$(6) $3 \frac{1}{5} \div \frac{5}{8}$
Answer (1)
Convert the mixed number to an improper fraction: 3 5 1 = 5 16 .
Divide by multiplying by the reciprocal: 5 16 ÷ 8 5 = 5 16 × 5 8 .
Multiply the fractions: 5 × 5 16 × 8 = 25 128 .
Convert the improper fraction to a mixed number: 25 128 = 5 25 3 . The final answer is 5 25 3 .
Explanation
Understanding the Problem We are asked to divide a mixed number by a fraction. The mixed number is 3 5 1 and the fraction is 8 5 .
Converting to an Improper Fraction First, we need to convert the mixed number 3 5 1 to an improper fraction. To do this, we multiply the whole number part (3) by the denominator (5) and add the numerator (1). This gives us 3 × 5 + 1 = 15 + 1 = 16 . So, the improper fraction is 5 16 .
Dividing by a Fraction Now, we need to divide 5 16 by 8 5 . Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 8 5 is 5 8 . So, we have 5 16 ÷ 8 5 = 5 16 × 5 8 .
Multiplying the Fractions Multiplying the fractions, we get 5 × 5 16 × 8 = 25 128 .
Converting Back to a Mixed Number Now, we convert the improper fraction 25 128 back to a mixed number. To do this, we divide 128 by 25. The quotient is 5 and the remainder is 3. So, 25 128 = 5 25 3 .
Final Answer Therefore, 3 5 1 ÷ 8 5 = 5 25 3 .
Examples
Imagine you are baking a cake and the recipe calls for 3 5 1 cups of flour. However, you only have a 8 5 -cup measuring scoop. This problem helps you determine how many scoops you need to measure out the correct amount of flour. In this case, you would need 5 25 3 scoops. Understanding fraction division is crucial in cooking, construction, and many other real-life scenarios where precise measurements are required.
