Question

Which simplified fraction is equal to 0.5ModifyingAbove 3 with bar?
StartFraction 24 Over 45 EndFraction
StartFraction 8 Over 15 EndFraction
StartFraction 48 Over 90 EndFraction
StartFraction 5 Over 9 EndFraction

Answer 1

The notation \( 0.5\overline{3} \) indicates a recurring decimal, which can be expressed as follows:

\[
0.5\overline{3} = 0.5333333\ldots
\]

To convert \( 0.5\overline{3} \) into a fraction, let’s denote it by \( x \):

\[
x = 0.5\overline{3}
\]

To eliminate the repeating part, we can manipulate the equation:

1. Multiply both sides by 10 to shift the decimal point:
\[
10x = 5.33333\ldots
\]

2. Multiply both sides by 100 to shift the decimal two places:
\[
100x = 53.33333\ldots
\]

Now we have:
\[
10x = 5.33333\ldots
\]
\[
100x = 53.33333\ldots
\]

Subtract the first equation from the second:
\[
100x - 10x = 53.33333... - 5.33333...
\]
\[
90x = 48
\]

Now solve for \( x \):
\[
x = \frac{48}{90}
\]

Next, we need to simplify \( \frac{48}{90} \):
The greatest common divisor (GCD) of 48 and 90 is 6.

Dividing both the numerator and the denominator by 6 gives:
\[
\frac{48 \div 6}{90 \div 6} = \frac{8}{15}
\]

Thus, the simplified fraction equal to \( 0.5\overline{3} \) is:

\[
\frac{8}{15}
\]

From the options provided, the answer is:

\(
\frac{8}{15}
\)