Exercises: decimal numbers (mixed)

Calculate efficiently.

For solving these problems successfully, an understanding of the commutative and associative property of addition is essential. Also, some skill in adding by endings is useful.

$12.3 + (- 11.34) + 82.7 =$

For this task you need the following basic knowledge: Addition and subtraction of decimal fractions
$12.3 + (- 11.34) + 82.7$
Using the communative property of addition, the sum can be rewritten:
$12.3 + 82.7 + (- 11.34)$
Now adding by endings and composing a multiple of 10 can be used:
$3 + 7 = 10, h e n c e 0.3 + 0.7 = 1$
Therefore: $12.3 + 82.7 = 12 + 82 + 1 = 95$
So: $12.3 + 82.7 + (- 11.34) = 95 + (- 11.34)$
$11.34$ can be decomposed in $11 a n d 34 h u n d r e d t h s$
Using this decomposition, $95 + (- 11.34)$ can be rewritten (using subtraction by place value):
$95 - 11 - 0.34 = 84 - 0.34 = 83.66$
Therefore:
$12.3 + (- 11.34) + 82.7 = 83.66$
$- 11.77 + 3.2 - 5.23$

For this task you need the following basic knowledge: Addition and subtraction of decimal fractions
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:
$- 11.77 + 3.2 - 5.23 = - 11.77 + 3.2 + (- 5.23)$
Using the commutative property of addition $- 11.77 + 3.2 + (- 5.23)$ can be rewritten:
$- 11.77 + (- 5.23) + 3.2$
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:
$77 + 23 = 100, h e n c e 0.77 + 0.23 = 1 (77 h u n d r e d t h s a d d e d t o 23 h u n d r e d t h s)$
Therefore:
$- 11.77 + (- 5.23) = - 11 + (- 0.77) + (- 5) + (- 0.23) = - 11 + (- 5) + (- 0.77) + (- 0.23)$
$= - 16 + (- 1) = - 17$
Therefore:
$- 11.77 + 3.2 - 5.23 = - 17 + 3.2$
$- 17 + 3.2 = - 17 + 3 + 0.2 = - 14 + 0.2 = - 13.8$
Therefore:
$- 11.77 + 3.2 - 5.23 = - 13.8$
$2.89 - 2.1 - 4.9$

For this task you need the following basic knowledge: Addition and subtraction of decimal fractions
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:
$2.89 + (- 2.1) + (- 4.9)$
Now, the associative property of addition can be used.
$2.89 + (- 2.1 + (- 4.9))$
Next, composing a multiple of 10 together with the decomposition of the negative decimals and the commutative property of addition comes into play:
$1 + 9 = 10, h e n c e 0.1 + 0.9 = 1 (1 t e n t h s a d d e d t o 9 t e n t h s)$
Decomposing the negative decimals and using the commutative property of addition:
$- 2,1 + (- 4.9) = - 2 + (- 0.1) + (- 4) + (- 0.9) = - 2 + (- 4) + (- 0.1) + (- 0.9) = - 7$
Therefore:
$2.89 - 2.1 - 4.9 = 2.89 + (- 7) = 2 + 0.89 + (- 7) = - 5 + 0.89$
Using composing a multiple of 10 again
$89 + 11 = 100, h e n c e 0.89 + 0.11 = 1 (89 h u n d r e d t h s a d d e d t o 11 h u n d r e d t h s)$
$- 5 + 0.89 = - 4 + (- 1) + 0.89 = - 4 + (- 0.11) = - 4.11$
Therefore:
$2.89 - 2.1 - 4.9 = - 4.11$

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