Multiply.
$2 \frac{2}{3} \times 1 \frac{2}{3}$
Write your answer as a mixed number in simplest form.
We need to compute the product of two mixed numbers: \(2 \frac{2}{3}\) and \(1 \frac{2}{3}\). A mixed number \(a \frac{b}{c}\) represents the sum \(a + \frac{b}{c}\), which can be converted to an improper fraction using the formula \(\frac{a \times c + b}{c}\). After multiplying the resulting improper fractions, we will convert the product back into a mixed number.
First, convert the mixed numbers into improper fractions.
For \(2 \frac{2}{3}\):
\[2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}\]
For \(1 \frac{2}{3}\):
\[1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}\]
Multiply the two improper fractions:
\[\frac{8}{3} \times \frac{5}{3} = \frac{8 \times 5}{3 \times 3} = \frac{40}{9}\]
To convert \(\frac{40}{9}\) into a mixed number, divide the numerator by the denominator:
\[40 \div 9 = 4 \text{ with a remainder of } 4.\]
Therefore, the improper fraction \(\frac{40}{9}\) is equivalent to:
\[4 \frac{4}{9}\]
The product is \(\boxed{4 \frac{4}{9}}\).
In baking, if a recipe calls for \(2 \frac{2}{3}\) cups of flour and you need to prepare \(1 \frac{2}{3}\) times the recipe, you are essentially performing the multiplication \(2 \frac{2}{3} \times 1 \frac{2}{3}\). This skill is essential for scaling recipes to accommodate more or fewer guests, ensuring that the proportions of ingredients remain consistent. By converting to improper fractions, you ensure precision in your measurements, leading to perfect culinary results.