Answer :
Let's solve each problem step by step.
### Problem 7:
Evaluate [tex]\(-\frac{3}{4} + \left(-\frac{1}{2}\right)\)[/tex]
1. First, represent [tex]\(-\frac{1}{2}\)[/tex] with a common denominator.
The common denominator for 4 and 2 is 4.
[tex]\[ -\frac{1}{2} = -\frac{1 \times 2}{2 \times 2} = -\frac{2}{4} \][/tex]
2. Now, add the two fractions with the common denominator.
[tex]\[ -\frac{3}{4} + \left(-\frac{2}{4}\right) = -\frac{3 + 2}{4} = -\frac{5}{4} \][/tex]
3. Express [tex]\(\frac{5}{4}\)[/tex] as a decimal.
[tex]\[ -\frac{5}{4} = -1.25 \][/tex]
So, the solution to [tex]\(-\frac{3}{4} + \left(-\frac{1}{2}\right)\)[/tex] is [tex]\(-1.25\)[/tex].
### Problem 8:
Evaluate [tex]\(-1.75 + 3\)[/tex]
1. Proceed with straightforward addition.
[tex]\[ -1.75 + 3 \][/tex]
2. Combine the numbers by aligning decimal points and adding.
[tex]\[ -1.75 + 3.00 = 1.25 \][/tex]
So, the solution to [tex]\(-1.75 + 3\)[/tex] is [tex]\(1.25\)[/tex].
Thus, the answers to the problems are:
1. [tex]\(-\frac{3}{4} + \left(-\frac{1}{2}\right) = -1.25\)[/tex]
2. [tex]\(-1.75 + 3 = 1.25\)[/tex]
### Problem 7:
Evaluate [tex]\(-\frac{3}{4} + \left(-\frac{1}{2}\right)\)[/tex]
1. First, represent [tex]\(-\frac{1}{2}\)[/tex] with a common denominator.
The common denominator for 4 and 2 is 4.
[tex]\[ -\frac{1}{2} = -\frac{1 \times 2}{2 \times 2} = -\frac{2}{4} \][/tex]
2. Now, add the two fractions with the common denominator.
[tex]\[ -\frac{3}{4} + \left(-\frac{2}{4}\right) = -\frac{3 + 2}{4} = -\frac{5}{4} \][/tex]
3. Express [tex]\(\frac{5}{4}\)[/tex] as a decimal.
[tex]\[ -\frac{5}{4} = -1.25 \][/tex]
So, the solution to [tex]\(-\frac{3}{4} + \left(-\frac{1}{2}\right)\)[/tex] is [tex]\(-1.25\)[/tex].
### Problem 8:
Evaluate [tex]\(-1.75 + 3\)[/tex]
1. Proceed with straightforward addition.
[tex]\[ -1.75 + 3 \][/tex]
2. Combine the numbers by aligning decimal points and adding.
[tex]\[ -1.75 + 3.00 = 1.25 \][/tex]
So, the solution to [tex]\(-1.75 + 3\)[/tex] is [tex]\(1.25\)[/tex].
Thus, the answers to the problems are:
1. [tex]\(-\frac{3}{4} + \left(-\frac{1}{2}\right) = -1.25\)[/tex]
2. [tex]\(-1.75 + 3 = 1.25\)[/tex]
