To find the difference of the fractions [tex]\(-2 \frac{1}{2} - \left(-1 \frac{3}{4}\right)\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(-2 \frac{1}{2}\)[/tex]:
[tex]\[
-2 \frac{1}{2} = -\left(2 + \frac{1}{2}\right) = -\frac{5}{2}
\][/tex]
- For [tex]\(-1 \frac{3}{4}\)[/tex]:
[tex]\[
-1 \frac{3}{4} = -\left(1 + \frac{3}{4}\right) = -\frac{7}{4}
\][/tex]
2. Subtract the second fraction from the first fraction:
[tex]\[
-\frac{5}{2} - \left(-\frac{7}{4}\right)
\][/tex]
Subtracting a negative fraction is the same as adding its positive counterpart:
[tex]\[
-\frac{5}{2} + \frac{7}{4}
\][/tex]
3. Find a common denominator to combine the fractions:
The common denominator for 2 and 4 is 4.
- Convert [tex]\(-\frac{5}{2}\)[/tex] into a fraction with a denominator of 4:
[tex]\[
-\frac{5}{2} = -\frac{5 \times 2}{2 \times 2} = -\frac{10}{4}
\][/tex]
- Now, we have:
[tex]\[
-\frac{10}{4} + \frac{7}{4} = \frac{-10 + 7}{4} = \frac{-3}{4}
\][/tex]
4. Simplify the resulting fraction:
The simplified fraction is:
[tex]\[
-\frac{3}{4}
\][/tex]
Therefore, the difference of the fractions is [tex]\(-\frac{3}{4}\)[/tex].
