Final answer:
To represent the statement 'Half of a number is more than one and one-third' as an inequality, you write it as 1/2 x > 4/3. The correct inequality symbol indicating that 1/2 x is greater than 4/3 is '>', making option B the correct choice.
Step-by-step explanation:
The statement 'Half of a number is more than one and one-third' needs to be represented as an inequality. To express this mathematically, you use variables and inequality symbols. In this case, the variable 'x' would represent the unknown number, and the appropriate inequality symbol needs to be chosen to accurately describe the relationship between half of this number and the value one and one-third.
Since we are comparing half of a number (1/2 x) with the value one and one-third, we are essentially saying 1/2 x is greater than 1 1/3. To convert one and one-third into an improper fraction, you multiply the whole number by the denominator of the fraction and add the numerator, resulting in 4/3 (since 1 x 3 + 1 = 4).
Now, the inequality can be written as 1/2 x > 4/3. Since the inequality states that half of 'x' is greater than four-thirds, the correct inequality symbol to use is '>' which means 'is greater than'. Therefore, the complete inequality is 1/2 x > 4/3, which corresponds to option B. Thus, the correct answer to the original question is B. >