Sure, let's solve these mathematical expressions step by step.
### Expression 1: [tex]\(\frac{9}{4} - 2\)[/tex]
1. Convert the whole number 2 to a fraction with the same denominator as [tex]\(\frac{9}{4}\)[/tex]:
[tex]\[
2 = \frac{8}{4}
\][/tex]
2. Subtract [tex]\(\frac{8}{4}\)[/tex] from [tex]\(\frac{9}{4}\)[/tex]:
[tex]\[
\frac{9}{4} - \frac{8}{4} = \frac{9 - 8}{4} = \frac{1}{4}
\][/tex]
So the result of the first expression is:
[tex]\[
\frac{9}{4} - 2 = 0.25
\][/tex]
### Expression 2: [tex]\(2 - \frac{1}{3}\)[/tex]
1. Convert the whole number 2 to a fraction with the same denominator as [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
2 = \frac{6}{3}
\][/tex]
2. Subtract [tex]\(\frac{1}{3}\)[/tex] from [tex]\(\frac{6}{3}\)[/tex]:
[tex]\[
\frac{6}{3} - \frac{1}{3} = \frac{6 - 1}{3} = \frac{5}{3}
\][/tex]
3. Convert [tex]\(\frac{5}{3}\)[/tex] to a decimal:
[tex]\[
\frac{5}{3} \approx 1.6666666666666667
\][/tex]
So the result of the second expression is:
[tex]\[
2 - \frac{1}{3} = 1.6666666666666667
\][/tex]
### Expression 3: [tex]\(2 - \frac{7}{3} - \frac{5}{2}\)[/tex]
1. Convert the whole number 2 to a fraction with a suitable common denominator with both [tex]\(\frac{7}{3}\)[/tex] and [tex]\(\frac{5}{2}\)[/tex]. The common denominator of 3 and 2 is 6:
[tex]\[
2 = \frac{12}{6}, \quad \frac{7}{3} = \frac{14}{6}, \quad \frac{5}{2} = \frac{15}{6}
\][/tex]
2. Perform the subtractions:
[tex]\[
\frac{12}{6} - \frac{14}{6} = \frac{12 - 14}{6} = \frac{-2}{6} = -\frac{1}{3}
\][/tex]
3. Now, subtract [tex]\(\frac{15}{6}\)[/tex] from [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
-\frac{1}{3} = -\frac{2}{6}
\][/tex]
[tex]\[
-\frac{2}{6} - \frac{15}{6} = \frac{-2 - 15}{6} = \frac{-17}{6} \approx -2.8333333333333335
\][/tex]
So the result of the third expression is:
[tex]\[
2 - \frac{7}{3} - \frac{5}{2} = -2.8333333333333335
\][/tex]
### Summary of Results:
1. [tex]\(\frac{9}{4} - 2 = 0.25\)[/tex]
2. [tex]\(2 - \frac{1}{3} = 1.6666666666666667\)[/tex]
3. [tex]\(2 - \frac{7}{3} - \frac{5}{2} = -2.8333333333333335\)[/tex]
