Answer :
To determine whether the sum of [tex]\(\left(-2 \frac{3}{4}\right)\)[/tex] and [tex]\(\frac{5}{9}\)[/tex] is rational, we follow these steps:
1. Convert [tex]\(-2 \frac{3}{4}\)[/tex] to an improper fraction:
- [tex]\(-2 \frac{3}{4}\)[/tex] can be written as [tex]\(-2 - \frac{3}{4}\)[/tex], which is [tex]\(-2.75\)[/tex].
2. Express [tex]\(\frac{5}{9}\)[/tex] as a decimal:
- [tex]\(\frac{5}{9} \approx 0.5555555555555556\)[/tex] (a repeating decimal).
3. Sum the two numbers:
- [tex]\(-2.75 + 0.5555555555555556 = -2.1944444444444446\)[/tex].
4. Determine the nature of the sum:
- The resultant sum, [tex]\(-2.1944444444444446\)[/tex], is a terminating decimal.
- Since it is a terminating decimal, it can be expressed as a fraction, and therefore, it is a rational number.
By follow through each step, we have concluded that:
- The sum of [tex]\(\left(-2 \frac{3}{4}\right)\)[/tex] and [tex]\(\frac{5}{9}\)[/tex] is a terminating decimal, which confirms that it is a rational number.
Thus, the correct statement is:
- The sum is a fraction.
1. Convert [tex]\(-2 \frac{3}{4}\)[/tex] to an improper fraction:
- [tex]\(-2 \frac{3}{4}\)[/tex] can be written as [tex]\(-2 - \frac{3}{4}\)[/tex], which is [tex]\(-2.75\)[/tex].
2. Express [tex]\(\frac{5}{9}\)[/tex] as a decimal:
- [tex]\(\frac{5}{9} \approx 0.5555555555555556\)[/tex] (a repeating decimal).
3. Sum the two numbers:
- [tex]\(-2.75 + 0.5555555555555556 = -2.1944444444444446\)[/tex].
4. Determine the nature of the sum:
- The resultant sum, [tex]\(-2.1944444444444446\)[/tex], is a terminating decimal.
- Since it is a terminating decimal, it can be expressed as a fraction, and therefore, it is a rational number.
By follow through each step, we have concluded that:
- The sum of [tex]\(\left(-2 \frac{3}{4}\right)\)[/tex] and [tex]\(\frac{5}{9}\)[/tex] is a terminating decimal, which confirms that it is a rational number.
Thus, the correct statement is:
- The sum is a fraction.
