we know that
[tex]5 \frac{3}{10}= \frac{5*10+3}{10} = \frac{53}{10}[/tex]
Step 1
Carlos's method
1) Find the absolute value of [tex]-\frac{53}{10}[/tex]
[tex]\left|-\frac{53}{10}\right|=\frac{53}{10}[/tex]
2) Find the opposite
[tex]opposite=-\frac{53}{10}[/tex]
Step 2
Jason's method
1) Find the opposite of [tex]-\frac{53}{10}[/tex]
[tex]opposite=\frac{53}{10}[/tex]
2) Find the absolute value
[tex]\left|\frac{53}{10}\right|=\frac{53}{10}[/tex]
Step 3
Compare the answers
[tex]\frac{53}{10} > -\frac{53}{10}[/tex]
therefore
The answer is
The greater value is obtained with the method of Jason