To find out how much Jeannie's puppy weighed at the beginning of May, we need to add the weight gains during March and April to the puppy's weight at the end of February.
1. Initial weight at the end of February:
[tex]\[
9 \frac{3}{4} \text{ pounds}
\][/tex]
2. Weight gained during March:
[tex]\[
2 \frac{1}{4} \text{ pounds}
\][/tex]
3. Weight gained during April:
[tex]\[
1 \frac{3}{8} \text{ pounds}
\][/tex]
First, let's convert these mixed numbers to improper fractions for easier addition:
- [tex]\( 9 \frac{3}{4} \)[/tex] can be converted into an improper fraction:
[tex]\[
9 \frac{3}{4} = \frac{9 \times 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4}
\][/tex]
- [tex]\( 2 \frac{1}{4} \)[/tex] can be converted into an improper fraction:
[tex]\[
2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\][/tex]
- [tex]\( 1 \frac{3}{8} \)[/tex] can be converted into an improper fraction:
[tex]\[
1 \frac{3}{8} = \frac{1 \times 8 + 3}{8} = \frac{8 + 3}{8} = \frac{11}{8}
\][/tex]
Next, let's add the improper fractions together. First, we need a common denominator to add these fractions. The least common multiple (LCM) of 4 and 8 is 8:
- Convert [tex]\(\frac{39}{4}\)[/tex] to have a denominator of 8:
[tex]\[
\frac{39}{4} = \frac{39 \times 2}{4 \times 2} = \frac{78}{8}
\][/tex]
- [tex]\(\frac{9}{4}\)[/tex] can be converted to have a denominator of 8:
[tex]\[
\frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8}
\][/tex]
- [tex]\(\frac{11}{8}\)[/tex] already has a denominator of 8, so it remains as [tex]\(\frac{11}{8}\)[/tex].
Now, we add the fractions together:
[tex]\[
\frac{78}{8} + \frac{18}{8} + \frac{11}{8} = \frac{78 + 18 + 11}{8} = \frac{107}{8}
\][/tex]
Convert [tex]\(\frac{107}{8}\)[/tex] back to a mixed number:
- Divide 107 by 8, which gives 13 with a remainder of 3:
[tex]\[
\frac{107}{8} = 13 \frac{3}{8}
\][/tex]
So, Jeannie's puppy weighs [tex]\(\boxed{13 \frac{3}{8}}\)[/tex] pounds at the beginning of May.
