Question

Use the number line to represent. -4 1/2 + 3 1/4. what is the sum?

Answer 1

Answer:

$\displaystyle A+B=-\frac{5}{4}$

Step-by-step explanation:

The Number Line

Let's call

$\displaystyle A=-4\frac{1}{2}$

$\displaystyle B=+3\frac{1}{4}$

Both numbers are given as mixed fractions. Let's convert them to improper fractions:

$\displaystyle A=-4\frac{1}{2}=-(4+\frac{1}{2})=-\frac{8+1}{2}=-\frac{9}{2}$

$\displaystyle B=3\frac{1}{4}=3+\frac{1}{4}=\frac{12+1}{4}=\frac{13}{4}$

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:

$\displaystyle A+B=-\frac{9}{2}+\frac{13}{4}$

$\displaystyle A+B=-\frac{18}{4}+\frac{13}{4}=\frac{-18+13}{4}$

$\boxed{\displaystyle A+B=-\frac{5}{4}}$