3. During the U.S. Civil War, $$ \frac{5}{9} $$ of the states fought for the Union, and $$ \frac{11}{36} $$ of the states fought for the Confederacy. The rest of the states were border

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To determine the fraction of states that were border states during the U.S. Civil War, let's break down the information provided:

1. **Fraction of States Fighting for the Union:** $$ \frac{5}{9} $$
2. **Fraction of States Fighting for the Confederacy:** $$ \frac{11}{36} $$

**Step 1: Find a Common Denominator**

To add these two fractions, we need a common denominator. The least common denominator (LCD) of 9 and 36 is 36.

- Convert $$ \frac{5}{9} $$ to a denominator of 36:
  $$
  \frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}
  $$

- $$ \frac{11}{36} $$ already has the denominator of 36.

**Step 2: Add the Fractions**

$$
\frac{20}{36} + \frac{11}{36} = \frac{31}{36}
$$

**Step 3: Determine the Fraction of Border States**

Since the total must add up to 1 (or $$ \frac{36}{36} $$), subtract the sum of the Union and Confederacy fractions from 1:

$$
1 - \frac{31}{36} = \frac{36}{36} - \frac{31}{36} = \frac{5}{36}
$$

**Answer:**
$$
\boxed{\dfrac{5}{36}}
$$
$$\frac{5}{36}$$ of the states were border states during the U.S. Civil War.

During the U.S. Civil War, of the states
fought for the Union, and of the
states fought for the Confederacy.
The rest of the states were border

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During the U.S. Civil War, of the states fought for the Union, and of the states fought for the Confederacy. The rest of the states were border