$4 \frac{1}{6} \times 6 \frac{2}{5}$
Answer (2)
Convert the 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 fraction: 30 800 = 3 80 .
Convert the improper fraction back to a mixed fraction: 3 80 = 26 3 2 . The final answer is 26 3 2 .
Explanation
Understanding the Problem We are asked to evaluate the expression 4 6 1 × 6 5 2 . These are mixed fractions, and to multiply them, we first need to convert them into improper fractions. A mixed fraction is a whole number and a proper fraction combined.
Converting to Improper Fractions - Part 1 First, convert the mixed fraction 4 6 1 to an improper fraction. Multiply the whole number (4) by the denominator (6) and add the numerator (1): 4 × 6 + 1 = 24 + 1 = 25 . Then, place this result over the original denominator (6). So, 4 6 1 = 6 25 .
Converting to Improper Fractions - Part 2 Next, convert the mixed fraction 6 5 2 to an improper fraction. Multiply the whole number (6) by the denominator (5) and add the numerator (2): 6 × 5 + 2 = 30 + 2 = 32 . Then, place this result over the original denominator (5). So, 6 5 2 = 5 32 .
Multiplying the Improper Fractions Now, multiply the two improper fractions: 6 25 × 5 32 . To do this, multiply the numerators together and the denominators together: 6 × 5 25 × 32 = 30 800 .
Simplifying the Fraction Simplify the resulting fraction 30 800 by dividing both the numerator and the denominator by their greatest common divisor, which is 10: 30 ÷ 10 800 ÷ 10 = 3 80 .
Converting Back to a Mixed Fraction Finally, convert the improper fraction 3 80 back to a mixed fraction. Divide 80 by 3: 80 ÷ 3 = 26 with a remainder of 2. So, the whole number part is 26, and the fractional part is 3 2 . Therefore, 3 80 = 26 3 2 .
Final Answer Thus, 4 6 1 × 6 5 2 = 26 3 2 .
Examples
Understanding fraction multiplication is crucial in many real-life scenarios. For instance, if you're baking a cake and need to scale up a recipe that calls for 2 2 1 cups of flour, and you want to make 1 3 1 times the original recipe, you would multiply these mixed fractions. Similarly, in construction, if you need to calculate the area of a rectangular space that measures 5 4 3 meters by 3 2 1 meters, you'd multiply these mixed fractions to find the area in square meters. These calculations ensure accuracy in measurements and proportions, whether in cooking, construction, or any field requiring precise scaling and sizing.
To multiply the mixed numbers 4 6 1 and 6 5 2 , first convert them to improper fractions, then multiply and simplify to get the final result of 26 3 2 .
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