Rational & Irrational Numbers Unit test:

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.