Answer:
[tex]2\frac{1}{4}[/tex]
Step-by-step explanation:
Operations With Fractions
Simplify the following operations:
[tex]\displaystyle -5\frac{1}{4}-\left(-7\frac{1}{2}\right)[/tex]
Convert the mixed fractions to improper fractions:
[tex]\displaystyle 5\frac{1}{4}= 5+\frac{1}{4}=\frac{21}{4}[/tex]
[tex]\displaystyle 7\frac{1}{2}=7+\frac{1}{2}=\frac{15}{2}[/tex]
Substituting:
[tex]\displaystyle -5\frac{1}{4}-\left(-7\frac{1}{2}\right)=-\frac{21}{4}-\left(-\frac{15}{2}\right)[/tex]
Simplifying:
[tex]\displaystyle -5\frac{1}{4}-\left(-7\frac{1}{2}\right)=-\frac{21}{4}+\frac{15}{2}[/tex]
Amplifying the second fraction by 2:
[tex]\displaystyle -5\frac{1}{4}-\left(-7\frac{1}{2}\right)=-\frac{21}{4}+\frac{30}{4}[/tex]
Adding both fractions:
[tex]\displaystyle -5\frac{1}{4}-\left(-7\frac{1}{2}\right)=\frac{9}{4}=2\frac{1}{4}[/tex]
Answer: [tex]\mathbf{2\frac{1}{4}}[/tex]
