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$2012 + 176 + 244 + 308$

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Now we are going to use commutative property for two numbers. That is, $a + b = b + a$. Therefore,

$\left( {2012 + 176} \right) + \left( {244 + 308} \right)$

$ = \left( {176 + 2012} \right) + \left( {308 + 244} \right)$

$ = 2188 + 552$

$ = 552 + 2188\quad \left[ {\because a + b = b + a} \right]$

$ = 2740$

Therefore, the required sum is $2740$ by using commutative property.

Now we will find the required sum by using associative property. For every real number $a,b$ and $c$, we can write $\left( {a + b} \right) + c = a + \left( {b + c} \right)$. This is the associative property of addition for three numbers. In the given problem, we need to find the sum of four numbers by using associative property. For this, we will consider one group of the first three numbers in which we will make one group of the first two numbers. That is, we write the given sum as $\left[ {\left( {2012 + 176} \right) + 244} \right] + 308$.

Now we are going to use associative property for three numbers. That is, $\left( {a + b} \right) + c = a + \left( {b + c} \right)$.

$\left[ {\left( {2012 + 176} \right) + 244} \right] + 308$

$ = \left[ {2012 + \left( {176 + 244} \right)} \right] + 308\quad \left[ {\because \left( {a + b} \right) + c = a + \left( {b + c} \right)} \right]$

$ = 2012 + \left[ {\left( {176 + 244} \right) + 308} \right]$

$ = 2012 + 176 + \left( {244 + 308} \right)\quad \left[ {\because \left( {a + b} \right) + c = a + \left( {b + c} \right)} \right]$

$ = \left( {2012 + 176} \right) + \left( {244 + 308} \right)$

$ = 2188 + 552$

$ = 2740$

Therefore, the required sum is $2740$ by using associative property.