Unit-fraction counting in a mixed number How many parts of size 1/8 are contained in 37 1/2?

Introduction / Context:
Problems that ask “how many 1/n are in a quantity” check a core ratio idea: the count equals total quantity divided by the unit size. When the quantity is a mixed number, convert to an improper fraction or a decimal to proceed cleanly.

Given Data / Assumptions:

• Total amount: 37 1/2.
• Unit size: 1/8.
• We want the exact number of such unit parts contained in the total.

Concept / Approach:
The count of unit fractions equals (Total) / (Unit). Division by a unit fraction 1/8 is equivalent to multiplying by 8. Converting 37 1/2 to 37.5 or to an improper fraction makes the multiplication straightforward.

Step-by-Step Solution:
Convert 37 1/2 to 37.5 (or 75/2).Compute count: 37.5 ÷ (1/8) = 37.5 * 8.Multiply: 37.5 * 8 = 300 (since 8 * 30 = 240 and 8 * 7.5 = 60; 240 + 60 = 300).Therefore, there are exactly 300 parts of size 1/8.

Verification / Alternative check:
Fraction route: (75/2) ÷ (1/8) = (75/2) * 8 = 75 * 4 = 300. Both methods agree precisely.

Why Other Options Are Wrong:
400 and 500 result from multiplying by 10 or 16 incorrectly.“Cannot be determined” is not applicable; the values are exact and sufficient.

Common Pitfalls:
Dividing by 8 instead of multiplying by 8; misreading 37 1/2 as 37/2; or mixing decimal and fraction methods mid-stream. Keep a single, consistent method.

Final Answer:
300