Question

Name the property that is illustrated by each statement in the picture a), b), and c)

Answer 1

Given:

(a)

`(1)/(2)(2x+2)`

Use distributive property is:

`a(x+y)=ax+ay\ldots\ldots\ldots\ldots.(distributive\text{ property)}`

`\begin{gathered} =(1)/(2)(2x+2) \\ =(1)/(2)(2x)+(1)/(2)(2) \\ =x+1 \end{gathered}`

(b)

`2a+(3b+c)`

Use aasociative property of addition:

`\begin{gathered} =a+(x+y) \\ =(a+x)+y \end{gathered}`

`\begin{gathered} =2a+(3b+c) \\ =(3b+c)+2a\ldots\ldots\ldots\ldots(\text{associative property of addition)} \end{gathered}`

(c)

`(1)/(4)\lbrack(-a+a)+4\rbrack`

`\begin{gathered} (1)/(4)\lbrack(-a+a)+4\rbrack=(1)/(4)\lbrack0+4\rbrack \\ \text{Use substraction property} \end{gathered}`