Final answer:
Angelina is correct; the sum of two rational numbers is rational. Rational numbers, expressible as fractions, remain rational when added, as their sum can also be expressed as a fraction.
Step-by-step explanation:
Angelina is correct in her conclusion that the sum of two rational numbers is rational. A rational number is defined as a number that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. The numbers 0.45 and 0.333 (which is the decimal representation of ⅓) are both rational because they can be written as fractions: 0.45 as ⅔ and 0.333 as ⅓.
When we add two rational numbers, the sum is also rational. This is because when adding fractions, we find a common denominator and then add the numerators. The result is still a fraction of two integers, which means the result is also a rational number. Therefore, when Angelina adds 0.45 to 0.333, she gets 0.783, which can also be expressed as a fraction, confirming that the sum is indeed rational.