$2 \frac{7}{11} \div \frac{7}{8}$
Answer (2)
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 .
Convert the improper fraction to a mixed number: 77 232 = 3 77 1 .
3 77 1
Explanation
Understanding the Problem We are given the expression 2 11 7 ÷ 8 7 and we need to evaluate it. This involves dividing a mixed number by a fraction.
Converting to Improper Fraction First, 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 = 11 2 × 11 + 7 = 11 22 + 7 = 11 29 .
Rewriting Division as Multiplication Now, we rewrite the division as multiplication by the reciprocal of 8 7 . The reciprocal of 8 7 is 7 8 . So, we have: 11 29 ÷ 8 7 = 11 29 × 7 8 .
Multiplying the Fractions Next, we multiply the fractions: 11 29 × 7 8 = 11 × 7 29 × 8 = 77 232 .
Converting to Mixed Number Now, we simplify the resulting fraction. The fraction 77 232 is an improper fraction, so we convert it back to a mixed number. To do this, we divide 232 by 77: 232 ÷ 77 = 3 with a remainder of 1. So, we have: 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 a portion that is 2 11 7 times the original, you would use the calculation above to determine the exact amount of flour needed. This ensures the recipe maintains its proportions and tastes as intended, demonstrating a practical application of fraction division in everyday cooking.
To solve 2 11 7 ÷ 8 7 , convert the mixed number to an improper fraction, rewrite the division as multiplication by the reciprocal, multiply the fractions, and then convert the result back to a mixed number. The final answer is 3 77 1 .
;
