To determine which statement is true, let's analyze each option one by one:
1. You can express the additive identity as [tex]\(a + 0 = a\)[/tex].
This statement is referring to the concept of the additive identity in mathematics. The additive identity property states that any number [tex]\(a\)[/tex], when added to 0, will result in the same number [tex]\(a\)[/tex]. In mathematical terms, [tex]\(a + 0 = a\)[/tex]. This statement is indeed true.
2. In the statement, [tex]\(a\left(\frac{1}{a}\right), a \neq 0, a\)[/tex] is a real number, and [tex]\(\frac{1}{a}\)[/tex] is its opposite.
This statement involves the concept of multiplicative inverses. For a non-zero real number [tex]\(a\)[/tex], [tex]\(\frac{1}{a}\)[/tex] is its multiplicative inverse, meaning [tex]\(a \cdot \frac{1}{a} = 1\)[/tex]. However, [tex]\(\frac{1}{a}\)[/tex] is not the opposite (or additive inverse) of [tex]\(a\)[/tex]; the opposite of [tex]\(a\)[/tex] is [tex]\(-a\)[/tex]. Therefore, this statement is false.
3. The number 7,235,000 is an irrational number.
An irrational number is a number that cannot be expressed as a fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex]. The number 7,235,000 is a whole number and can be written as a fraction [tex]\(\frac{7235000}{1}\)[/tex], making it a rational number. Therefore, this statement is false.
4. The number [tex]\(\frac{1}{3}\)[/tex] is a natural number.
Natural numbers are the set of positive integers starting from 1, 2, 3, and so on. The number [tex]\(\frac{1}{3}\)[/tex] is a positive fraction and not a whole number. Hence, it is not a natural number. Therefore, this statement is false.
After evaluating all the statements, we find that the true statement is:
You can express the additive identity as [tex]\(a + 0 = a\)[/tex].
