 years, 7 months ago

Gave some feedback: Should not be used

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Elliott Fletcher commented 7 years, 8 months ago

I wasn't sure if you still wanted to keep this question or not since you've split it into two seperate questions, but i thought because the content of this question is still different to that in the questions that you have created then i could just rename this question from "Equivalent Fractions" to "Converting between Mixed Numbers and Improper Fractions".

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

I'm splitting these into separate questions, so here's a checkpoint with everything together.

Restore this checkpoint

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

In the advice, I don't find the justifications for parts a and b very clear at all. I'd say, for example, " $\frac{3}{18} = \frac{3}{3} \times \frac{1}{6}$ ", not " $1 \times 3 = 3$ and $6 \times 3 = 18$ to give $\frac{3}{18}$ ". The latter looks like it's working backwards. Your worked solution should reproduce the steps a student could take to get to the right answer.

The formatting in the advice for part c has gone awry, with some lines centred that shouldn't be.

Restore this checkpoint

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Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher commented 7 years, 9 months ago

I think this question is really good and works well. I just noticed a few grammatical things that might need to be changed.

Main Parts

a) good

b) good

c) good, but i think you should say "reduce them down to their simplest form" instead of "reduce down to their simplest form".

d) the i and ii should be in italics as they are in part c) (maybe shouldn't be bold too).

Not entirely sure, but i think there should be full stops after each of the fractions with the gaps on them in parts c and d.

Advice

I can't tell if you have done this or not, but it might be worth checking that when you are typing the a), b), c) etc in the advice, that you are just setting the format of each of them to "heading 4" and not making them bold as well.

I think "was" should be "is" in a) and b)

I would get rid of the "and", after the semi-colon, on the fifth line of a)

In c),

I think you need to add a line of text before your definitions of improper fractions and mixed numbers, for example i would write

"A mixed number is a number consisting of an integer and a proper fraction,

I.e a number of the form

a (b)/(c) where a is an integer and b/c is a proper fraction"

In d),

in i) and ii) i would add an extra line after you say what the new numerator of the proper fraction is. I think you need to simplify the proper fraction first before combining it with the integer to form the mixed number. I would say "Therefore, the proper fraction is ...". Then simplify it and then combine the simplified proper fraction with the integer at the end. Also, i think when you give the final answer i think you should put the improper fraction that you are changing before it to make the full transformation clear, e.g 13/6 = 2 1/6.

I would also change "This is in this question" to "In this question, this is".

Otheriwise, this looks good!

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Has some problems

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Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Lauren Richards 7 years, 9 months ago

Gave some feedback: Has some problems

○

Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

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

'Which fraction is the odd one out?"... the first, because they are one digit numbers?

I think it's too vague. "Select the fraction which is not equivilant" would be more precise, or if you want to keep the phrase because it's catchy: "Which is the odd one out? Select the fraction which is not equivilant."

In (c) and (d), include $=$ inside the LaTeX.

In the advice you have "time(s)", because the variable round could take the value 1. You could replace this text, making use of the jme function if: {if(rounds=1,"time","times")}.

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Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Lauren Richards 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Converting between Mixed Numbers and Improper Fractions	Should not be used	Lauren Richards	20/11/2019 14:47
Select the fraction not equivalent to the others - small denominators	Ready to use	Christian Lawson-Perfect	20/11/2019 14:42
Select the fraction not equivalent to the others - large denominators	Ready to use	Christian Lawson-Perfect	20/11/2019 14:42
Welche Bruchzahl ist verschieden von allen anderen? (Kleine Nenner)	Ready to use	Ulrich Görtz	15/10/2020 07:54
Welcher Bruch stimmt nicht mit den anderen überein? (Große Nenner)	Ready to use	Ulrich Görtz	26/11/2020 10:29
NG2 - Converting mixed numbers to top heavy	Ready to use	Andrew Neate	10/04/2024 09:35
NG7 - Simplify (cancel down) Fractions - top heavy	Ready to use	Andrew Neate	10/04/2024 09:36
Merryn's copy of Converting between Mixed Numbers and Improper Fractions	Ready to use	Merryn Horrocks	08/03/2024 01:17

There are 26 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	8
b	integer	8
c	integer	8
d	integer	11
gcd	number	8
ab	integer	64
cd	integer	88
f	integer	3
g	integer	2
h	integer	15
gcd_gh	number	1
g_coprime	number	2
h_coprime	number	15
num	number	47
l	integer	6
j	integer	9
k	integer	13
gcd_jk	number	1
j_coprime	number	9
k_coprime	number	13
num2	number	87
s	integer	26
t	integer	7
rounds	integer	3
gap1	integer	5
gcd_gap1t	number	1
gap1_coprime	number	5
t_coprime	number	7
x	integer	19
y	integer	8
roundx	integer	2
gap4	integer	3
gcda	number	1
gcdb	number	1
gcd_gap4y	number	1
gap4_coprime	number	3
y_coprime	number	8

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

A random number from 1-12.

