Question

Which of the following statements are true? Select all that apply For all real numbers a and b, a+b=b+a For all real numbers a and b, ab=ba For all real numbers a and b, a-b=b-a For all real numbers a and b, a/b=b/a For all real numbers a,b, and c, (a+b)+c=a+(b+c) For all real numbers a,b, and c, (a-b)-c=a-(b-c) For all real numbers a,b, and c, a(b+c)=ab+ac Thanks for any help provided!

Answer 1

Statements 1,2,5,7 are correct. But I think statement 6 is incorrect but I’m not a 100% sure about that one.

Answer 2

Answer: Hello there!

if a and b are real numbers:

1) For all real numbers a and b, a+b=b+a: This is true, it is called the commutative property of the addition.

2) For all real numbers a and b, ab=ba: This is true, it is called the commutative property of the multiplication.

3) For all real numbers a and b, a-b=b-a: This is false, a counter example is if we took a = 1 and b = 0; then a -b = 1, and b - a = -1.

4) For all real numbers a and b, a/b=b/a: This is false, if we took a= 4 and b = 2, then a/b = 4/2 = 2, and b/a = 2/4 = 1/2, which are different.

5) For all real numbers a,b, and c, (a+b)+c=a+(b+c): This is true, it is called the distributive property of the addition.

6) For all real numbers a,b, and c, (a-b)-c=a-(b-c): this is false; in the left side of the equation we have (a -b) -c, that if we remove the parenthesis is equal to a -b -c

in the right side we have a -( b - c) if we remove the parenthesis and distribute the minus sign, we get: a -b + c

7) For all real numbers a,b, and c, a(b+c)=ab+ac: This is true, it is called the distributive property of the multiplication.