From personal advice to professional guidance, IDNLearn.com has the answers you seek. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.
Sagot :
To determine which option shows the best use of the associative and commutative properties for simplifying the expression [tex]\(\frac{2}{5} - 15 + 8 - \frac{1}{5} + 3\)[/tex], let's carefully examine each option.
### Option A
[tex]\[ \left[\frac{2}{5} + 8 + (-15)\right] + \left[3 + \left(-\frac{1}{5}\right)\right] \][/tex]
### Option B
[tex]\[ \left[3 + \frac{2}{5} + (-15)\right] + \left[\left(-\frac{1}{5}\right) + 8\right] \][/tex]
### Option C
[tex]\[ \left[\frac{2}{5} + (-15)\right] + \left[8 + \left(-\frac{1}{5}\right) + 3\right] \][/tex]
### Option D
[tex]\[ \left[\frac{2}{5} + \left(-\frac{1}{5}\right)\right] + \left[8 + 3 + (-15)\right] \][/tex]
To identify the best use of associative and commutative properties, we can check how the grouping of terms makes simplification easier:
#### Option A
Grouping [tex]\(\frac{2}{5} + 8 + (-15)\)[/tex] and [tex]\(3 + (-\frac{1}{5})\)[/tex] does help somewhat, but it does not primarily group the similar fraction terms together for easier cancellation.
#### Option B
Grouping [tex]\(3 + \frac{2}{5} + (-15)\)[/tex] and [tex]\(\left(-\frac{1}{5}\right) + 8\)[/tex] again does not prioritize simplifying similar fractional terms first.
#### Option C
Grouping [tex]\(\frac{2}{5} + (-15)\)[/tex] and [tex]\(\left[8 + \left(-\frac{1}{5}\right) + 3\right]\)[/tex] does not make simplifying the fractions straightforward.
#### Option D
Grouping [tex]\(\frac{2}{5} + \left(-\frac{1}{5}\right)\)[/tex] and [tex]\(\left[8 + 3 + (-15)\right]\)[/tex]:
1. [tex]\(\frac{2}{5} + \left(-\frac{1}{5}\right) = \frac{2}{5} - \frac{1}{5} = \frac{1}{5}\)[/tex]
2. [tex]\(8 + 3 + (-15) = 8 + 3 - 15 = -4\)[/tex]
So, by simplifying:
[tex]\[ \frac{1}{5} + (-4) = -3.8 \][/tex]
Therefore, the grouping in option D simplifies the expression most effectively by using the associative and commutative properties to simplify the fractions first and then the integer terms. Therefore, the best answer is:
[tex]\[ \boxed{D} \][/tex]
### Option A
[tex]\[ \left[\frac{2}{5} + 8 + (-15)\right] + \left[3 + \left(-\frac{1}{5}\right)\right] \][/tex]
### Option B
[tex]\[ \left[3 + \frac{2}{5} + (-15)\right] + \left[\left(-\frac{1}{5}\right) + 8\right] \][/tex]
### Option C
[tex]\[ \left[\frac{2}{5} + (-15)\right] + \left[8 + \left(-\frac{1}{5}\right) + 3\right] \][/tex]
### Option D
[tex]\[ \left[\frac{2}{5} + \left(-\frac{1}{5}\right)\right] + \left[8 + 3 + (-15)\right] \][/tex]
To identify the best use of associative and commutative properties, we can check how the grouping of terms makes simplification easier:
#### Option A
Grouping [tex]\(\frac{2}{5} + 8 + (-15)\)[/tex] and [tex]\(3 + (-\frac{1}{5})\)[/tex] does help somewhat, but it does not primarily group the similar fraction terms together for easier cancellation.
#### Option B
Grouping [tex]\(3 + \frac{2}{5} + (-15)\)[/tex] and [tex]\(\left(-\frac{1}{5}\right) + 8\)[/tex] again does not prioritize simplifying similar fractional terms first.
#### Option C
Grouping [tex]\(\frac{2}{5} + (-15)\)[/tex] and [tex]\(\left[8 + \left(-\frac{1}{5}\right) + 3\right]\)[/tex] does not make simplifying the fractions straightforward.
#### Option D
Grouping [tex]\(\frac{2}{5} + \left(-\frac{1}{5}\right)\)[/tex] and [tex]\(\left[8 + 3 + (-15)\right]\)[/tex]:
1. [tex]\(\frac{2}{5} + \left(-\frac{1}{5}\right) = \frac{2}{5} - \frac{1}{5} = \frac{1}{5}\)[/tex]
2. [tex]\(8 + 3 + (-15) = 8 + 3 - 15 = -4\)[/tex]
So, by simplifying:
[tex]\[ \frac{1}{5} + (-4) = -3.8 \][/tex]
Therefore, the grouping in option D simplifies the expression most effectively by using the associative and commutative properties to simplify the fractions first and then the integer terms. Therefore, the best answer is:
[tex]\[ \boxed{D} \][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.