$12.3+\left(-11.34\right)+82.7$

Using the communative property of addition, the sum can be rewritten:

$12.3+82.7+\left(-11.34\right)$

Now adding by endings and composing a multiple of 10 can be used:

$3+7=10,\ hence\ 0.3+0.7=1$

Therefore: $12.3+82.7=12+82+1=95$

So: $12.3+82.7+\left(-11.34\right)=95+\left(-11.34\right)$

$\ \ \ 11.34\ \$can be decomposed in $11\ and\ 34\ hundredths$

Using this decomposition, $\ \ 95+\left(-11.34\right)\$can be rewritten (using subtraction by place value):

$\ \ \ 95-11-0.34=84-0.34=83.66\ \$

Therefore:

$12.3+\left(-11.34\right)+82.7=83.66$

Working efficiently involves using the commutative and associative properties of addition. Therefore $\ \ \ -11.77+3.2-5.23\ \$is rewritten as a sum with two negative decimals:

$\ \ \ -11.77+3.2-5.23\ =-11.77+3.2+\left(-5.23\right)\ \$

Using the commutative property of addition $\ \ \ -11.77+3.2+\left(-5.23\right)\ \$can be rewritten:

$\ \ \ -11.77+\left(-5.23\right)+3.2\ \$

Arithmetic skills come into play as well:

Using composing a multiple of 10 together with decomposing the negative decimals and the commutative property of addition, the negative decimals can be added easily:

$\ \ \ 77+23=100,\ \ \ hence\ \ 0.77+0.23=1\ \left(77\ hundredths\ added\ to\ \ 23\ hundredths\right)\ \$

Therefore:

$-11.77+\left(-5.23\right)=-11+\left(-0.77\right)+\left(-5\right)+\left(-0.23\right)=-11+\left(-5\right)+\left(-0.77\right)+\left(-0.23\right)$

$=-16+\left(-1\right)=-17$

Therefore:

$\ \ \ -11.77+3.2-5.23\ =\ -17+3.2$

$\ \ \ -17+3.2=-17+3+0.2=-14+0.2=-13.8$

Therefore:

$\ \ \ -11.77+3.2-5.23=-13.8$

Working efficiently involves using the commutative and associative property of addition. Therefore $2.89-2.1-4.9$ is rewritten as a sum with two negative decimals:

$\ \ \ 2.89+\left(-2.1\right)+\left(-4.9\right)$

Now, the associative property of addition can be used.

$\ \ \ 2.89+\left(-2.1+\left(-4.9\right)\right)$

Next, composing a multiple of 10 together with the decomposition of the negative decimals and the commutative property of addition comes into play:

$\ \ \ 1+9=10,\ \ hence\ \ \ 0.1+0.9\ =\ 1\ \ \ \left(1\ tenths\ added\ to\ 9\ tenths\right)$

Decomposing the negative decimals and using the commutative property of addition:

$\ \ \ -2{,}1+\left(-4.9\right)=-2+\left(-0.1\right)+\left(-4\right)+\left(-0.9\right)=-2+\left(-4\right)+\left(-0.1\right)+\left(-0.9\right)=-7$

Therefore:

$\ \ \ 2.89-2.1-4.9=2.89+\left(-7\right)=2+0.89+\left(-7\right)=-5+0.89$

Using composing a multiple of 10 again

$89+11=100,\ \ \ hence\ \ \ 0.89+0.11\ =\ 1\ \ \left(89\ hundredths\ added\ to\ 11\ hundredths\right)$

$-5+0.89=-4+\left(-1\right)+0.89=-4+\left(-0.11\right)=-4.11\$

Therefore:

$\ \ \ 2.89-2.1-4.9=-4.11$