To determine where Noa first made an error, let's analyze each step of his work:
Step 1: Noa computes: \[ 45 \frac{1}{3} - 37 \frac{5}{8} \]
This is correct as he properly states the subtraction of the two numbers.
Step 2: He converts the mixed numbers to improper fractions:
- \( 45 \frac{1}{3} = \frac{136}{3} \)
- \( 37 \frac{5}{8} = \frac{301}{8} \)
Then he attempts to find a common denominator, which is 24. However, he seems to incorrectly convert the fractions:
- \( 45 \frac{1}{3} \) should be converted as follows: \[ 45 \frac{1}{3} = 45 + \frac{1}{3} = \frac{135}{3} + \frac{1}{3} = \frac{136}{3} \] which correctly converts to: \[ \frac{136}{3} \times \frac{8}{8} = \frac{1088}{24} \]
- \( 37 \frac{5}{8} \): \[ 37 \frac{5}{8} = 37 + \frac{5}{8} = \frac{296}{8} + \frac{5}{8} = \frac{301}{8} \] which converts to: \[ \frac{301}{8} \times \frac{3}{3} = \frac{903}{24} \]
Therefore, he mistakenly represents: \[ 45 \frac{1}{3} = 45 \frac{8}{24} \] and: \[ 37 \frac{5}{8} = 37 \frac{15}{24} \]
These conversions are incorrect in their representation as fractions, where he converts the whole numbers improperly.
Step 3: In this step he states: \[ 44 \frac{32}{24} - 37 \frac{15}{24} \] This itself doesn't make sense as he doesn’t keep the proper fractions and their conversions correct from Step 2.
Step 4: The subtraction is done here, but since the previous steps were flawed, the entire conclusion is based on incorrect fractions.
Final decision: Noa first made an error in Step 2 when trying to convert the fractions into a common denominator format. Thus the answer is: Step 2.