## Precalculus: Mathematics for Calculus, 7th Edition

(a) Distance: $\frac{18}{35}$ (b) Distance: $19$ (c) Distance: $0.8$
(a) The distance between the numbers $\frac{7}{15}$ and $-\frac{1}{21}$ is $d(a,b) = |\frac{7}{15} - (-\frac{1}{21})| =|\frac{7}{15} + \frac{1}{21}|=|\frac{49}{105} + \frac{5}{105}| = |\frac{54}{105}| =\frac{54}{105} = \frac{18}{35}$ (b) The distance between the numbers $-38$ and $-57$ is $d(a,b) = |-38 - (-57)| = | -38 + 57 | = |19| = 19$ (c) The distance between the numbers $-2.6$ and $-1.8$ is $d(a,b) = |-2.6 - (-1.8)| = |-2.6+1.8 | = |-0.8| = 0.8$