$2 \frac{1}{4} \cdot 3 \frac{5}{9}$
Answer (1)
Convert the mixed fractions to improper fractions: 2 a rc 1 4 = a rc 9 4 and 3 a rc 5 9 = a rc 32 9 .
Multiply the improper fractions: \farc 9 4 a rc 32 9 = a rc 9 a rc 32 4 a rc 9 .
Simplify the fraction: \farc 9 a rc 32 4 a rc 9 = 8 .
The final answer is 8 .
Explanation
Understanding the Problem We are asked to evaluate the expression 2 a rc 1 4 a rc 5 9 . This involves multiplying two mixed fractions. To do this, we will first convert the mixed fractions into improper fractions, then multiply the improper fractions, and finally simplify the result.
Converting to Improper Fractions First, convert the mixed fractions to improper fractions.
2 a rc 1 4 = a rc ( 2 a rc 4 ) + 1 4 = a rc 8 + 1 4 = a rc 9 4
3 a rc 5 9 = a rc ( 3 a rc 9 ) + 5 9 = a rc 27 + 5 9 = a rc 32 9
Multiplying Improper Fractions Now, multiply the improper fractions:
\farc 9 4 a rc 32 9 = a rc 9 a rc 32 4 a rc 9
Simplifying the Result Simplify the resulting fraction:
\farc 9 a rc 32 4 a rc 9 = a rc 9 9 a rc 32 4 = 1 a rc 8 = 8
Examples
Understanding how to multiply mixed fractions is useful in many real-life situations, such as when you need to scale a recipe. For example, if a recipe calls for 2 a rc 1 4 cups of flour and you want to triple the recipe, you would need to calculate 3 a rc 2 a rc 1 4 . Knowing how to multiply mixed fractions allows you to accurately adjust the quantities of ingredients needed.
