Question

Classify the sum:
7/4-k + k/8
irrational
rational
integer
whole number

Answer 1

To classify the expression \( \frac{7}{4} - k + \frac{k}{8} \), we can start by rewriting it in terms of \( k \).

1. First, combine the terms involving \( k \):
\[
-k + \frac{k}{8} = -\frac{8k}{8} + \frac{k}{8} = -\frac{8k - k}{8} = -\frac{7k}{8}
\]

2. Now, substitute this back into the expression:
\[
\frac{7}{4} - \frac{7k}{8}
\]

3. To combine these terms, we need a common denominator. The least common denominator of 4 and 8 is 8:
\[
\frac{7}{4} = \frac{7 \cdot 2}{4 \cdot 2} = \frac{14}{8}
\]

4. Now, the expression can be written as:
\[
\frac{14}{8} - \frac{7k}{8} = \frac{14 - 7k}{8}
\]

The sum \( \frac{14 - 7k}{8} \) can be classified based on the value of \( k \):

- If \( k \) is a rational number, then \( 14 - 7k \) is also a rational expression. Since the denominator is 8 (a rational number), the overall expression is rational.
- If \( k \) is an integer, then \( 14 - 7k \) is also an integer, making the expression an integer as well.
- If \( k \) is a whole number (non-negative integer), then the result will still be a rational number.

In summary, the classification of the expression depends on the value of \( k \) but will generally be classified as a **rational** number. If \( k \) is an integer, it will also be an integer. If \( k \) is a whole number, it will be a whole number.

Thus, the answer is:
**Rational**