Question

what is the distance between -1 1/2 +5. Find absolute value

Answer 1

To find the absolute value of -1 1/2 +5​ you make the addition:

You can write the mixed number also as -3/2 (because -1 is equal to -2/2 and -2/2 and 1/2 is -3/2).

You add fractions as follow:

$\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}$

You can write the 5 as 5/1:

$-\frac{3}{2}+\frac{5}{1}=\frac{-3\cdot1+5\cdot2}{2\cdot1}=\frac{-3+10}{2}=\frac{7}{2}$

As the addition of the given numbers is 7/2, the absolute value or the distance is:

$\lvert\pm a\rvert=a$

$\lvert-1\frac{1}{2}+5\rvert=\lvert\frac{7}{2}\rvert=\frac{7}{2}$Then, the distance is 7/2