Math / Algebra

QuestionUsing the Associative Property
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 $a b(c d)$ is an equivalent expression. The expression $(a+b)+c+d$ is an equivalent expression. The expression $a+b(c+d)$ is an equivalent expression.

Studdy Solution

STEP 1

What is this asking? We need to find expressions that are equal to $a+b+(c+d)$ by just moving the parentheses around. Watch out! Don't change the order of the variables, just the parentheses!
Also, remember the associative property only works for addition and multiplication, not a mix of both.

STEP 2

1. Understand the Associative Property
2. Apply the Associative Property
3. Identify Equivalent Expressions

STEP 3

The associative property says that when you're adding or multiplying a bunch of numbers, it doesn't matter how you group them with parentheses!
It's like saying, if you're adding $1 + 2 + 3$ , it doesn't matter if you do $(1 + 2) + 3$ or $1 + (2 + 3)$ , you still get 6!

STEP 4

Let's start with our original expression: $a+b+(c+d)$ .
We can move the parentheses around without changing the order of the variables.

STEP 5

Let's move those parentheses!
We can group $a$ and $b$ together like this: $(a+b)+c+d$ .
See how we kept everything in the same order?

STEP 6

We can also group $b$ , $c$ , and $d$ together, but we need to keep their order the same!
This gives us $a+(b+c)+d$ , which is another equivalent expression.
Remember, we're just shifting the parentheses, not the variables!

STEP 7

Now, let's check the options.
Is $a+(b+c)+d$ equivalent?
Yes! We just found that one in the previous step.

STEP 8

Is $(a+b)+c+d$ equivalent?
Yes! This is also one we found by moving the parentheses.

STEP 9

Is $a b(c d)$ equivalent?
No way!
This uses multiplication, and we're only dealing with addition here.
Plus, it's missing those plus signs!

STEP 10

Is $a+b(c+d)$ equivalent?
Nope! This mixes addition and multiplication without any parentheses around the addition part.
That changes the order of operations, so it's not the same.

STEP 11

The correct answers are: $a+(b+c)+d$ is an equivalent 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.

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Studdy Solution

STEP 1

What is this asking? We need to find expressions that are equal to $a+b+(c+d)$ by just moving the parentheses around. Watch out! Don't change the order of the variables, just the parentheses!
Also, remember the associative property only works for addition and multiplication, not a mix of both.

STEP 2

1. Understand the Associative Property
2. Apply the Associative Property
3. Identify Equivalent Expressions

STEP 3

The associative property says that when you're adding or multiplying a bunch of numbers, it doesn't matter how you group them with parentheses!
It's like saying, if you're adding $1 + 2 + 3$ , it doesn't matter if you do $(1 + 2) + 3$ or $1 + (2 + 3)$ , you still get 6!

STEP 4

Let's start with our original expression: $a+b+(c+d)$ .
We can move the parentheses around without changing the order of the variables.

STEP 5

Let's move those parentheses!
We can group $a$ and $b$ together like this: $(a+b)+c+d$ .
See how we kept everything in the same order?

STEP 6

We can also group $b$ , $c$ , and $d$ together, but we need to keep their order the same!
This gives us $a+(b+c)+d$ , which is another equivalent expression.
Remember, we're just shifting the parentheses, not the variables!

STEP 7

Now, let's check the options.
Is $a+(b+c)+d$ equivalent?
Yes! We just found that one in the previous step.

STEP 8

Is $(a+b)+c+d$ equivalent?
Yes! This is also one we found by moving the parentheses.

STEP 9

Is $a b(c d)$ equivalent?
No way!
This uses multiplication, and we're only dealing with addition here.
Plus, it's missing those plus signs!

STEP 10

Is $a+b(c+d)$ equivalent?
Nope! This mixes addition and multiplication without any parentheses around the addition part.
That changes the order of operations, so it's not the same.

STEP 11

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Studdy Solution

STEP 1

STEP 2

1. Understand the Associative Property2. Apply the Associative Property3. Identify Equivalent Expressions

STEP 3

STEP 4

Let's **start** with our original expression: a+b+(c+d)a+b+(c+d)a+b+(c+d).We can move the parentheses around *without* changing the order of the variables.

STEP 5

Let's **move** those parentheses!We can group aaa and bbb together like this: (a+b)+c+d(a+b)+c+d(a+b)+c+d.See how we kept everything in the same order?

STEP 6

We can also **group** bbb, ccc, and ddd together, but we need to keep their order the same!This gives us a+(b+c)+da+(b+c)+da+(b+c)+d, which is another equivalent expression.Remember, we're just shifting the parentheses, not the variables!

STEP 7

Now, let's **check** the options.Is a+(b+c)+da+(b+c)+da+(b+c)+d equivalent?Yes! We just found that one in the previous step.

STEP 8

Is (a+b)+c+d(a+b)+c+d(a+b)+c+d equivalent?Yes! This is also one we found by moving the parentheses.

STEP 9

Is ab(cd)a b(c d)ab(cd) equivalent?No way!This uses multiplication, and we're only dealing with addition here.Plus, it's missing those plus signs!

STEP 10

Is a+b(c+d)a+b(c+d)a+b(c+d) equivalent?Nope! This mixes addition and multiplication without any parentheses around the addition part.That changes the order of operations, so it's not the same.

STEP 11

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Understand the Associative Property
2. Apply the Associative Property
3. Identify Equivalent Expressions

Let's start with our original expression: $a+b+(c+d)$ .
We can move the parentheses around without changing the order of the variables.

Let's move those parentheses!
We can group $a$ and $b$ together like this: $(a+b)+c+d$ .
See how we kept everything in the same order?

We can also group $b$ , $c$ , and $d$ together, but we need to keep their order the same!
This gives us $a+(b+c)+d$ , which is another equivalent expression.
Remember, we're just shifting the parentheses, not the variables!

Now, let's check the options.
Is $a+(b+c)+d$ equivalent?
Yes! We just found that one in the previous step.

Is $(a+b)+c+d$ equivalent?
Yes! This is also one we found by moving the parentheses.

Is $a b(c d)$ equivalent?
No way!
This uses multiplication, and we're only dealing with addition here.
Plus, it's missing those plus signs!

Is $a+b(c+d)$ equivalent?
Nope! This mixes addition and multiplication without any parentheses around the addition part.
That changes the order of operations, so it's not the same.