Merryn's copy of Division of fractions

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Merryn Horrocks 1 year ago

Created this as a copy of Division of fractions.

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	9
c	integer	7
d	integer	13
bd	integer	117
ad	integer	130
gcd	number	10
ad_gcd	number	13
bcd_gcd	number	11
bd_c	integer	110

			Name	Type	Generated Value

f	integer	4
g	integer	11
f_coprime	number	4
g_coprime	number	11
h	integer	10
j	integer	11
h_coprime	number	10
j_coprime	number	11
fj	number	44
gh	number	110
gcd1	number	22

			Name	Type	Generated Value

f1	integer	2
g1	integer	6
f1_coprime	number	1
g1_coprime	number	3
h1	integer	8
j1	integer	11
h1_coprime	number	8
j1_coprime	number	11
f1j1	number	11
g1h1	number	24
gcd2	number	1

			Name	Type	Generated Value

f3	integer	3
g3	integer	3
h3	integer	8
g3_coprime	number	3
h3_coprime	number	8
f4	integer	3
g4	integer	3
h4	integer	5
g4_coprime	number	3
h4_coprime	number	5
f3h3	number	24
f4h4	number	15
num	number	135
denom	number	144
gcd3	number	9

			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:

Advice
"Part d)" - prompt

Parts

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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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This question is used in the following exams:

MPR Practice Questions by Merryn Horrocks in MESH.
Fractions Multiplication and Division by P Oak in P's workspace.

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Taxonomy: mathcentre

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Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

Merryn Horrocks 1 year ago

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Generated value: `integer`

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Gap-fill

a)

b)

c)

d)

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Merryn's copy of Division of 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

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`