A. 21
B. 22
C. [tex]$15 \frac{1}{2}$[/tex]
D. 15
E. None of these
Answer (1)
Convert the mixed fractions to improper fractions: 5 6 5 = 6 35 and 3 5 3 = 5 18 .
Multiply the improper fractions: 6 35 × 5 18 = 6 × 5 35 × 18 .
Simplify the resulting fraction by canceling common factors: 6 × 5 35 × 18 = 21 .
The final answer is 21 .
Explanation
Problem Setup First, we need to evaluate the expression 5"." 6 5 × 3 5 3 . This involves multiplying two mixed numbers.
Converting to Improper Fractions To multiply mixed numbers, we first convert them to improper fractions. The mixed number 5 6 5 can be converted to an improper fraction as follows: 5 6 5 = 6 5 × 6 + 5 = 6 30 + 5 = 6 35 Similarly, the mixed number 3 5 3 can be converted to an improper fraction as follows: 3 5 3 = 5 3 × 5 + 3 = 5 15 + 3 = 5 18
Multiplying Improper Fractions Now, we multiply the two improper fractions: 6 35 × 5 18 = 6 × 5 35 × 18
Simplifying the Result We can simplify the fraction by canceling common factors. Notice that 35 and 5 have a common factor of 5, and 18 and 6 have a common factor of 6: 6 × 5 35 × 18 = 6 × 5 7 × 5 × 3 × 6 = 1 7 × 3 = 21
Comparing with Options The result of the multiplication is 21. Now we compare this result with the given options.
Final Answer The correct answer is A) 21.
Examples
Understanding mixed number multiplication is crucial in everyday situations, such as when you're scaling recipes. For instance, if a recipe calls for 2 2 1 cups of flour and you want to triple the recipe, you need to multiply 2 2 1 by 3. Converting to improper fractions, you get 2 5 × 3 = 2 15 = 7 2 1 cups of flour. This ensures accurate measurements and delicious results!
