Question

Austin has 3 3/8 yards of ribbon. He uses 2/3 of the ribbon to decorate a poster.

How many yards of ribbon does Austin use to decorate the poster

Answer 1

To determine how much ribbon Austin uses, we start with the total amount of ribbon he has, which is \(3 \frac{3}{8}\) yards. We can convert this mixed number into an improper fraction.

1. Convert \(3 \frac{3}{8}\) to an improper fraction:
\[
3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}
\]

2. Now we need to find \( \frac{2}{3} \) of \( \frac{27}{8} \):
\[
\text{Amount of ribbon used} = \frac{2}{3} \times \frac{27}{8}
\]

3. Multiply the fractions:
\[
= \frac{2 \times 27}{3 \times 8} = \frac{54}{24}
\]

4. Simplify \( \frac{54}{24} \):
- The greatest common divisor (GCD) of 54 and 24 is 6.
- Divide the numerator and the denominator by 6:
\[
= \frac{54 \div 6}{24 \div 6} = \frac{9}{4}
\]

5. Convert \( \frac{9}{4} \) back into a mixed number:
\[
\frac{9}{4} = 2 \frac{1}{4}
\]

Thus, the amount of ribbon Austin uses to decorate the poster is \( \boxed{2 \frac{1}{4}} \) yards.