$2 \frac{7}{11} \div \frac{7}{8}$
Answer (1)
Convert the mixed number to an improper fraction: 2 11 7 = 11 29 .
Rewrite the division as multiplication by the reciprocal: 11 29 ÷ 8 7 = 11 29 × 7 8 .
Multiply the fractions: 11 29 × 7 8 = 77 232 .
Simplify the fraction: 77 232 = 3 77 1 .
3 77 1
Explanation
Understanding the Problem We are asked to evaluate the expression 2 11 7 ÷ 8 7 . This involves dividing a mixed number by a fraction.
Converting to Improper Fraction First, we convert the mixed number 2 11 7 to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (11) and add the numerator (7):
2 × 11 + 7 = 22 + 7 = 29 . So, the improper fraction is 11 29 .
Multiplying by the Reciprocal Now we rewrite the division as multiplication by the reciprocal of the fraction 8 7 . The reciprocal of 8 7 is 7 8 . Therefore, the expression becomes 11 29 × 7 8 .
Multiplying the Fractions Next, we multiply the two fractions: 11 29 × 7 8 = 11 × 7 29 × 8 = 77 232 .
Simplifying the Fraction Now, we simplify the resulting fraction. Since 232 and 77 do not share any common factors other than 1, the fraction 77 232 is already in its simplest form. We can convert this improper fraction to a mixed number by dividing 232 by 77. 232 ÷ 77 = 3 with a remainder of 232 − 3 × 77 = 232 − 231 = 1 . So, 77 232 = 3 77 1 .
Final Answer Therefore, 2 11 7 ÷ 8 7 = 77 232 = 3 77 1 .
Examples
Understanding fraction division is crucial in many real-life scenarios, such as scaling recipes. For instance, if a recipe calls for 8 7 cup of flour and you only want to make 2 11 7 times the recipe, you need to divide 2 11 7 by 8 7 to determine the adjusted amount of flour needed. This calculation ensures the proportions remain correct, maintaining the recipe's integrity. Mastering fraction division enables accurate adjustments in cooking, baking, and various other fields requiring proportional scaling.
