Answer :
To find which choice rewrites the expression [tex]\(40 + 30 + 10\)[/tex] correctly using the commutative property and simplifies it correctly, let's investigate each option:
1. Option 1: [tex]\(40 + 10 + 10 + 10 + 10 = 50 + 10 + 10 + 10 = 60 + 10 + 10 = 70 + 10 = 80\)[/tex]
- Here, the original expression [tex]\(40 + 30 + 10\)[/tex] was rewritten as [tex]\(40 + 10 + 10 + 10 + 10\)[/tex].
- This is a correct rearrangement using the commutative property because [tex]\(30\)[/tex] was split into four [tex]\(10\)[/tex]s.
- Simplification steps:
- [tex]\(40 + 10 + 10 + 10 + 10\)[/tex] simplifies to [tex]\(50 + 10 + 10 + 10\)[/tex],
- Then to [tex]\(60 + 10 + 10\)[/tex],
- Then to [tex]\(70 + 10\)[/tex],
- Finally to [tex]\(80\)[/tex].
2. Option 2: [tex]\(40 + 10 + 10 + 10 + 10 = 50 + 10 + 10 = 60 + 10 = 70\)[/tex]
- Here again, the original expression was rewritten as [tex]\(40 + 10 + 10 + 10 + 10\)[/tex].
- This is also a correct rearrangement using the commutative property.
- Simplification steps:
- [tex]\(40 + 10 + 10 + 10 + 10\)[/tex] simplifies to [tex]\(50 + 10 + 10\)[/tex],
- Then to [tex]\(60 + 10\)[/tex],
- Finally to [tex]\(70\)[/tex].
3. Option 3: [tex]\(40 + 10 + 30 = 50 + 30 = 80\)[/tex]
- The original expression [tex]\(40 + 30 + 10\)[/tex] was reordered as [tex]\(40 + 10 + 30\)[/tex] using the commutative property.
- Simplification steps:
- [tex]\(40 + 10\)[/tex] simplifies to [tex]\(50\)[/tex],
- Then [tex]\(50 + 30\)[/tex] simplifies to [tex]\(80\)[/tex].
4. Option 4: [tex]\(40 + 10 + 30 = 50 + 40 = 90\)[/tex]
- The original expression [tex]\(40 + 30 + 10\)[/tex] was reordered as [tex]\(40 + 10 + 30\)[/tex] using the commutative property.
- However, the simplification was done incorrectly:
- [tex]\(40 + 10\)[/tex] simplifies to [tex]\(50\)[/tex],
- But [tex]\(50 + 30\)[/tex] should simplify to [tex]\(80\)[/tex], not [tex]\(90\)[/tex].
Out of these choices, Option 3 correctly rewrites [tex]\(40 + 30 + 10\)[/tex] using the commutative property and then simplifies it correctly to [tex]\(80\)[/tex].
Therefore, the correct choice is:
Option 3: [tex]\(40 + 10 + 30 = 50 + 30 = 80\)[/tex]
1. Option 1: [tex]\(40 + 10 + 10 + 10 + 10 = 50 + 10 + 10 + 10 = 60 + 10 + 10 = 70 + 10 = 80\)[/tex]
- Here, the original expression [tex]\(40 + 30 + 10\)[/tex] was rewritten as [tex]\(40 + 10 + 10 + 10 + 10\)[/tex].
- This is a correct rearrangement using the commutative property because [tex]\(30\)[/tex] was split into four [tex]\(10\)[/tex]s.
- Simplification steps:
- [tex]\(40 + 10 + 10 + 10 + 10\)[/tex] simplifies to [tex]\(50 + 10 + 10 + 10\)[/tex],
- Then to [tex]\(60 + 10 + 10\)[/tex],
- Then to [tex]\(70 + 10\)[/tex],
- Finally to [tex]\(80\)[/tex].
2. Option 2: [tex]\(40 + 10 + 10 + 10 + 10 = 50 + 10 + 10 = 60 + 10 = 70\)[/tex]
- Here again, the original expression was rewritten as [tex]\(40 + 10 + 10 + 10 + 10\)[/tex].
- This is also a correct rearrangement using the commutative property.
- Simplification steps:
- [tex]\(40 + 10 + 10 + 10 + 10\)[/tex] simplifies to [tex]\(50 + 10 + 10\)[/tex],
- Then to [tex]\(60 + 10\)[/tex],
- Finally to [tex]\(70\)[/tex].
3. Option 3: [tex]\(40 + 10 + 30 = 50 + 30 = 80\)[/tex]
- The original expression [tex]\(40 + 30 + 10\)[/tex] was reordered as [tex]\(40 + 10 + 30\)[/tex] using the commutative property.
- Simplification steps:
- [tex]\(40 + 10\)[/tex] simplifies to [tex]\(50\)[/tex],
- Then [tex]\(50 + 30\)[/tex] simplifies to [tex]\(80\)[/tex].
4. Option 4: [tex]\(40 + 10 + 30 = 50 + 40 = 90\)[/tex]
- The original expression [tex]\(40 + 30 + 10\)[/tex] was reordered as [tex]\(40 + 10 + 30\)[/tex] using the commutative property.
- However, the simplification was done incorrectly:
- [tex]\(40 + 10\)[/tex] simplifies to [tex]\(50\)[/tex],
- But [tex]\(50 + 30\)[/tex] should simplify to [tex]\(80\)[/tex], not [tex]\(90\)[/tex].
Out of these choices, Option 3 correctly rewrites [tex]\(40 + 30 + 10\)[/tex] using the commutative property and then simplifies it correctly to [tex]\(80\)[/tex].
Therefore, the correct choice is:
Option 3: [tex]\(40 + 10 + 30 = 50 + 30 = 80\)[/tex]
