Question
left parenthesis negative four thirds right parenthesis left parenthesis three thirds right parenthesis equals negative StartFraction 12 Over 9 EndFraction
Question content area bottom
Part 1
The statement is an example of which property?
A.
identity
B.
inverse
Question content area bottom
Part 1
The statement is an example of which property?
A.
identity
B.
inverse
Answers
GPT-4o mini
To evaluate the given statement \((- \frac{4}{3}) \left( \frac{3}{3} \right) = -\frac{12}{9}\), let's analyze what is happening:
1. The left side is multiplying a negative fraction, \(-\frac{4}{3}\), by \(\frac{3}{3}\), which is equivalent to 1.
2. Any number multiplied by 1 remains unchanged, hence:
\[
(-\frac{4}{3}) \left( \frac{3}{3} \right) = -\frac{4}{3}
\]
3. The right side simplifies to:
\[
-\frac{12}{9} = -\frac{4}{3} \quad \text{(after simplification)}
\]
Since both sides are equal (i.e., \(-\frac{4}{3} = -\frac{4}{3}\)), this equality demonstrates the **identity property** of multiplication, which states that any number multiplied by one (or the identity element for multiplication, which is \(\frac{3}{3} = 1\)) remains unchanged.
Therefore, the correct answer is:
A. identity
1. The left side is multiplying a negative fraction, \(-\frac{4}{3}\), by \(\frac{3}{3}\), which is equivalent to 1.
2. Any number multiplied by 1 remains unchanged, hence:
\[
(-\frac{4}{3}) \left( \frac{3}{3} \right) = -\frac{4}{3}
\]
3. The right side simplifies to:
\[
-\frac{12}{9} = -\frac{4}{3} \quad \text{(after simplification)}
\]
Since both sides are equal (i.e., \(-\frac{4}{3} = -\frac{4}{3}\)), this equality demonstrates the **identity property** of multiplication, which states that any number multiplied by one (or the identity element for multiplication, which is \(\frac{3}{3} = 1\)) remains unchanged.
Therefore, the correct answer is:
A. identity