Question

which of the following expressions are equivalent to 8\frac{4}{5}+(3\frac{2}{10}-1\frac{1}{5})? choose 2 answers: a (8\frac{4}{5}+3\frac{2}{10})+1\frac{1}{5} b (8\frac{4}{5}+3\frac{2}{10})+(-1\frac{1}{5}) c -(-8\frac{4}{5})+3\frac{2}{10}-(-1\frac{1}{5}) d -(-8\frac{4}{5})-(-3\frac{2}{10})+(-1\frac{1}{5})

Explanation:

Step1: Recall the associative property of addition

The original expression is \(8\frac{4}{5}+(3\frac{2}{10}-1\frac{1}{5})\). We know that \(a+(b - c)=(a + b)+(-c)\). Here \(a = 8\frac{4}{5}\), \(b=3\frac{2}{10}\) and \(c = 1\frac{1}{5}\), so \(8\frac{4}{5}+(3\frac{2}{10}-1\frac{1}{5})=(8\frac{4}{5}+3\frac{2}{10})+(- 1\frac{1}{5})\).

Step2: Analyze the double - negative rule

\(-(-x)=x\). The original expression \(8\frac{4}{5}+(3\frac{2}{10}-1\frac{1}{5})\) can also be written as \(-(-8\frac{4}{5})-(-3\frac{2}{10})+(-1\frac{1}{5})\) since \(8\frac{4}{5}=-(-8\frac{4}{5})\), \(3\frac{2}{10}=-(-3\frac{2}{10})\) and \(3\frac{2}{10}-1\frac{1}{5}=3\frac{2}{10}+(-1\frac{1}{5})\).

Answer:

B. \((8\frac{4}{5}+3\frac{2}{10})+(-1\frac{1}{5})\)
D. \(-(-8\frac{4}{5})-(-3\frac{2}{10})+(-1\frac{1}{5})\)