Division of fractions

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Christian Lawson-Perfect	said	Ready to use	7 years, 9 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, 9 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 9 months ago

Saved a 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 scrapped part e) as it didn't really fit with the question and it should now be fine.

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Lauren Richards commented 7 years, 10 months ago

Vicky, I have tried to change part e to be variables but struggled and it needs a bit of work still.

It is coming out as a whole integer at the end which is correct, but some of the numbers earlier in the question are unrealistic and in some cases at the start I am also getting mixed numbers with a 0 on the numerator and can't work out how to stop that at the moment.

I worked backwards, so created mixed numbers from improper fractions but the user will start with the mixed numbers.

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Vicky Hall 7 years, 10 months ago

Gave some feedback: Has some problems

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Vicky Hall commented 7 years, 10 months ago

I'm not sure if this is a problem across all parts but when I tried the question, the fraction $\displaystyle\frac{2}{30}$ appeared in part b). All fractions should be in their simplest form so make sure the numbers you use are coprime.

In part c), the answer I got was $\displaystyle\frac{525}{352}$ which is huge! The reason for this is that the denominators in the fractions in the question are large, so make them smaller. Otherwise, the student will just do the sum with a calculator to avoid the multiplication being too tedious. Remember, this is to test division of fractions rather than multiplication.

Make the numbers in part e) variables.

In the advice, remove any colons that appear before your solutions.

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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

Created this.

Name	Status	Author	Last Modified
Division of fractions	Ready to use	Lauren Richards	20/11/2019 14:37
Jo-Ann's copy of Division of fractions	Ready to use	Jo-Ann Lyons	08/10/2018 14:46
NG6 Divide Fractions	Ready to use	Oliver Spenceley	10/04/2024 09:36
Merryn's copy of Dividing fractions	Ready to use	Merryn Horrocks	08/03/2024 01:13
Merryn's copy of Division of fractions	Ready to use	Merryn Horrocks	08/03/2024 01:17

There are 19 other versions that do you not have access to.

Question statement

Evaluate the following sums involving division of fractions. Simplify your answers where possible.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	10
b	integer	2
c	integer	2
d	integer	11
bd	integer	22
ad	integer	110
gcd	number	10
ad_gcd	number	11
bcd_gcd	number	2
bd_c	integer	20

			Name	Type	Generated Value

f	integer	6
g	integer	7
f_coprime	number	6
g_coprime	number	7
h	integer	4
j	integer	6
h_coprime	number	2
j_coprime	number	3
fj	number	18
gh	number	14
gcd1	number	2

			Name	Type	Generated Value

f1	integer	6
g1	integer	8
f1_coprime	number	3
g1_coprime	number	4
h1	integer	5
j1	integer	10
h1_coprime	number	1
j1_coprime	number	2
f1j1	number	6
g1h1	number	4
gcd2	number	2

			Name	Type	Generated Value

f3	integer	2
g3	integer	2
h3	integer	6
g3_coprime	number	1
h3_coprime	number	3
f4	integer	3
g4	integer	5
h4	integer	7
g4_coprime	number	5
h4_coprime	number	7
f3h3	number	6
f4h4	number	21
num	number	49
denom	number	78
gcd3	number	1

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Random number between 1 and 20

Used by part d)

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:

This variable doesn't seem to be used anywhere.

Parts

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Part c) Gap-fill
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Part d) Gap-fill
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Gap-fill

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

$\displaystyle\frac{\var{f_coprime}}{\var{g_coprime}}\div\frac{\var{h_coprime}}{\var{j_coprime}}=$ Gap 0. Gap 1.

Advice

a)

When faced with dividing fractions, it much easier to switch one of the fractions around and multiply them together instead of divide them.

$\left( \frac{\var{f_coprime}}{\var{g_coprime}}\div\frac{\var{h_coprime}}{\var{j_coprime}} \right) \equiv \left( \frac{\var{f_coprime}}{\var{g_coprime}}\times\frac{\var{j_coprime}}{\var{h_coprime}} \right) = \frac{\var{fj}}{\var{gh}}$

Then, simplify by finding the highest common divisor in the numerator and denominator which in this case is $\var{gcd1}$ .

