Answer :
- Use the identity property to simplify: $38 + 69 + 52 + 0 = 38 + 69 + 52$.
- Apply the commutative property: $38 + 69 + 52 = 38 + 52 + 69$.
- Calculate intermediate sums: $38 + 52 = 90$.
- Find the final sum: $90 + 69 = 159$, so the answer is $\boxed{159}$.
### Explanation
1. Understanding the Problem
We are given an incomplete equation and asked to fill in the blanks using properties of addition to find the sum. The properties we'll use are the associative and commutative properties, as well as the identity property of addition (adding 0 doesn't change the number). Let's fill in the blanks step-by-step.
2. Filling the First Blank
First, we have $38+69+52+0 = 38+69+(52+\square)$. According to the identity property of addition, adding 0 to any number doesn't change its value. So, $52 + 0 = 52$. Therefore, the first blank should be filled with 0.
3. Filling the Second Blank
Now we have $38+69+(52+0) = 38+69+\square$. Since $52+0 = 52$, the next blank should be filled with 52. So, the equation becomes $38+69+52$.
4. Filling the Third Blank
Next, we have $38+69+52 = 38+\square+69$. Here, we use the commutative property of addition, which states that we can add numbers in any order. So, we can swap 69 and 52 to get $38+52+69$. Thus, the third blank should be filled with 52.
5. Filling the Fourth Blank
Now we have $38+52+69 = \square+69$. We need to add $38+52$. $38+52 = 90$. So, the fourth blank should be filled with 90.
6. Finding the Final Sum
Finally, we have $90+69 = \square$. We need to add $90+69$. $90+69 = 159$. So, the final blank should be filled with 159.
7. The Final Answer
Therefore, the complete equation is:
$\begin{aligned}
38+69+52+0 & =38+69+(52+0) \\
& =38+69+52 \\
& =38+52+69 \\
& =90+69 \\
& = 159
\end{aligned}$
The final sum is 159.
### Examples
Understanding the properties of addition, like the associative and commutative properties, is crucial in everyday situations. For instance, when calculating expenses, you can group and reorder the amounts to make the addition easier. Imagine you're buying groceries: $38 for fruits, $69 for vegetables, and $52 for snacks. Using these properties, you can quickly add $38 + $52 first to get $90, then add $69 to get a total of $159. This makes mental calculations faster and reduces the chance of errors.
- Apply the commutative property: $38 + 69 + 52 = 38 + 52 + 69$.
- Calculate intermediate sums: $38 + 52 = 90$.
- Find the final sum: $90 + 69 = 159$, so the answer is $\boxed{159}$.
### Explanation
1. Understanding the Problem
We are given an incomplete equation and asked to fill in the blanks using properties of addition to find the sum. The properties we'll use are the associative and commutative properties, as well as the identity property of addition (adding 0 doesn't change the number). Let's fill in the blanks step-by-step.
2. Filling the First Blank
First, we have $38+69+52+0 = 38+69+(52+\square)$. According to the identity property of addition, adding 0 to any number doesn't change its value. So, $52 + 0 = 52$. Therefore, the first blank should be filled with 0.
3. Filling the Second Blank
Now we have $38+69+(52+0) = 38+69+\square$. Since $52+0 = 52$, the next blank should be filled with 52. So, the equation becomes $38+69+52$.
4. Filling the Third Blank
Next, we have $38+69+52 = 38+\square+69$. Here, we use the commutative property of addition, which states that we can add numbers in any order. So, we can swap 69 and 52 to get $38+52+69$. Thus, the third blank should be filled with 52.
5. Filling the Fourth Blank
Now we have $38+52+69 = \square+69$. We need to add $38+52$. $38+52 = 90$. So, the fourth blank should be filled with 90.
6. Finding the Final Sum
Finally, we have $90+69 = \square$. We need to add $90+69$. $90+69 = 159$. So, the final blank should be filled with 159.
7. The Final Answer
Therefore, the complete equation is:
$\begin{aligned}
38+69+52+0 & =38+69+(52+0) \\
& =38+69+52 \\
& =38+52+69 \\
& =90+69 \\
& = 159
\end{aligned}$
The final sum is 159.
### Examples
Understanding the properties of addition, like the associative and commutative properties, is crucial in everyday situations. For instance, when calculating expenses, you can group and reorder the amounts to make the addition easier. Imagine you're buying groceries: $38 for fruits, $69 for vegetables, and $52 for snacks. Using these properties, you can quickly add $38 + $52 first to get $90, then add $69 to get a total of $159. This makes mental calculations faster and reduces the chance of errors.
