Question

Choose the property that justifies the outcomes 'match them'

4x+(5x+3)=9x+3
5(3x8)=15x8
1/5x5=1
a+b=b+a

multiplicative inverses
additive inverses
associative property of multiplication
associative property of addition

Answer 1

1.
`4x+(5x+3)=(4x+5x)+3=9x+3` -- associative property of addition (
`a+(b+c)=(a+b)+c`);

2.
`5\cdot (3\cdot 8)=(5\cdot 3)\cdot 8=15\cdot 8` -- associative property of multiplication (
`(a\cdot b)\cdot c=a\cdot (b\cdot c)`);

3.
`(1)/(5)\cdot 5=1` -- multiplicative inverses (
`a\cdot a^(-1)=a^(-1)\cdot a=1`);

4. a+b=b+a -- commutative addition

5. a+b=b+a=0 -- additive inverses