Sure, let's go through the problem step-by-step:
We are given the expression to solve:
[tex]\[ 135 \frac{1}{2} - \frac{2}{3} \][/tex]
1. Separate the whole number and fractional parts of the first term:
The first term is [tex]\( 135 \frac{1}{2} \)[/tex], which can be separated into:
[tex]\[ 135 \text{ (whole number)} \][/tex]
[tex]\[ \frac{1}{2} \text{ (fractional part)} \][/tex]
2. Convert the fractions to have a common denominator:
The two fractions we need to subtract are:
[tex]\[ \frac{1}{2} \text{ and } \frac{2}{3} \][/tex]
We need a common denominator to subtract these fractions. The least common multiple (LCM) of 2 and 3 is 6.
To convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 6:
[tex]\[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \][/tex]
To convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with a denominator of 6:
[tex]\[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \][/tex]
3. Subtract the fractions:
Now we subtract the fractions [tex]\(\frac{3}{6}\)[/tex] and [tex]\(\frac{4}{6}\)[/tex]:
[tex]\[ \frac{3}{6} - \frac{4}{6} = \frac{3 - 4}{6} = \frac{-1}{6} \][/tex]
4. Combine the result with the whole number:
Since we have [tex]\(\frac{-1}{6}\)[/tex], we need to adjust the whole number accordingly:
[tex]\[ 135 - \frac{1}{6} \][/tex]
To perform this operation, subtract 1 from the whole number and add the fraction:
[tex]\[ 135 - 1 = 134 \][/tex]
[tex]\[ 134 + \left(1 - \frac{1}{6}\right) \][/tex]
[tex]\[ 1 - \frac{1}{6} = \frac{6}{6} - \frac{1}{6} = \frac{5}{6} \][/tex]
Therefore, combining these we get:
[tex]\[ 134 \frac{5}{6} \][/tex]
So, the simplified form of [tex]\( 135 \frac{1}{2} - \frac{2}{3} \)[/tex] is:
[tex]\[ 134 \frac{5}{6} \][/tex]
