Question

Match each equation with the property being illustrated. There will be 3 equations with each property.

Answer 1

Given:

The objective is to match all the 3 equations with 3 properties Distributive property, Commutative property and Associative propoerty.

The distributive property is defined as, multiplication of a sum of two terms by an individual term. For example,

`a(b+c)=ab+ac`

Then, the given equations matches with the given condition are,

`\begin{gathered} (x-8)4=4x-32 \\ -6(-2+5)=12-30 \\ 3(x+2)=3x+6 \end{gathered}`

Next, the Commutative proerty is defined as, multiplication of first term and second term will be equal to multiplication of second term and first term. For example,

`a\cdot b=b\cdot a`

Then, the given equations matches with the given condition are,

`\begin{gathered} 6x=x\cdot6 \\ 5\cdot7=7\cdot5 \\ 4(2x=(4\cdot2)x \end{gathered}`

Then, the Associative property is defined as, sum of first term and second term will be equal to sum of second term and first term. For example

`a+(b+c)=(a+b)+c`

Then, the given equations matches with the given condition are,

`\begin{gathered} 7+(9+1)=(7+9)+1 \\ (-7-2)-4=-7(-2-4) \\ 6+8=8+6 \end{gathered}`

Hence, the required matches of propoerty are obtained.