what is the value of 0.75 - 0.overline{3}? write your answer as a fraction in lowest terms.

Explanation:

Step1: Convert decimals to fractions

$0.75=\frac{75}{100}=\frac{3}{4}$, and $0.\overline{3}=\frac{1}{3}$ (since if $x = 0.\overline{3}=0.333\cdots$, then $10x=3.333\cdots$, and $10x - x=3$, so $9x = 3$ and $x=\frac{1}{3}$).

Step2: Find a common - denominator

The common denominator of 4 and 3 is 12. So $\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$ and $\frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12}$.

Step3: Subtract the fractions

$\frac{9}{12}-\frac{4}{12}=\frac{9 - 4}{12}=\frac{5}{12}$.

Answer:

$\frac{5}{12}$