TMN3704 Assignment 4 2025 (EXCEPTIONAL ANSWERS) DUE 14 August 2025

TMN3704
Assignment 4
DUE 14 August 2025

,TMN3704

Assignment 4

DUE 14 August 2025



Question 1.5.1: What error did Moeli make?

Problem Statement:

Moeli attempted to simplify the addition of fractions:




His response:




Step 1: Understand the correct method for adding fractions

To add fractions, find a common denominator, convert each fraction to an equivalent

fraction with that denominator, add the numerators, and simplify if necessary. For + ,
the denominators are 3 and 6. The least common denominator (LCD) is 6.

Step 2: Perform the correct calculation

• Convert to a fraction with denominator 6: .

• Add to : + = = .

• Simplify : Divide numerator and denominator by 3, giving .

Step 3: Analyze Moeli’s response

Moeli’s steps:

• .

• This becomes + .

• Moeli then states = , which is incorrect.




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, Step 4: Identify the error

• First error:
Moeli incorrectly manipulated the fractions.

For ,
Moeli wrote

, which is not equivalent to (since would be correct for a

denominator of 15). Similarly, for , Moeli wrote , which is correct but

inconsistent with the denominator used for .

• Second error:

Moeli added fractions with different denominators ( + ) without finding a

common denominator, leading to the incorrect claim that = .

• Third error:

The equality = is mathematically incorrect, as = and = , which are not
equal.

Final Answer: Moeli’s errors were: (1) incorrectly manipulating fractions to get

instead of for , (2) adding fractions with different denominators without finding a

common denominator, and (3) incorrectly stating = .




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