Fraction multiplication

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Christian Lawson-Perfect	said	Ready to use	7 years, 10 months ago
Lauren Richards	said	Needs to be tested	7 years, 10 months ago
Vicky Hall	said	Has some problems	7 years, 10 months ago

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Elliott Fletcher 7 years, 9 months ago

Published this.

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Christian Lawson-Perfect 7 years, 10 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 10 months ago

Saved a checkpoint:

Looks good!

Restore this checkpoint

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Lauren Richards 7 years, 10 months ago

Gave some feedback: Needs to be tested

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Lauren Richards commented 7 years, 10 months ago

I have deleted the part d) from this question and added in a much simpler question on squaring fractions.

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Christian Lawson-Perfect 7 years, 10 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect commented 7 years, 10 months ago

This looks good, but part d seems vindictively hard! What's it assessing?

From the advice, it looks like:

BODMAS - this isn't what the question's about

Squaring fractions - have a smaller question on this earlier, e.g. "calculate $\left(\frac{a}{b}\right)^2$ ".

Division of fractions - again, not what the question's about.

I reckon you could just delete part d, or spin it into a separate question.

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Lauren Richards 7 years, 10 months ago

Gave some feedback: Needs to be tested

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Lauren Richards 7 years, 10 months ago

Gave some feedback: Has some problems

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Elliott Fletcher commented 7 years, 10 months ago

Hi Lauren,

It seems that the answer to part c is rewarded 0 marks, i would maybe just reward 2 marks to this part as you have with the other parts.

Also, for part c, i would write "days" next to the answer box, just so it's a bit clearer what the units of the answer are.

I think there is also a slight issue in the advice section for part b, as sometimes the first fraction \displaystyle\simplify{{k}/{j}}, simplifies too much, for example i saw that number as 5 but i think the intended number was 15/3 because then later in the code when you are multiplying the numerators and denominators of both fractions this shows 15 x \var{numif} and 3 x \var{h}, so because the question shows the first fraction in it's simplified form, it's not immediately clear where the other two numbers come from. To fix this, i would maybe set the gcd of k and j to be equal to 1.

Let me know if you have any questions, otherwise i think it looks good!

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Lauren Richards commented 7 years, 10 months ago

Thank you for the feedback. I have enacted your suggestions and corrected the mistakes.

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Lauren Richards 7 years, 10 months ago

Gave some feedback: Needs to be tested

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Vicky Hall commented 7 years, 10 months ago

I would change the staement to say something like 'evaluate the following multiplications, giving each fraction in its simplest form'.

In part b), the expected answer is incorrect. When I tried it, the fraction in its lowest terms was $\displaystyle\frac{81}{104}$ but the expected answer said $\displaystyle\frac{162}{208}$ . The correct answer appears in the advice though.

In part c) the fractions $\displaystyle\frac{3}{7}$ and $\displaystyle\frac{1}{3}$ should be variables. I know you've picked these numbers so that the answer always comes out as a whole number of days, which of course it must, but it would be much better to get Numbas to produce the variables so that the sum will always work out nicely, otherwise students can only do the question once. Also, display these fractions using \frac.

In the advice, you tend to use colons before stating a result. For example, '...final answer is: $\displaystyle\frac{81}{104}$ '. You don't need the colon here, just give the number.

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Vicky Hall 7 years, 10 months ago

Gave some feedback: Has some problems

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Lauren Richards 7 years, 10 months ago

Gave some feedback: Needs to be tested

○

Lauren Richards 7 years, 11 months ago

Created this.

Name	Status	Author	Last Modified
Fraction multiplication	Ready to use	Lauren Richards	20/11/2019 14:39
Jo-Ann's copy of Fraction multiplication	draft	Jo-Ann Lyons	08/10/2018 13:57
NG5 Multiply Fractions	Ready to use	Oliver Spenceley	10/04/2024 09:35

There are 20 other versions that do you not have access to.

Question statement

Evaluate the following multiplications, giving each fraction in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
b	integer	4
c	integer	11
d	integer	8
a_coprime	number	6
b_coprime	number	1
c_coprime	number	11
d_coprime	number	2
gcd_ac	number	1
gcd_bd	number	4
ab	number	6
cd	number	22
gcd	number	2

			Name	Type	Generated Value

f	integer	1
g	integer	5
g_coprime	number	5
h	integer	8
h_coprime	number	8
gcd_gh	number	1
k	integer	3
k_coprime	number	3
j	integer	13
j_coprime	number	13
gcd_kj	number	1
fh	number	8
numif	number	13
num	number	39
denom	number	104
gcda	number	1
gcdb	number	13
gcd2	number	13

			Name	Type	Generated Value

aa	integer	2
bb	integer	56
cc	rational	8
dd	integer	1
ddcc	rational	8
ee	rational	2

			Name	Type	Generated Value

l	integer	12
m	integer	10
gcd_lm	number	2
l_coprime	number	6
m_coprime	number	5
gcd_lcmc	number	1
l_coprime2	number	36
m_coprime2	number	25

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..12 except c)

JME function reference

Description

Random number from 1 to 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`

← Depends on:

This variable doesn't seem to be used anywhere.

