Question

name laniyah foster date applying the standard how might this standard appear on a test? 3) write an “x” in the box beside each expression that is equivalent to (-5\frac{3}{5} + 1\frac{1}{5}). select all that apply. (square) (-5 + (-\frac{3}{5}) + 1 + \frac{1}{5}) (square) (5 + \frac{3}{5} + (-1) + (-\frac{1}{5})) (square) (-5 + \frac{3}{5} + 1 + \frac{1}{5}) (square) (-5 + 1 + (-\frac{3}{5}) + \frac{1}{5}) check out my worked example #1a

Explanation:

Step1: Recall mixed number to sum

A mixed number \( -5\frac{3}{5} \) can be written as \( -5 + (-\frac{3}{5}) \) (since \( 5\frac{3}{5}=5+\frac{3}{5} \), so negative is \( -5-\frac{3}{5}=-5+(-\frac{3}{5}) \)), and \( 1\frac{1}{5}=1+\frac{1}{5} \). So \( -5\frac{3}{5}+1\frac{1}{5}=-5+(-\frac{3}{5}) + 1+\frac{1}{5} \), which matches the first option.

Step2: Check commutative property

Using the commutative property of addition (order of addition can be changed), \( -5+(-\frac{3}{5}) + 1+\frac{1}{5}=-5 + 1+(-\frac{3}{5})+\frac{1}{5} \), which matches the fourth option.

Step3: Analyze incorrect options

• Second option: \( 5+\frac{3}{5}+(-1)+(-\frac{1}{5}) \) has positive 5 and -1, which is wrong as original has -5 and +1.
• Third option: \( -5+\frac{3}{5}+1+\frac{1}{5} \) has \( +\frac{3}{5} \) instead of \( -\frac{3}{5} \), so wrong.

Answer:

• \( \boldsymbol{-5+(-\frac{3}{5})+1+\frac{5}{1}} \) (first box)
• \( \boldsymbol{-5 + 1+(-\frac{3}{5})+\frac{1}{5}} \) (fourth box)