Question

Classify the sum:
7/4-k + k/8

Answer 1

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

First, let's combine the \( -k \) and \( \frac{k}{8} \) terms. We can express \( -k \) in terms of eighths:

\[
-k = -\frac{8k}{8}
\]

Now, we can combine the two \( k \) terms:

\[
-\frac{8k}{8} + \frac{k}{8} = \frac{-8k + k}{8} = \frac{-7k}{8}
\]

Now, we can rewrite the entire expression:

\[
\frac{7}{4} - k + \frac{k}{8} = \frac{7}{4} + \frac{-7k}{8}
\]

Now we have:

\[
\frac{7}{4} - \frac{7k}{8}
\]

Next, we can rewrite \( \frac{7}{4} \) with a common denominator of 8 for easier addition/subtraction:

\[
\frac{7}{4} = \frac{14}{8}
\]

Thus, the expression becomes:

\[
\frac{14}{8} - \frac{7k}{8}
\]

Now we can combine the fractions:

\[
\frac{14 - 7k}{8}
\]

This is our simplified expression.

To classify this sum, we can note that it is a linear expression in terms of \( k \) because it can be written in the form \( ax + b \) where \( a \) and \( b \) are constants. Specifically, it is a linear function of \( k \) with:

- A slope of \( -\frac{7}{8} \)
- A y-intercept of \( \frac{14}{8} \) (or \( \frac{7}{4} \))

Thus, we can conclude that the sum \( \frac{7}{4} - k + \frac{k}{8} \) is a linear expression in \( k \).