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Which choice shows [tex]$40+30+10$[/tex] rewritten correctly using the commutative property and then simplified correctly?

A. [tex]$40+10+10+10+10=50+10+10+10=60+10+10=70+10=80$[/tex]

B. [tex][tex]$40+10+10+10+10=50+10+10=60+10=70$[/tex][/tex]

C. [tex]$40+10+30=50+30=80$[/tex]

D. [tex]$40+10+30=50+40=90$[/tex]

Sagot :

GinnyAnswer
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]
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