Answer:
[tex]\displaystyle A+B=-\frac{5}{4}[/tex]
Step-by-step explanation:
The Number Line
Let's call
[tex]\displaystyle A=-4\frac{1}{2}[/tex]
[tex]\displaystyle B=+3\frac{1}{4}[/tex]
Both numbers are given as mixed fractions. Let's convert them to improper fractions:
[tex]\displaystyle A=-4\frac{1}{2}=-(4+\frac{1}{2})=-\frac{8+1}{2}=-\frac{9}{2}[/tex]
[tex]\displaystyle B=3\frac{1}{4}=3+\frac{1}{4}=\frac{12+1}{4}=\frac{13}{4}[/tex]
The decimal values are A = -9/2=-4.5, B=13/4 = 3.25
Now represent the points in the number line. See the image below
Finally, calculate their sum:
[tex]\displaystyle A+B=-\frac{9}{2}+\frac{13}{4}[/tex]
[tex]\displaystyle A+B=-\frac{18}{4}+\frac{13}{4}=\frac{-18+13}{4}[/tex]
[tex]\boxed{\displaystyle A+B=-\frac{5}{4}}[/tex]
