Question

Simplest form of \( \frac{148}{185} \) is

• A. \( \frac{4}{5} \)
• B. \( \frac{5}{7} \)
• C. \( \frac{5}{4} \)
• D. \( \frac{7}{5} \)

Hint:

When simplifying fractions with large numbers, look for less common prime factors like 11, 13, 17, 19, 37, etc., after checking for the easy ones (2, 3, 5). In this case, recognizing that 185 is `5 * 37` is the key. Then you can check if 148 is also divisible by 37.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
To find the simplest form of a fraction, we need to divide both the numerator and the denominator by their Highest Common Factor (HCF).
Step 2: Key Formula or Approach:
We will find the HCF of 148 and 185 using prime factorization.
Step 3: Detailed Explanation:
First, find the prime factors of the numerator, 148.
\[ 148 = 2 \times 74 = 2 \times 2 \times 37 = 2^2 \times 37 \] Next, find the prime factors of the denominator, 185. Since it ends in 5, it is divisible by 5.
\[ 185 = 5 \times 37 \] The highest common factor (HCF) is the common prime factor, which is 37.
Now, divide both the numerator and the denominator by their HCF (37).
\[ \frac{148 \div 37}{185 \div 37} = \frac{4}{5} \] Step 4: Final Answer:
The simplest form of \( \frac{148}{185} \) is \( \frac{4}{5} \).