Express the decimals 0.875 and 0.375 as fractions in simplest form and choose the correct pair.

Introduction / Context:
This question checks your ability to convert two terminating decimals into fractions and then simplify those fractions. It is a direct extension of basic decimal to fraction conversion and is useful when working with ratios, probabilities, and percentage calculations.

Given Data / Assumptions:

• First decimal: 0.875.
• Second decimal: 0.375.
• We must express both as fractions in simplest form and then select the correct pair.

Concept / Approach:
For a decimal with three digits after the decimal point, we can initially write it as a fraction over 1000 and then simplify by dividing numerator and denominator by their greatest common divisor. We apply this procedure separately to 0.875 and 0.375 and then match the results with the options.

Step-by-Step Solution:
Step 1: Convert 0.875 to a fraction. It has three decimal places, so write 0.875 as 875/1000. Step 2: Simplify 875/1000. Both 875 and 1000 are divisible by 125. 875 / 125 = 7 and 1000 / 125 = 8, so 0.875 = 7/8. Step 3: Convert 0.375 to a fraction. It also has three decimal places, so write 0.375 as 375/1000. Step 4: Simplify 375/1000. Both are divisible by 125. 375 / 125 = 3 and 1000 / 125 = 8, so 0.375 = 3/8. Step 5: Therefore, the correct pair is 7/8 and 3/8.

Verification / Alternative check:
We can verify by reconverting the fractions to decimals. 7/8 equals 0.875, because 1/8 is 0.125 and 7 times that is 0.875. Similarly, 3/8 equals 0.375, since 3 times 0.125 is 0.375. This confirms that the pair 7/8 and 3/8 is correct. None of the other answer choices correspond to these decimal values when converted back.

Why Other Options Are Wrong:
3/11 and 7/11 are repeating decimals with denominators 11 and do not equal 0.875 or 0.375.
7/9 and 9/13 give different decimal values far from 0.875 and 0.375.
7/9 and 9/11 also do not match the given decimals and do not simplify to eighths.

Common Pitfalls:
A common mistake is to divide 875 and 1000 by 25 or 5 but not continue simplification, leaving the fraction not fully reduced. Another issue is miscounting decimal places and writing 0.875 as 875/100 or 875/10000. Always match the number of decimal digits with the correct power of 10 in the denominator and then simplify completely.

Final Answer:
The correct pair of fractions is 7/8 and 3/8.