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Gap-fill

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

$\displaystyle\frac{\var{a_coprime}}{\var{c_coprime}}\times\frac{\var{b_coprime}}{\var{d_coprime}}$ = Gap 0. Gap 1.

Advice

a)

To multiply $\displaystyle\frac{\var{a_coprime}}{\var{c_coprime}}\times\frac{\var{b_coprime}}{\var{d_coprime}}$ , address the numerators and denominators separately.

Multiply the numerators across both fractions.

$\var{a_coprime}\times\var{b_coprime}=\var{ab}$ ,

and then multiply the denominators across both fractions.

$\var{c_coprime}\times\var{d_coprime}=\var{cd}$ .

The values of the multiplied numerators and denominators will be the numerator and denominator of the new fraction: $\displaystyle\frac{\var{ab}}{\var{cd}}$ .

This answer may need simplifying down, and to do this, find the greatest common divisor in both the numerator and denominator and divide by this number.

The greatest common divisor of $\var{ab}$ and $\var{cd}$ is $\var{gcd}$ .

By using $\var{gcd}$ to cancel down the fraction, the final answer is $\displaystyle\simplify{{ab}/{cd}}$ .

b)

To multiply $\displaystyle\simplify{{k_coprime}/{j_coprime}}\times\var{f}\frac{\var{g_coprime}}{\var{h_coprime}}$ , we first need to change the mixed number term into an improper fraction.

To do this, we need to multiply $(\var{f}\times\var{h_coprime}=\var{fh})$ and add it to what was already on the numerator of the fraction, $\var{g_coprime}$ .

$\displaystyle\frac{(\var{fh}+\var{g_coprime})}{\var{h_coprime}}= \displaystyle\frac{\var{numif}}{\var{h_coprime}}$ .

Next, we multiply the numerators and denominators across both fractions separately, as done in part a).

$\var{k_coprime}\times\var{numif} = \var{num}$ ,

$\var{j_coprime}\times\var{h_coprime}=\var{denom}$ .

This gives the unsimplified version of the new fraction $\displaystyle\frac{\var{num}}{\var{denom}}$ .

To simplify, find the greatest common divisor in both the numerator and denominator and divide by this number.

The greatest common divisor of $\var{num}$ and $\var{denom}$ is $\var{gcdb}$ .

By using $\var{gcdb}$ to cancel down the fraction, the final answer is $\displaystyle\simplify{{num}/{denom}}$ .

c)

To square a fraction means to multiply the fraction by itself. To do this, multiply the numerators and denominators across individually.

$\displaystyle\bigg(\frac{\var{l_coprime}}{\var{m_coprime}}\bigg)^2=\frac{\var{l_coprime}}{\var{m_coprime}}\times\frac{\var{l_coprime}}{\var{m_coprime}}=\frac{\var{l_coprime^2}}{\var{m_coprime^2}}.$

From this, we should look if it is possible to simplify by finding the highest common divisor of $\var{l_coprime^2}$ and $\var{m_coprime^2}.$

The greatest common divisor is $\var{gcd_lcmc}$ .

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

By simplifying with this value, the final answer is

$\displaystyle\frac{\var{l_coprime2}}{\var{m_coprime2}}$ .

d)

Helen was on holiday for $28$ days and spent $\displaystyle\frac{\var{aa}}{7}$ of her time in Spain.

$\displaystyle\frac{\var{aa}}{7}\times\frac{28}{1}=\frac{\var{bb}}{7}=\var{cc}$ days in Spain.

Whilst in Spain, she spends $\displaystyle\frac{\var{dd}}{4}$ of her time in Barcelona.

$\displaystyle\frac{\var{dd}}{4}\times\frac{\var{cc}}{1}=\frac{\var{ddcc}}{4}=\var{ee}$ days in Barcelona.

Give a worked solution to the whole question.

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Elliott Fletcher 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 10 months ago

Christian Lawson-Perfect 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Christian Lawson-Perfect 7 years, 10 months ago

Christian Lawson-Perfect commented 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Elliott Fletcher commented 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Vicky Hall commented 7 years, 10 months ago

Vicky Hall 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards 7 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

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Fraction multiplication

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 10 months ago

Christian Lawson-Perfect 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Christian Lawson-Perfect 7 years, 10 months ago

Christian Lawson-Perfect commented 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Elliott Fletcher commented 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Vicky Hall commented 7 years, 10 months ago

Vicky Hall 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards 7 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`