To determine the number of hours \( h \) that Moira still needs to read to finish the book, we can set up an equation based on the total hours she needs and the hours she has already read.
- Moira needs \( 2 \frac{1}{4} \) hours to finish the book.
- She has already read \( 1 \frac{7}{8} \) hours.
First, we can express these mixed numbers as improper fractions:
-
Convert \( 2 \frac{1}{4} \):
\[
2 \frac{1}{4} = 2 \times 4 + 1 = \frac{8 + 1}{4} = \frac{9}{4}
\]
-
Convert \( 1 \frac{7}{8} \):
\[
1 \frac{7}{8} = 1 \times 8 + 7 = \frac{8 + 7}{8} = \frac{15}{8}
\]
Now, we can set up the equation to find \( h \):
\[
h + 1 \frac{7}{8} = 2 \frac{1}{4}
\]
In terms of improper fractions, the equation becomes:
\[
h + \frac{15}{8} = \frac{9}{4}
\]
Now let's express \( \frac{9}{4} \) as an equivalent fraction with a denominator of 8 for ease of calculation:
\[
\frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8}
\]
Thus, the equation can be rewritten as:
\[
h + \frac{15}{8} = \frac{18}{8}
\]
To find \( h \), we can rearrange the equation:
\[
h = \frac{18}{8} - \frac{15}{8}
\]
This simplifies to:
\[
h = \frac{3}{8}
\]
Thus, the completed equation that can be used to determine the number of hours \( h \) that Moira still needs to read is:
\[
h + 1 \frac{7}{8} = 2 \frac{1}{4}
\]