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:

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Part b) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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5. Gap Gap 4. Number entry
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6. Gap Gap 5. Number entry
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Gap-fill

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

Write these mixed numbers as their improper fraction equivalents and reduce them down to their simplest form.

$\displaystyle{\var{f}\frac{\var{g_coprime}}{\var{h_coprime}}} =$ Gap 0. Gap 1. .

ii)

$\displaystyle{\var{l}\frac{\var{j_coprime}}{\var{k_coprime}}} =$ Gap 2. Gap 3. .

Advice

c)

A mixed number is a number consisting of an integer and a proper fraction, i.e. a number in the form $a \displaystyle \frac{b}{c}$ where $a$ is an integer and $\displaystyle\frac{b}{c}$ is a proper fraction: $b$ is smaller than $c$ .

An improper fraction is a fraction where the numerator is larger than the denominator, i.e. a number of the form $\displaystyle\frac{d}{e}$ where the numerator, $d$ , is greater than the denominator, $e$ .

To convert a mixed number into an improper fraction, multiply the integer part of the mixed number, $a$ , by the denominator, $c$ .

The numerator of the improper fraction will be equal to this added to what was already on the numerator of the proper fraction.

The denominator of the proper fraction will stay the same when it converts to an improper fraction to give a final answer of

$\displaystyle\frac{({a}\times{c})+b}{c}$ .

${\var{f}\frac{\var{g_coprime}}{\var{h_coprime}}} = \frac{({\var{f}}\times{\var{h_coprime}})+{\var{g_coprime}}}{{\var{h_coprime}}}=\simplify{{num}/{h_coprime}}\text{.}$

ii)

${\var{l}\frac{\var{j_coprime}}{\var{k_coprime}}} = \frac{({\var{l}}\times{\var{k_coprime}})+{\var{j_coprime}}}{{\var{k_coprime}}} =\simplify{{num2}/{k_coprime}}\text{.}$

d)

To convert an improper fraction into a mixed number, you have to think about how many times the denominator can go into the numerator, and whatever is left over becomes the new numerator of the proper fraction.

i) $\displaystyle\frac{\var{s}}{\var{t}}$ :

$\var{s}$ can be divided by $\var{t}$ fully $\var{rounds}$ {if(rounds=1,"time","times")}, with $\var{gap1}$ remaining.

$\var{rounds}$ becomes the integer part of the mixed number and $\var{gap1}$ becomes the new numerator of the proper fraction.

$\displaystyle\frac{\var{s}}{\var{t}} = \var{rounds}\frac{\var{gap1}}{\var{t}}$ .

It may be possible to simplify the proper fraction further by finding the highest common divisor of the numerator and denominator. In this question, this is $\var{gcd_gap1t}$ .

Therefore, it is not possible to simplify this further, and the final answer shall be

Simplifying by this value gives the final answer

$\displaystyle\var{rounds}\frac{\var{gap1_coprime}}{\var{t_coprime}}$ .

ii) $\displaystyle\frac{\var{x}}{\var{y}}$ :

$\var{x}$ can be divided by $\var{y}$ fully $\var{roundx}$ {if(roundx=1,"time","times")}, with $\var{gap4}$ left over.

$\var{roundx}$ becomes the integer part of the mixed number and $\var{gap4}$ becomes the new numerator of the proper fraction.

$\displaystyle\frac{\var{x}}{\var{y}} = \var{roundx}\frac{\var{gap4}}{\var{y}}$ .

It may be possible to simplify the proper fraction further by finding the highest common divisor of the numerator and denominator. In this question, this is $\var{gcd_gap4y}$ .

Therefore, it is not possible to simplify this further, and the final answer shall be

Simplifying by this value gives the final answer

$\displaystyle\var{roundx}\frac{\var{gap4_coprime}}{\var{y_coprime}}$ .

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?
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This question is used in the following exams:

Transition Number Notation by Chris Templet in Chris's workspace.
All the good stuff by Chris Templet in Chris's workspace.

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Converting between Mixed Numbers and Improper Fractions

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Comment

Checkpoint description

Chris Graham commented 7 years, 7 months ago

Chris Graham 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Lauren Richards 7 years, 9 months ago

Elliott Fletcher commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

c)

d)

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Error

Converting between Mixed Numbers and Improper Fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Chris Graham commented 7 years, 7 months ago

Chris Graham 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Lauren Richards 7 years, 9 months ago

Elliott Fletcher commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

c)

d)

Generated value: `integer`