Question
Use the associative property to create equivalent expressions to a + b + (c + d). Which statements are true? Select four options.
The associative property allows us to change the grouping of terms that are added together.
When changing the grouping, the order of the terms stays the same; only the parentheses change position.
The expression a + (b + c) + d is an equivalent expression.
The expression ab(cd) is an equivalent expression.
The expression (a+ b) + c + d is an equivalent expression.
The expression a + b(c + d) is an equivalent expression.
The associative property allows us to change the grouping of terms that are added together.
When changing the grouping, the order of the terms stays the same; only the parentheses change position.
The expression a + (b + c) + d is an equivalent expression.
The expression ab(cd) is an equivalent expression.
The expression (a+ b) + c + d is an equivalent expression.
The expression a + b(c + d) is an equivalent expression.
Answers
GPT-4o mini
To use the associative property on the expression \( a + b + (c + d) \), we can change the grouping of the terms without changing the order of the terms in the addition. Here’s an analysis of the provided statements:
1. **The associative property allows us to change the grouping of terms that are added together.**
**True.** This is the definition of the associative property.
2. **When changing the grouping, the order of the terms stays the same; only the parentheses change position.**
**True.** This statement accurately describes how the associative property works.
3. **The expression \( a + (b + c) + d \) is an equivalent expression.**
**True.** By the associative property, we can group \( b + c \) together, and the expression will still have the same value.
4. **The expression \( ab(cd) \) is an equivalent expression.**
**False.** This expression reflects multiplication, not addition, so it is not equivalent to the original expression.
5. **The expression \( (a + b) + c + d \) is an equivalent expression.**
**True.** This is another valid grouping using the associative property.
6. **The expression \( a + b(c + d) \) is an equivalent expression.**
**False.** This expression changes the operation; it implies multiplication between \( b \) and \( (c + d) \), which is not equivalent to the original expression.
Based on this analysis, the true statements are:
- The associative property allows us to change the grouping of terms that are added together.
- When changing the grouping, the order of the terms stays the same; only the parentheses change position.
- The expression \( a + (b + c) + d \) is an equivalent expression.
- The expression \( (a + b) + c + d \) is an equivalent expression.
1. **The associative property allows us to change the grouping of terms that are added together.**
**True.** This is the definition of the associative property.
2. **When changing the grouping, the order of the terms stays the same; only the parentheses change position.**
**True.** This statement accurately describes how the associative property works.
3. **The expression \( a + (b + c) + d \) is an equivalent expression.**
**True.** By the associative property, we can group \( b + c \) together, and the expression will still have the same value.
4. **The expression \( ab(cd) \) is an equivalent expression.**
**False.** This expression reflects multiplication, not addition, so it is not equivalent to the original expression.
5. **The expression \( (a + b) + c + d \) is an equivalent expression.**
**True.** This is another valid grouping using the associative property.
6. **The expression \( a + b(c + d) \) is an equivalent expression.**
**False.** This expression changes the operation; it implies multiplication between \( b \) and \( (c + d) \), which is not equivalent to the original expression.
Based on this analysis, the true statements are:
- The associative property allows us to change the grouping of terms that are added together.
- When changing the grouping, the order of the terms stays the same; only the parentheses change position.
- The expression \( a + (b + c) + d \) is an equivalent expression.
- The expression \( (a + b) + c + d \) is an equivalent expression.