Merryn's copy of Converting between Mixed Numbers and Improper Fractions

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Merryn Horrocks 1 year ago

Created this as a copy of Converting between Mixed Numbers and Improper Fractions.

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	4
b	integer	2
c	integer	8
d	integer	1
gcd	number	8
ab	integer	8
cd	integer	8
f	integer	3
g	integer	15
h	integer	20
gcd_gh	number	5
g_coprime	number	3
h_coprime	number	4
num	number	15
l	integer	4
j	integer	8
k	integer	13
gcd_jk	number	1
j_coprime	number	8
k_coprime	number	13
num2	number	60
s	integer	26
t	integer	10
rounds	integer	2
gap1	integer	6
gcd_gap1t	number	2
gap1_coprime	number	3
t_coprime	number	5
x	integer	13
y	integer	8
roundx	integer	1
gap4	integer	5
gcda	number	1
gcdb	number	1
gcd_gap4y	number	1
gap4_coprime	number	5
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`

This variable doesn't seem to be used anywhere.

Parts

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

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 exam:

MPR Practice Questions by Merryn Horrocks in MESH.

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Merryn's copy of Converting between Mixed Numbers and Improper Fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

c)

d)

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Error

Merryn's copy of Converting between Mixed Numbers and Improper Fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

c)

d)

Generated value: `integer`