Certainly! Let's break down each expression and look at the simplified form step-by-step:
### Expression 1: [tex]\(\frac{1}{2} a - \frac{1}{3} b\)[/tex]
1. Identify the coefficients of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- Coefficient of [tex]\(a\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
- Coefficient of [tex]\(b\)[/tex] is [tex]\(-\frac{1}{3}\)[/tex].
2. Combine the terms:
- The expression remains as it is because we are already in its simplest form.
Thus, the simplified form of the first expression is:
[tex]\[ \frac{1}{2}a - \frac{1}{3}b \][/tex]
### Expression 2: [tex]\(-a + \frac{2}{3} b\)[/tex]
1. Identify the coefficients of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- Coefficient of [tex]\(a\)[/tex] is [tex]\(-1\)[/tex].
- Coefficient of [tex]\(b\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
2. Combine the terms:
- The expression remains as it is because we are already in its simplest form.
Thus, the simplified form of the second expression is:
[tex]\[ -a + \frac{2}{3}b \][/tex]
### Expression 3: [tex]\(\frac{3}{4} a - b\)[/tex]
1. Identify the coefficients of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- Coefficient of [tex]\(a\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
- Coefficient of [tex]\(b\)[/tex] is [tex]\(-1\)[/tex].
2. Combine the terms:
- The expression remains as it is because we are already in its simplest form.
Thus, the simplified form of the third expression is:
[tex]\[ \frac{3}{4}a - b \][/tex]
### Summary
Hence, the three given expressions in their simplest forms are:
1. [tex]\(\frac{1}{2}a - \frac{1}{3}b\)[/tex]
2. [tex]\(-a + \frac{2}{3}b\)[/tex]
3. [tex]\(\frac{3}{4}a - b\)[/tex]
These are exactly as what we have discussed and confirmed.