This gives a final answer of $\displaystyle\simplify{{fj}/{gh}}$ .

b)

$\frac{\var{f1_coprime}}{\var{g1_coprime}}\div\frac{\var{h1_coprime}}{\var{j1_coprime}} \equiv \left( \frac{\var{f1_coprime}}{\var{g1_coprime}}\times\frac{\var{j1_coprime}}{\var{h1_coprime}} \right)=\frac{\var{f1j1}}{\var{g1h1}}$

Then, simplify by finding the highest common divisor in the numerator and denominator which in this case is $\var{gcd2}$ .

This gives a final answer of $\displaystyle\simplify{{f1j1}/{g1h1}}$ .

c)

${\var{f3}\frac{\var{g3_coprime}}{\var{h3_coprime}}}\div{\var{f4}\frac{\var{g4_coprime}}{\var{h4_coprime}}}$

The first thing to do is to change the mixed numbers into improper fractions.

An improper fraction is a fraction where the numerator is greater than the denominator. To change a mixed fraction to an improper fraction, multiply the integer part of the mixed number by the denominator, and add it to the existing numerator to make the new numerator of the improper fraction. The denominator will stay the same.

${\var{f3}\frac{\var{g3_coprime}}{\var{h3_coprime}}}\equiv\frac{(\var{f3}\times\var{h3_coprime})+\var{g3_coprime}}{\var{h3_coprime}}=\frac{\var{f3h3}+\var{g3_coprime}}{\var{h3_coprime}}=\frac{\var{f3h3+g3_coprime}}{\var{h3_coprime}}$

${\var{f4}\frac{\var{g4_coprime}}{\var{h4_coprime}}}\equiv\frac{(\var{f4}\times\var{h4_coprime})+\var{g4_coprime}}{\var{h4_coprime}}=\frac{\var{f4h4}+\var{g4_coprime}}{\var{h4_coprime}}=\frac{\var{f4h4+g4_coprime}}{\var{h4_coprime}}$

We now have our mixed numbers as improper fractions.

$\frac{\var{f3h3+g3_coprime}}{\var{h3_coprime}}\div\frac{\var{f4h4+g4_coprime}}{\var{h4_coprime}}$

Now, use the same method as in parts a) and b) to divide by switching around one fraction and changing the division symbol to multiplication.

$\frac{\var{f3h3+g3_coprime}}{\var{h3_coprime}}\div\frac{\var{f4h4+g4_coprime}}{\var{h4_coprime}}\equiv\frac{\var{f3h3+g3_coprime}}{\var{h3_coprime}}\times\frac{\var{h4_coprime}}{\var{f4h4+g4_coprime}}=\frac{\var{num}}{\var{denom}}$

Finally, the last thing to do is to simplify your answer down by finding the highest common divisor in the numerator and denominator, which in this case is $\var{gcd3}$ .

By doing this, you will get a final answer of

$\simplify{{num}/{denom}}$

d)

$\frac{\var{a}}{(\simplify[all,!collectNumbers]{{b}-{c}/{d}})}$

Consider the denominator first, as following the rules of BODMAS, you should address brackets first.

You need to get a common denominator for both terms on the denominator, like this:

$\var{b}\times\frac{\var{d}}{\var{d}} = \frac{\var{bd}}{\var{d}}$

This now allows you to complete the addition or subtraction as both terms have a common denominator.

${\simplify[all,!collectNumbers]{{bd}/{d}-{c}/{d}}} = \frac{\var{bd_c}}{\var{d}}$

This means that the expression is now:

$\frac{\var{a}}{\frac{\var{bd_c}}{\var{d}}}$

Dealing with this requires a bit of manipulation. You have to change the divisor of the denominator to be a mulitplier of the numerator. The denominator, ${\var{bd_c}}$ was being divided by ${\var{d}}$ but by flipping it around, the numerator, ${\var{a}}$ will be mulitplied by ${\var{d}}$ . The value of the expression remains the same.

$\frac{\var{a}}{\frac{\var{bd_c}}{\var{d}}}\equiv \frac{(\var{a})\times(\var{d})}{\var{bd_c}}= \frac{\var{ad}}{\var{bd_c}}$

From this, you can try to cancel the expression down by finding the highest common factor of the numerator and denominator, to give a final answer of

$\simplify{{ad}/{bd_c}}$

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Taxonomy: mathcentre

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Elliott Fletcher 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Vicky Hall 7 years, 10 months ago

Vicky Hall commented 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

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Division of fractions

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, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Vicky Hall 7 years, 10 months ago

Vicky Hall commented 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Lauren Richards 7 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`