Merryn's copy of Fractions: adding and subtracting, numerical

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Merryn Horrocks

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Created this as a copy of Fractions: adding and subtracting, numerical.

Name	Status	Author	Last Modified
Fractions: adding and subtracting, numerical, already with common denominator	Ready to use	Ben Brawn	11/02/2025 23:17
Fractions: adding and subtracting, algebraic, already with common denominator	Ready to use	Ben Brawn	26/03/2025 02:38
Fractions: adding and subtracting, numerical	Ready to use	Ben Brawn	11/02/2025 23:20
Fractions: adding and subtracting, algebraic	Ready to use	Ben Brawn	26/03/2025 02:38
Fractions: multiplying, algebraic	Ready to use	Ben Brawn	26/03/2025 04:18
Merryn's copy of Fractions: adding and subtracting, numerical	Ready to use	Merryn Horrocks	07/03/2024 01:07
Merryn's copy of Fractions: adding and subtracting, numerical, already with common denominator	Ready to use	Merryn Horrocks	07/03/2024 01:07

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Question statement

Express the following as a single fraction (using / as the fraction bar).

Give any introductory information the student needs.

			Name	Type	Generated Value

numbers	list	[ 7, 5 ]
num1	integer	7
num2	integer	5
addSub	integer	-1
cf	integer	2
extrafactor	list	[ 2, 1 ]
den1	integer	4
den2	integer	2
ansden	integer	4
ansnum	integer	-3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
shuffle([2,3,5,7,11,13,17,19,23,29])[0..2]

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 7, 5 ]

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Number entry
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$=$ Unnamed gap

Advice

We need to get the denominators to be the same, preferably the lowest common denominator, at which point, we can simply addsubtract the new numerators and put the result over the common denominator.

Since $\var{den1}=\var{cf}\times\var{extrafactor[0]}$ and $\var{den2}=\var{cf}\times \var{extrafactor[1]}$ the lowest common denominator will be the product $\var{cf}\times \var{extrafactor[0]}\times \var{extrafactor[1]}$ , that is, $\var{ansden}$ . Therefore, we will multiply the first fraction by $\frac{\var{extrafactor[1]}}{\var{extrafactor[1]}}$ and the second fraction by $\frac{\var{extrafactor[0]}}{\var{extrafactor[0]}}$ as follows.

$\begin{align*}\dfrac{\var{num1}}{\var{den1}}+\dfrac{\var{num2}}{\var{den2}}&=\dfrac{\var{num1}\times \var{extrafactor[1]}}{\var{den1}\times \var{extrafactor[1]}}+\dfrac{\var{num2}\times \var{extrafactor[0]}}{\var{den2}\times \var{extrafactor[0]}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}}{\var{ansden}}+\dfrac{\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}+\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{ansNum}}{\var{ansden}}\end{align*}$

$\begin{align*}\dfrac{\var{num1}}{\var{den1}}-\dfrac{\var{num2}}{\var{den2}}&=\dfrac{\var{num1}\times \var{extrafactor[1]}}{\var{den1}\times \var{extrafactor[1]}}-\dfrac{\var{num2}\times \var{extrafactor[0]}}{\var{den2}\times \var{extrafactor[0]}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}}{\var{ansden}}-\dfrac{\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}-\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{ansNum}}{\var{ansden}}\end{align*}$

Since $\var{den2}=\var{cf}\times \var{extrafactor[1]}$ and the other denominator is $\var{den1}$ , the lowest common denominator will be the product $\var{cf}\times \var{extrafactor[1]}$ , that is, $\var{ansden}$ . Therefore, we will multiply the first fraction by $\frac{\var{extrafactor[1]}}{\var{extrafactor[1]}}$ as follows.

$\begin{align*}\dfrac{\var{num1}}{\var{den1}}+\dfrac{\var{num2}}{\var{den2}}&=\dfrac{\var{num1}\times \var{extrafactor[1]}}{\var{den1}\times \var{extrafactor[1]}}+\dfrac{\var{num2}}{\var{den2}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}}{\var{ansden}}+\dfrac{\var{num2}}{\var{ansden}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}+\var{num2}}{\var{ansden}}\\[3pt]&=\dfrac{\var{ansNum}}{\var{ansden}}\end{align*}$

$\begin{align*}\dfrac{\var{num1}}{\var{den1}}-\dfrac{\var{num2}}{\var{den2}}&=\dfrac{\var{num1}\times \var{extrafactor[1]}}{\var{den1}\times \var{extrafactor[1]}}-\dfrac{\var{num2}}{\var{den2}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}}{\var{ansden}}-\dfrac{\var{num2}}{\var{ansden}}\\[3pt]&=\dfrac{\var{num1*extrafactor[1]}-\var{num2}}{\var{ansden}}\\[3pt]&=\dfrac{\var{ansNum}}{\var{ansden}}\end{align*}$

Since $\var{den1}=\var{cf}\times\var{extrafactor[0]}$ and the other denominator is $\var{den2}$ , the lowest common denominator will be the product $\var{cf}\times \var{extrafactor[0]}$ , that is, $\var{ansden}$ . Therefore, we will multiply the second fraction by $\frac{\var{extrafactor[0]}}{\var{extrafactor[0]}}$ as follows.

$\begin{align*}\dfrac{\var{num1}}{\var{den1}}+\dfrac{\var{num2}}{\var{den2}}&=\dfrac{\var{num1}}{\var{den1}}+\dfrac{\var{num2}\times \var{extrafactor[0]}}{\var{den2}\times \var{extrafactor[0]}}\\[3pt]&=\dfrac{\var{num1}}{\var{ansden}}+\dfrac{\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{num1}+\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{ansNum}}{\var{ansden}}\end{align*}$

$\begin{align*}\dfrac{\var{num1}}{\var{den1}}-\dfrac{\var{num2}}{\var{den2}}&=\dfrac{\var{num1}}{\var{den1}}-\dfrac{\var{num2}\times \var{extrafactor[0]}}{\var{den2}\times \var{extrafactor[0]}}\\[3pt]&=\dfrac{\var{num1}}{\var{ansden}}-\dfrac{\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{num1}-\var{num2*extrafactor[0]}}{\var{ansden}}\\[3pt]&=\dfrac{\var{ansNum}}{\var{ansden}}\end{align*}$

Since there are no common factors between the two denominators (other than $1$ ) the lowest common denominator will just be the product of the two denominators. Therefore, we will multiply the first fraction by $\frac{\var{extrafactor[1]}}{\var{extrafactor[1]}}$ and the second fraction by $\frac{\var{extrafactor[0]}}{\var{extrafactor[0]}}$ as follows.

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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 Fractions: adding and subtracting, numerical

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Taxonomy: mathcentre

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Merryn Horrocks 1 year, 1 month ago

Merryn Horrocks 1 year, 1 month ago

Merryn Horrocks 1 year, 1 month ago

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Generated value: `list`

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Merryn's copy of Fractions: adding and subtracting, numerical

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 1 month ago

Merryn Horrocks 1 year, 1 month ago

Merryn Horrocks 1 year, 1 month ago

Error in variable testing condition

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Generated value: list

Parts

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Generated value: `list`