Question

applying the standard
how might this standard appear on a test?

1. evaluate each expression. indicate the properties of operations (commutative property of addition, associative property of addition) where appropriate.

a) -5 + 6 + (-2) - 4
b) 22 - 8 + (-3) + 10
c) 60 + (-75) + 33 - 87 - (-15)
d) 11.6 - (-12.4) + 15.3 - 9
e) \\(\frac{2}{3} - \frac{5}{12} - (-\frac{1}{6}) + \frac{1}{2}\\)
f) \\(32 + (-12\frac{7}{8}) + \frac{1}{2}\\)

Explanation:

Step1: Evaluate part a) \(-5 + 6 + (-2) - 4\)

First, use the commutative property to reorder: \(-5 + 6 - 2 - 4\). Then add/subtract from left to right: \((-5 + 6) + (-2 - 4) = 1 + (-6) = -5\).

Step2: Evaluate part b) \(22 - 8 + (-3) + 10\)

Reorder using commutative property: \(22 + 10 - 8 - 3\). Then calculate: \((22 + 10) + (-8 - 3) = 32 + (-11) = 21\).

Step3: Evaluate part c) \(60 + (-75) + 33 - 87 - (-15)\)

Simplify \(-(-15)=15\), reorder: \(60 + 33 + 15 - 75 - 87\). Calculate: \((60 + 33 + 15) + (-75 - 87) = 108 + (-162) = -54\).

Step4: Evaluate part d) \(11.6 - (-12.4) + 15.3 - 9\)

Simplify \(-(-12.4)=12.4\), reorder: \(11.6 + 12.4 + 15.3 - 9\). Calculate: \((11.6 + 12.4) + (15.3 - 9) = 24 + 6.3 = 30.3\).

Step5: Evaluate part e) \(\frac{2}{3} - \frac{5}{12} - (-\frac{1}{6}) + \frac{1}{2}\)

Simplify \(-(-\frac{1}{6})=\frac{1}{6}\), find common denominator (12): \(\frac{8}{12} - \frac{5}{12} + \frac{2}{12} + \frac{6}{12}\). Add/subtract: \(\frac{8 - 5 + 2 + 6}{12} = \frac{11}{12}\).

Step6: Evaluate part f) \(32 + (-12\frac{7}{8}) + \frac{1}{2}\)

Convert to eighths: \(-12\frac{7}{8}=-\frac{103}{8}\), \(\frac{1}{2}=\frac{4}{8}\). Reorder: \(32 - \frac{103}{8} + \frac{4}{8}\). Calculate: \(32 + (-\frac{103}{8} + \frac{4}{8}) = 32 - \frac{99}{8} = 32 - 12\frac{3}{8} = 19\frac{5}{8}\).

Answer:

s:
a) \(-5\)
b) \(21\)
c) \(-54\)
d) \(30.3\)
e) \(\frac{11}{12}\)
f) \(19\frac{5}{8}\)