What is (+8) - (-8)? and what is (-4) + (-5)?

Remark

Brackets are wonderful things. They clarify many a situation that is otherwise not clear. But they can be confusing as well and until you get used to what they do, it is best to remove them and look at the signs they leave behind.

Example One

(+8) -(-8)  Let's ignore the first set of brackets for the moment and just focus on the second ones. If you remove them, you get

(+8) - - 8   What does that tell you? You have 2 minus signs in a row. There are no numbers between them, just the two minus signs in a row.  When you have an even number of signs, The sign changes to a plus. The rule is two minus's in a row give a plus. So what you have now is

(+8) + 8 To complete the problem remove the set of brackets that I said to ignore.

+8 + 8 = 16 The plus sign has no effect on the answer in this case.

Example Two

(-4) + (-5)   Again ignore the first bracket set. Just remove the second set.

(-4) + - 5    Here you have an odd number of minus signs. The five becomes -5

(-4) - 5       Now remove the first set of brackets.

-4 - 5 = -9 is your answer. The main point is what happened to the 5?

Comment.

You can have as many + or - signs in a row as your are asked to consolidate.

If you have (3) - - - - - - - - - - 9 = 12. I think there are 10 minus signs between the 3 and the 9. The 9 becomes plus and the answer is 3 + 9 = 12

On the other hand you could have 3 - - - 9 = 3 - 9 = - 6 because there are an odd number of signs (3), the 9 becomes - and the answer is - 6.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft