Mathematics: 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

It would be 12...Step-by-step explanation:...

Mike watches a caterpillar climbing on a tree - id2672293, milkshakegrande101

denym58

04.01.2022

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

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

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

∵ 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

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