What is the result when you convert .375 to a fraction and reduce? A) 3/8 · B) 3 75/100 · C) 375/1000 · D) 15/40
The correct answer is A. 3/8. When you express .375 as a fraction, you first write it as 375/1000, then divide both the numerator and denominator by their greatest common factor (125) to get 3/8 — the simplest form.
Why 3/8 Is the Correct Reduced Fraction
The decimal 0.375 has three digits after the decimal point, so it sits over 1,000: 375/1000. To reduce any fraction you need the greatest common factor (GCF) of the numerator and denominator. Break each number down: 375 = 3 × 5 × 5 × 5, and 1000 = 2 × 2 × 2 × 5 × 5 × 5. The shared factors are 5 × 5 × 5 = 125. Divide both parts by 125 and you land on 375 ÷ 125 = 3 for the numerator and 1000 ÷ 125 = 8 for the denominator. The result, 3/8, cannot be simplified any further because 3 is prime and does not divide evenly into 8.
You can verify by reversing the process: 3 ÷ 8 = 0.375. That confirms the conversion is exact — no rounding, no repeating decimal, just a clean equivalence.
Why the Other Choices Are Wrong
B) 3 75/100 equals the mixed number 3.75 — ten times larger than 0.375. This option likely trips up anyone who misreads the decimal point or accidentally shifts it one place to the right. If you see a whole number sitting in front of a fraction in an answer choice, check whether the original decimal is less than 1. Here 0.375 is clearly less than 1, so no whole-number part should exist.
C) 375/1000 is mathematically equal to 0.375, so the value itself is correct. The problem is that the question asks you to reduce the fraction. 375 and 1000 share a common factor of 125, meaning 375/1000 is not in simplest form. This is the most tempting wrong answer because students who know how to convert but skip the simplification step will pick it and feel confident.
D) 15/40 also equals 0.375 (15 ÷ 40 = 0.375), yet it too is not fully reduced. Both 15 and 40 are divisible by 5, giving 3/8. Think of 15/40 as a halfway-simplified version — someone divided 375 and 1000 each by 25 instead of the full 125. Partial reduction is not enough when the question demands the simplest form.
Understanding Decimal-to-Fraction Conversion
Every terminating decimal can be written as a fraction whose denominator is a power of 10. Count the decimal places: one digit gives 10, two digits give 100, three digits give 1,000, and so on. Once you have that raw fraction, the remaining work is finding the GCF and dividing. For numbers ending in 5 or 0, the GCF almost always involves factors of 5 — and often factors of 2 as well, since powers of 10 are built from 2s and 5s. Recognizing this pattern speeds up simplification considerably.
Expressing 0.375 as a fraction is a common exercise precisely because it produces a clean, familiar result (3/8) that students can cross-check on a number line or by long division.
Quick Tips for Similar Questions
Memorize the “eighths” family — they show up constantly: 0.125 = 1/8, 0.25 = 2/8 = 1/4, 0.375 = 3/8, 0.5 = 4/8 = 1/2, 0.625 = 5/8, 0.75 = 6/8 = 3/4, 0.875 = 7/8. Once you know these, any multiple-choice question involving these decimals is instantly recognizable.
When a question says “convert and reduce,” treat any answer that is not in lowest terms as automatically wrong, even if its decimal value is correct. Scan each answer choice: if both numbers share an obvious common factor (both even, both ending in 0 or 5), that choice has not been fully simplified. This single habit eliminates traps like 375/1000 and 15/40 in seconds.
