Question

To divide
8
1
​
by 1
2
1
​
, start by writing 1
2
1
​
as a fraction greater than 1.

Elyse's Fruit Punch Recipe
÷ 1
2
1
​

÷ 1
2
1
​

Water
(cups) Fruit Punch Mix
(cups)
1
2
1
​

8
1
​

1 ?
8
1
​
÷ 1
2
1
​

=
8
1
​
÷

Answer 1

To divide \( 8 \frac{1}{1} \) (which is equivalent to \( 8 + 1 = 9 \)) by \( 1 \frac{2}{1} \) (equivalent to \( 1 + 2 = 3 \)), we first need to express \( 1 \frac{2}{1} \) as an improper fraction.

1. **Convert Mixed Numbers to Improper Fractions**:
- \( 8 \frac{1}{1} = \frac{9}{1} \)
- \( 1 \frac{2}{1} = \frac{3}{1} \)

2. **To Divide Two Fractions**:
- When dividing by a fraction, multiply by its reciprocal.
- So, \( \frac{9}{1} \div \frac{3}{1} = \frac{9}{1} \times \frac{1}{3} \)

3. **Multiply the Fractions**:
- \( \frac{9}{1} \times \frac{1}{3} = \frac{9 \times 1}{1 \times 3} = \frac{9}{3} \)

4. **Simplify the Fraction**:
- \( \frac{9}{3} = 3 \)

Therefore, the answer to the problem \( 8 \frac{1}{1} \div 1 \frac{2}{1} \) is \( 3 \).

Thus, your division looks like this:
\[
8 \frac{1}{1} \div 1 \frac{2}{1} = \frac{9}{1} \div \frac{3}{1} = \frac{9}{3} = 3
\]