$4 \frac{1}{6} \times 6 \frac{2}{5}$
Answer (2)
Convert mixed fractions to improper fractions: 4 6 1 = 6 25 and 6 5 2 = 5 32 .
Multiply the improper fractions: 6 25 × 5 32 = 30 800 .
Simplify the resulting fraction: 30 800 = 3 80 .
Convert the improper fraction back to a mixed fraction: 3 80 = 26 3 2 .
26 3 2
Explanation
Convert to Improper Fractions We are asked to evaluate the product of two mixed fractions: 4 6 1 × 6 5 2 . To do this, we first convert each mixed fraction to an improper fraction.
First Fraction To convert 4 6 1 to an improper fraction, we multiply the whole number part (4) by the denominator (6) and add the numerator (1), then put the result over the original denominator (6). So, 4 6 1 = 6 4 × 6 + 1 = 6 24 + 1 = 6 25 .
Second Fraction Similarly, to convert 6 5 2 to an improper fraction, we multiply the whole number part (6) by the denominator (5) and add the numerator (2), then put the result over the original denominator (5). So, 6 5 2 = 5 6 × 5 + 2 = 5 30 + 2 = 5 32 .
Multiply Improper Fractions Now we multiply the two improper fractions: 6 25 × 5 32 . We can simplify this by canceling common factors between the numerators and denominators. We have 6 25 × 5 32 = 6 5 × 5 × 5 32 = 6 5 × 32 = 6 5 × 32 . Since 32 = 2 × 16 and 6 = 2 × 3 , we can further simplify: 6 5 × 32 = 2 × 3 5 × 2 × 16 = 3 5 × 16 = 3 80 .
Convert Back to Mixed Fraction Finally, we convert the improper fraction 3 80 back to a mixed fraction. We divide 80 by 3 to get 26 with a remainder of 2. So, 3 80 = 26 3 2 .
Final Answer Therefore, 4 6 1 × 6 5 2 = 26 3 2 .
Examples
Understanding how to multiply mixed fractions is useful in many real-life situations, such as when you're scaling a recipe. For example, if a recipe calls for 2 2 1 cups of flour and you want to triple the recipe, you would need to multiply 2 2 1 by 3. Converting to improper fractions, you'd have 2 5 × 3 = 2 15 = 7 2 1 cups of flour. This skill is also helpful in calculating areas and volumes, especially when dealing with measurements that aren't whole numbers.
To multiply the mixed numbers 4 6 1 and 6 5 2 , we first convert them to improper fractions, multiply these fractions, simplify the result, and convert it back to a mixed number. The final result is 26 3 2 . The process involves basic operations of fractions and requires understanding of converting between mixed and improper fractions.
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