Sure, let's verify the distributive property using the rational numbers 36 and 192 on a square grid.
The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex].
Let's verify this step-by-step:
1. Step 1: Define the values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
Here, [tex]\(a = 36\)[/tex], [tex]\(b = 192\)[/tex], and [tex]\(c = 1\)[/tex].
2. Step 2: Calculate the left-hand side of the distributive property:
[tex]\(a(b + c)\)[/tex].
Substitute the values in:
[tex]\( 36(192 + 1) \)[/tex].
First, calculate the expression within the parenthesis:
[tex]\( 192 + 1 = 193 \)[/tex].
Then multiply by [tex]\(a\)[/tex]:
[tex]\( 36 \times 193 = 6948 \)[/tex].
3. Step 3: Calculate the right-hand side of the distributive property:
[tex]\(ab + ac\)[/tex].
First, calculate each term individually:
[tex]\( 36 \times 192 = 6912 \)[/tex] and [tex]\( 36 \times 1 = 36 \)[/tex].
Then add the results:
[tex]\( 6912 + 36 = 6948 \)[/tex].
4. Step 4: Compare the results.
The left-hand side and the right-hand side both equal 6948.
Therefore, [tex]\( 36(192 + 1) = (36 \times 192) + (36 \times 1) \)[/tex], verifying that the distributive property holds for the given rational numbers.
Given the comparisons:
- Left-hand side: 6948
- Right-hand side: 6948
We confirm that the distributive property holds true in this case [tex]\( (6948 = 6948) \)[/tex]. Hence, the statement is correct.
