Question

match each equation on the left to the mathematical property it uses on the right. (4 + 5)+2 = 4+(5 + 2) commutative property of addition 2(2x + 4)=4x + 8 commutative property of multiplication (7·x)·3 = 7·(x·3) associative property of addition (8·x·2)=(x·8·2) associative property of multiplication (7 + 3)+1 = 1+(7 + 3) distributive property click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. need help? watch this video.

Explanation:

Step1: Recall the definitions of properties

The commutative property of addition states \(a + b=b + a\), the commutative property of multiplication states \(a\times b = b\times a\), the associative property of addition states \((a + b)+c=a+(b + c)\), the associative property of multiplication states \((a\times b)\times c=a\times(b\times c)\), and the distributive property states \(a(b + c)=ab+ac\).

Step2: Analyze \((4 + 5)+2=4+(5 + 2)\)

This is in the form \((a + b)+c=a+(b + c)\) which is the associative property of addition.

Step3: Analyze \(2(2x + 4)=4x+8\)

Using \(a(b + c)=ab + ac\) where \(a = 2\), \(b=2x\) and \(c = 4\), so it is the distributive property.

Step4: Analyze \((7\cdot x)\cdot3=7\cdot(x\cdot3)\)

This is in the form \((a\times b)\times c=a\times(b\times c)\) which is the associative property of multiplication.

Step5: Analyze \((8\cdot x\cdot2)=(x\cdot8\cdot2)\)

This is in the form \(a\times b\times c=b\times a\times c\) which is the commutative property of multiplication.

Step6: Analyze \((7 + 3)+1=1+(7 + 3)\)

This is in the form \(a + b=b + a\) which is the commutative property of addition.

Answer:

\((4 + 5)+2=4+(5 + 2)\): associative property of addition
\(2(2x + 4)=4x+8\): distributive property
\((7\cdot x)\cdot3=7\cdot(x\cdot3)\): associative property of multiplication
\((8\cdot x\cdot2)=(x\cdot8\cdot2)\): commutative property of multiplication
\((7 + 3)+1=1+(7 + 3)\): commutative property of addition