Certainly! Let's tackle this problem step-by-step.
1. Convert the mixed numbers to improper fractions:
- The weight of the backpack with the math book is [tex]\( 18 \frac{7}{8} \)[/tex].
- The weight of the backpack without the math book is [tex]\( 14 \frac{7}{9} \)[/tex].
To convert these mixed numbers to improper fractions:
[tex]\[
18 \frac{7}{8} = \frac{18 \times 8 + 7}{8} = \frac{144 + 7}{8} = \frac{151}{8}
\][/tex]
[tex]\[
14 \frac{7}{9} = \frac{14 \times 9 + 7}{9} = \frac{126 + 7}{9} = \frac{133}{9}
\][/tex]
2. Find a common denominator to subtract the fractions:
The least common multiple (LCM) of 8 and 9 is 72.
Convert each fraction to have this common denominator:
[tex]\[
\frac{151}{8} = \frac{151 \times 9}{8 \times 9} = \frac{1359}{72}
\][/tex]
[tex]\[
\frac{133}{9} = \frac{133 \times 8}{9 \times 8} = \frac{1064}{72}
\][/tex]
3. Subtract the fractions:
[tex]\[
\frac{1359}{72} - \frac{1064}{72} = \frac{1359 - 1064}{72} = \frac{295}{72}
\][/tex]
4. Convert the improper fraction back to a mixed number:
[tex]\[
\frac{295}{72} = 4 \frac{7}{72}
\][/tex]
Therefore, the weight of Eliza's math book is:
[tex]\[
4 \frac{11}{72} \text{ pounds}
\][/tex]
Among the given choices, the correct answer is:
[tex]\[ \boxed{4 \frac{11}{72}} \text{ pounds} \][/tex]
