Question

ed ema final exam fall 2025
which of the following best correctly explains and shows how to reduce a rational number? the best correct answer should use the vocabulary \divisibility/divisible\ and factors and explain how you know you are done simplifying/reducing the rational number, and the example work should explain and show each step. (1 point)
a
to reduce a rational number you use the factors of the numerator and denominator. you have to use a factor that both the numerator and denominator are divisible by. to simplify/reduce you divide the numerator and denominator by their largest common factor until either one is a prime number, and the other number is not divisible by that prime number or the numerator and denominator are not divisible by the same number.
example: \\(\frac{25}{40}\\) --> both the numerator and denominator are divisible by 5 --> \\(25 \div 5 = 5\\) and \\(40 \div 5 = 8\\) --> so \\(\frac{25}{40} = \frac{5}{8}\\) and 5 is a prime number, and 8 is not divisible by 5, so this is simplified/reduced fully.
b
to reduce a rational number you divide the numerator and denominator by the same number.
example: \\(\frac{25}{40}\\) --> \\(25 \div 5 = 5\\) and \\(40 \div 5 = 8\\) --> so \\(\frac{25}{40} = \frac{5}{8}\\)
c
to reduce a rational number you use the factors of the numerator and denominator. yo know you have fully simplified/reduced the rational number when the numerator and denominator are not divisible by the same number
example: \\(\frac{25}{40} = \frac{5}{8}\\)
d
\\(\frac{25}{40}\\) --> both the numerator and denominator are divisible by 5 --> \\(25 \div 5 = 5\\) and \\(40 \div 5 = 8\\) --> so \\(\frac{25}{40} = \frac{5}{8}\\) and 5 is a prime number, and 8 is not divisible by 5, so this is simplified/reduced fully

Explanation:

To determine the best answer, we analyze each option:

• Option A: It correctly explains using factors (specifically the largest common factor) that both numerator and denominator are divisible by, and defines when simplification is done (until one is prime and the other not divisible by it or they share no common divisors). The example also shows each step with the vocabulary "divisible" and factors.
• Option B: Lacks the key vocabulary "divisibility/divisible" in the explanation and doesn't explain when simplification is complete.
• Option C: Has a typo ("Yo" instead of "You") and the explanation is incomplete (doesn't mention using a common factor or the process clearly), and the example is just the result.
• Option D: Only provides the example with some explanation but lacks the initial clear explanation of the process of reducing a rational number (like defining the use of factors and divisibility).

So Option A is the best as it meets all the requirements: uses the required vocabulary, explains the process (including when to stop), and shows the example with steps.

Answer:

A. To reduce a rational number you use the factors of the numerator and denominator. You have to use a factor that both the numerator and denominator are divisible by. To simplify/reduce you divide the numerator and denominator by their largest common factor until either one is a prime number, and the other number is not divisible by that prime number OR the numerator and denominator are not divisible by the same number. Example: $\frac{25}{40}$ --> both the numerator and denominator are divisible by 5 --> $25 \div 5 = 5$ and $40 \div 5 = 8$ --> so $\frac{25}{40} = \frac{5}{8}$ and 5 is a prime number, and 8 is not divisible by 5, so this is simplified/reduced fully.