Question

$\left[\right(-8)+\_\_\_\_\_\_]+\_\_\_\_\_\_\_\_=\_\_\_\_\_\_\_\_+\left[\right(-3)+\_\_\_\_\_\_\_\_]=-3$. Fill in the blanks to make the statement true.

Answer 1

The given expression is in the form of the $associativepropertyofaddition.$

The addition follows associative property i.e. regardless of how numbers are parenthesized the final sum of the numbers will be the same.

The $associativeproperty$of and $multiplication$states that the way of a grouping of numbers doesn’t matter; the result will be the same. One can group numbers in any way but the answer will remain the same. Parenthesis can be done, irrespective of the order of terms. Let $x,y,andz$ be any three integers, then

i) $x+(y+z)=(x+y)+z$

ii ) $x\times (y\times z)=(x\times y)\times z$

above is showing the $associativeproperty$

According to the given question, using the below property

$(x+y)+z=x+(y+z)$

$x=-8$ $y=-3$ $z=8$

$\left[\right(–8)+(-3)]+8=(-8)+\left[\right(–3)+8]=–3$

$(-11)+8=(-8)+5=-3$

$-3=-3=-3$

Hence, $\left[\right(–8)+(-3)]+8=(-8)+\left[\right(–3)+8]=–3$