$6 \frac{2}{4} \div 3 \frac{1}{5} =$
Answer (2)
Convert mixed numbers to improper fractions: 6 4 2 = 4 26 and 3 5 1 = 5 16 .
Divide the improper fractions: 4 26 ÷ 5 16 = 4 26 × 16 5 = 64 130 .
Simplify the resulting fraction: 64 130 = 32 65 .
Convert the improper fraction back to a mixed number: 32 65 = 2 32 1 .
Explanation
Problem Analysis We are asked to divide two mixed numbers: 6 4 2 and 3 5 1 . To do this, we will first convert the mixed numbers into improper fractions, then perform the division, and finally simplify the result back into a mixed number if possible.
Convert to Improper Fraction First, convert 6 4 2 to an improper fraction. We have 6 4 2 = 4 6 × 4 + 2 = 4 24 + 2 = 4 26 .
Convert to Improper Fraction Next, convert 3 5 1 to an improper fraction. We have 3 5 1 = 5 3 × 5 + 1 = 5 15 + 1 = 5 16 .
Divide the Fractions Now, divide the two improper fractions: 4 26 ÷ 5 16 . To divide fractions, we multiply by the reciprocal of the second fraction: 4 26 × 16 5 = 4 × 16 26 × 5 = 64 130 .
Simplify the Fraction Simplify the fraction 64 130 . Both the numerator and denominator are divisible by 2: 64 130 = 64 ÷ 2 130 ÷ 2 = 32 65 .
Convert to Mixed Number Convert the improper fraction 32 65 back to a mixed number. We divide 65 by 32: 65 ÷ 32 = 2 with a remainder of 1 . So, 32 65 = 2 32 1 .
Final Answer Therefore, 6 4 2 ÷ 3 5 1 = 2 32 1 .
Examples
Understanding how to divide mixed numbers is useful in many real-life situations, such as cooking and construction. For example, if you need to divide 6 4 2 cups of flour evenly into 3 5 1 batches of cookies, you would perform this division to determine that each batch requires 2 32 1 cups of flour. This ensures that you distribute the ingredients correctly and maintain the recipe's proportions.
The division of the mixed numbers 6 4 2 and 3 5 1 results in 2 32 1 . This is achieved by first converting the mixed numbers to improper fractions, performing the division, simplifying the result, and finally converting back to a mixed number. The complete calculation shows each step clearly.
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