Question

The simplest form of \( 0.\overline{3} + 0.\overline{4} \) is

• A. \( \frac{7}{10} \)
• B. \( \frac{7}{9} \)
• C. \( \frac{7}{11} \)
• D. \( \frac{7}{99} \)

Hint:

Convert repeating decimals to fractions before performing arithmetic operations. This approach helps in accurately determining the results of operations involving periodic decimals.

Answer 1

The Correct Option is B

Step 1: Express the repeating decimals as fractions: \[ 0.\overline{3} = \frac{1}{3}, \quad 0.\overline{4} = \frac{4}{9} \] Step 2: Add the two fractions: \[ \frac{1}{3} + \frac{4}{9} = \frac{3}{9} + \frac{4}{9} = \frac{7}{9} \] Thus, the simplest form of the sum is \( \boxed{\frac{7}{9}} \).