Yes, the sum of the two rational numbers will produce a rational number.
To explain further:
- The number \( \frac{47}{3} \) is a rational number because it can be expressed as a fraction of two integers (47 and 3).
- The number 21 can also be expressed as a fraction: it can be written as \( \frac{21}{1} \), which is also a rational number.
When you add two rational numbers, the sum is always rational.
Now, let's calculate the sum:
\[ \frac{47}{3} + 21 = \frac{47}{3} + \frac{21}{1} \]
To add these two fractions, we need a common denominator. The least common denominator of 3 and 1 is 3. So, we convert 21 into a fraction with a denominator of 3:
\[ 21 = \frac{21 \times 3}{1 \times 3} = \frac{63}{3} \]
Now, we can add them:
\[ \frac{47}{3} + \frac{63}{3} = \frac{47 + 63}{3} = \frac{110}{3} \]
The result \( \frac{110}{3} \) is also a rational number. Therefore, the sum of \( \frac{47}{3} \) and \( 21 \) is rational.