To find out how much sugar Jordan used, we need to calculate $\frac{3}{5}$ of the original recipe's sugar amount, which is $2 \frac{1}{3}$ cups.

Step 1: Convert the mixed number $2 \frac{1}{3}$ to an improper fraction.

$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

Step 2: Multiply $\frac{3}{5}$ by $\frac{7}{3}$.

$\frac{3}{5} \times \frac{7}{3} = \frac{3 \times 7}{5 \times 3} = \frac{21}{15}$

Step 3: Simplify the fraction $\frac{21}{15}$.

The greatest common divisor (GCD) of 21 and 15 is 3. So, divide both the numerator and denominator by 3:

$\frac{21}{15} = \frac{7}{5}$

Step 4: Convert $\frac{7}{5}$ into a mixed number.

$\frac{7}{5} = 1 \frac{2}{5}$

Conclusion:

Jordan used $1 \frac{2}{5}$ cups of sugar.

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Would you like to go over how to simplify fractions or any other details?

Related questions:

1. How do you multiply fractions and mixed numbers?
2. What is the method to convert mixed numbers into improper fractions?
3. How do you simplify a fraction?
4. How can you find the amount of ingredients when adjusting a recipe?
5. What is the relationship between fractions and percentages in recipes?

Tip: When adjusting a recipe, remember that multiplying the amount by a fraction or decimal works similarly, and converting mixed numbers makes calculations easier!