Question

Mike watches a caterpillar climbing on a tree trunk. He writes the expression -5/8 - (-1/8 - 1/2) to show the change, in feet, of the caterpillar’s height on the tree trunk. Which of the following expressions are equivalent to
-5/8 - (-1/8 - 1/2) ?
Choose all that apply.
A. -5/8 + (1/8 + 1/2)
B. -5/8 + 5/8
C. -5/8 - (1/8 + 1/2)
D. -5/8 - (-1/8 + (-1/2))
E. -5/8 + (1/8 - 1/2)
F. -5/8 - 1/8 - 1/2

Answer 1

Answer:

A. $\frac{-5}{8}+(\frac{1}{8}+\frac{1}{2})$

B. $\frac{-5}{8}+(\frac{5}{8})$

D. $\frac{-5}{8}-(\frac{-1}{8}+(\frac{-1}{2}))$

Step-by-step explanation:

- Mike watches a caterpillar climbing on a tree trunk

- He writes the expression $\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})$

- We need to find the equivalent expressions to this expression

A.

∵ The expression $\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})$ has a

   common sign negative in the bracket

∴ $\frac{-5}{8}-(-)(\frac{1}{8}+\frac{1}{2})$

∵ (-)(-) = (+)

∴ $\frac{-5}{8}+(\frac{1}{8}+\frac{1}{2})$

∵ The expression $\frac{-5}{8}+(\frac{1}{8}+\frac{1}{2})$ is

   equivalent to the expression $\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})$

B.

∵ In the expression $\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})$, lets

  add the two terms in the bracket

  $(\frac{-1}{8}-\frac{1}{2})=(\frac{-1}{8}-\frac{1(4)}{2(4)})=(\frac{-1}{8}-\frac{4}{8})=(\frac{-5}{8})$

∴ The expression = $\frac{-5}{8}-(\frac{-5}{8})$

∵ (-)(-) = (+)

∴ The expression = $\frac{-5}{8}+(\frac{5}{8})$

∴ The expression $\frac{-5}{8}+(\frac{5}{8})$ is equivalent to

   the expression $\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})$

D.

∵ In the expression $\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})$, we can

  write the bracket as $(\frac{-1}{8}-\frac{1}{2})=(\frac{-1}{8}+(\frac{-1}{2}))$

  because (+)(-) = (-)

∴ The expression $\frac{-5}{8}+(\frac{5}{8})$ is equivalent to

   the expression $\frac{-5}{8}-(\frac{-1}{8}+(\frac{-1}{2}))$

* The equivalent expressions are A , B and D