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Several properties are used to evaluate this expression. Identify the property used in each step.

[tex]\[
\begin{array}{l}
21 + (36 + 0 + 19) \\
21 + (36 + 19) \\
21 + (19 + 36) \\
(21 + 19) + 36
\end{array}
\][/tex]

[tex]\[
\begin{array}{l}
\square \\
\square \\
\square \\
\square
\end{array}
\][/tex]

1. 21 + (36 + 0 + 19): \_\_\_\_\_
2. 21 + (36 + 19): \_\_\_\_\_
3. 21 + (19 + 36): \_\_\_\_\_
4. (21 + 19) + 36: \_\_\_\_\_

Identify the property used in each step (e.g., Commutative Property, Associative Property, Identity Property).



Answer :

GinnyAnswer
Certainly! Let's break down the steps used to evaluate the expression [tex]\( 21 + (36 + 0 + 19) \)[/tex]:

### Step 1: Simplify [tex]\( 36 + 0 + 19 \)[/tex] to [tex]\( 36 + 19 \)[/tex]

The identity property of addition tells us that adding zero to a number does not change the value of that number. Hence, [tex]\( 36 + 0 = 36 \)[/tex].

So, we have:

[tex]\[ 21 + (36 + 0 + 19) \rightarrow 21 + (36 + 19) \][/tex]

Property used: Identity property of addition, [tex]\( 0 \)[/tex] is the additive identity

### Step 2: Rearrange [tex]\( 21 + (36 + 19) \)[/tex] to [tex]\( 21 + (19 + 36) \)[/tex]

The commutative property of addition states that changing the order of the numbers being added does not change the sum. So, we can switch the positions of [tex]\( 36 \)[/tex] and [tex]\( 19 \)[/tex]:

[tex]\[ 21 + (36 + 19) \rightarrow 21 + (19 + 36) \][/tex]

Property used: Commutative property of addition, [tex]\( a + b = b + a \)[/tex]

### Step 3: Combine similar expressions

The associative property of addition tells us that when adding three or more numbers, the way in which the numbers are grouped does not change the sum. Thus:

[tex]\[ 21 + (19 + 36) \rightarrow (21 + 19) + 36 \][/tex]

Property used: Associative property of addition, [tex]\( (a + b) + c = a + (b + c) \)[/tex]

### Summary of Properties Used:

1. Identity property of addition: [tex]\( 21 + (36 + 0 + 19) \rightarrow 21 + (36 + 19) \)[/tex]
2. Commutative property of addition: [tex]\( 21 + (36 + 19) \rightarrow 21 + (19 + 36) \)[/tex]
3. Associative property of addition: [tex]\( 21 + (19 + 36) \rightarrow (21 + 19) + 36 \)[/tex]

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