Question

Which of the following expressions are equivalent to (6.2+6.2)+9.4(6.2+6.2)+9.4left parenthesis, 6, point, 2, plus, 6, point, 2, right parenthesis, plus, 9, point, 4? Choose 2 answers: Choose 2 answers: (Choice A) A 6.2 + (6.2 + 9.4)6.2+(6.2+9.4)6, point, 2, plus, left parenthesis, 6, point, 2, plus, 9, point, 4, right parenthesis (Choice B) B -(-6.2+6.2)+9.4−(−6.2+6.2)+9.4minus, left parenthesis, minus, 6, point, 2, plus, 6, point, 2, right parenthesis, plus, 9, point, 4 (Choice C) C -(6.2+6.2)+9.4−(6.2+6.2)+9.4minus, left parenthesis, 6, point, 2, plus, 6, point, 2, right parenthesis, plus, 9, point, 4 (Choice D) D 9.49.49, point, 4 (Choice E) E 6.2-(-6.2-9.4)6.2−(−6.2−9.4)

Answer 1

Answer:

6.2 + (6.2 + 9.4) ⇒ A

6.2 - (-6.2 - 9.4) ⇒ E

Step-by-step explanation:

* Lets revise some definitions to solve the problem

- Associative property states that you can re-group numbers and you

 will get the same answer [(a + b) + c = a + (b + c)]

- Additive inverse of a number means reverse the sign of the number

 the additive inverse of x is -x

- The expression is  (6.2 + 6.2) + 9.4

- We want to find which of the following expressions are equivalent

 to this expression

- By using associative property we can write the expression as

 6.2 + (6.2 + 9.4)

∴ (6.2 + 6.2) + 9.4 = 6.2 + (6.2 + 9.4)

- Multiply (-) by the additive inverse of number is the number itself

 If a number is x and its additive inverse is -x, then (-) × (-x) = x

∵ -6.2 is additive inverse of 6.2

∵ (-)(-6.2) = 6.2

∵ -9.4 is additive inverse of 9.4

∵ (-)(-9.4) = 9.4

∴ 6.2 - (-6.2 - 9.4) = 6.2 + 6.2 + 9.4

∴ (6.2 + 6.2) + 9.4 = 6.2 - (-6.2 - 9.4)

* The answers are A and E