Question

What is (-7/10) — 2/15
What is -4/9 — 2/15
Write all these in simplest form.

Mrs. Escalante was riding a bicycle in a bike
Path. After riding 2/3 of a mile,she discovered
that she needed to travel 3/4 of a mile to
reach the end of the path. How long is the bike
path? Write an operating to solve this problem. Explain your reasoning.
Then solve the problem. Write in simplest form.

Answer 1

To subtract fractions, the following procedure is followed:

$\frac{a}{b} -\frac{c}{d} =\frac{(ad-cb)}{bd}$

For the first case:

$a = -7$

$b = 10$

$c = 2$

$d = 15$

Then the result of subtraction is:

$\frac{(-7)*15 - 2*10}{10 * 15}$

$= \frac{(-105-20)}{150}$

$= \frac{-5}{6}$

For the second case:

$a = -4$

$b = 9$

$c = 2$

$d = 15$

Then the result of subtraction is:

$\frac{(-4)*15 - 2*9}{9 * 15}$

$= \frac{-60-18}{135}$

$= \frac{-26}{45}$

For the third case:

Mrs. Escalante traveled $\frac{2}{3}$ of a mile and $\frac{3}{4}$ of a mile

Then Mrs. Escarlante traveled $\frac{2}{3}+\frac{3}{4}$ of a mile.

Adding both fractions we have the final route:

Adding $\frac{(2 * 4 + 3 * 3)}{3*4} =\frac{8 + 9}{12}= \frac{17}{12}$ miles = 1.42 miles