NG3 Add Fractions

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From users who are members of Skills Audits for Maths and Stats :

Will Morgan	said	Ready to use	1 year, 2 months ago
Oliver Spenceley	said	Needs to be tested	1 year, 2 months ago

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Will Morgan 1 year ago

Published this.

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Will Morgan 1 year, 2 months ago

Gave some feedback: Ready to use

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Oliver Spenceley 1 year, 2 months ago

Gave some feedback: Needs to be tested

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Oliver Spenceley 1 year, 2 months ago

Created this as a copy of Addition and subtraction of fractions.

Name	Status	Author	Last Modified
Addition and subtraction of fractions	Ready to use	Lauren Richards	20/11/2019 14:32
Jo-Ann's copy of Addition and subtraction of fractions	Ready to use	Jo-Ann Lyons	14/01/2019 15:43
surbhi's copy of Addition and subtraction of fractions	draft	surbhi gautam	14/01/2019 15:47
Addition und Subtraktion von Brüchen	Ready to use	Ulrich Görtz	26/11/2020 10:32
NG3 Add Fractions	Ready to use	Oliver Spenceley	10/04/2024 09:35
NG4 Subtract fractions	Ready to use	Andrew Neate	10/04/2024 09:35
AE4 - Multiplication of algebraic fractions 1	Ready to use	Andrew Neate	28/02/2025 13:53

There are 39 other versions that do you not have access to.

Question statement

Evaluate the following addition, giving the fraction in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
a_coprime	number	1
b	integer	10
b_coprime	number	10
gcd_ab	number	1
c	integer	3
c_coprime	number	1
d	integer	6
d_coprime	number	2
gcd_cd	number	3
lcm	number	10
a_coprimed_coprime	number	2
c_coprimeb_coprime	number	10
lcm_b	number	1
lcm_d	number	5
alcm_b	number	1
clcm_d	number	5
alcmclcm	number	6
gcd	number	2
num	number	3
denom	number	5

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..5)

JME function reference

Description

PART A variable a - random number between 1 and 5.

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:

a_coprime
gcd_ab

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

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

Advice

$\displaystyle\frac{\var{a_coprime}}{\var{b_coprime}}+\frac{\var{c_coprime}}{\var{d_coprime}}$

To add or subtract fractions, we need to have a common denominator on both fractions.

To get a common denominator, we need to find the lowest common multiple of the two denominators.

The lowest common multiple of $\var{b_coprime}$ and $\var{d_coprime}$ is $\var{lcm}.$

This will be the new denominator, and we need to multiply each fraction individually to ensure we get this denominator.

For $\displaystyle\frac{\var{a_coprime}}{\var{b_coprime}}$ , we need to multiply the fraction by $\displaystyle\frac{\var{lcm_b}}{\var{lcm_b}}$ to give $\displaystyle\frac{\var{alcm_b}}{\var{lcm}}.$

For $\displaystyle\frac{\var{c_coprime}}{\var{d_coprime}}$ , we need to multiply the fraction by $\displaystyle\frac{\var{lcm_d}}{\var{lcm_d}}$ to give $\displaystyle\frac{\var{clcm_d}}{\var{lcm}}.$

Now that we have each fraction in terms of a common denominator, we can now add the fractions together.

$\displaystyle\frac{\var{alcm_b}}{\var{lcm}}+\frac{\var{clcm_d}}{\var{lcm}}=\frac{(\var{alcm_b}+\var{clcm_d})}{\var{lcm}}=\frac{\var{alcmclcm}}{\var{lcm}}.$

From this, we can try to simplify the result down by finding the greatest common divisor of the numerator and denominator and dividing the whole fraction by this amount.

The greatest common divisor of $\var{alcmclcm}$ and $\var{lcm}$ is $\var{gcd}.$

Simplifying using this value gives a final answer of $\displaystyle\frac{\var{num}}{\var{denom}}.$

Therefore, the expression cannot be simplified further, and $\displaystyle\frac{\var{num}}{\var{denom}}$ is the final answer.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Will Morgan 1 year ago

Will Morgan 1 year, 2 months ago

Oliver Spenceley 1 year, 2 months ago

Oliver Spenceley 1 year, 2 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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NG3 Add Fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 1 year ago

Will Morgan 1 year, 2 months ago

Oliver Spenceley 1 year, 2 months ago

Oliver Spenceley 1 year, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`