Divide: \frac{5}{8} \div \frac{3}{4} ? \frac{1}{8} ? \frac{5}{6} ? \frac{3}{4} ? 1\frac{1}{2}
The Correct Answer and Explanation is:
The correct answer to \\frac{5}{8} \div \frac{3}{4}\ is \\frac{5}{6}\.
Explanation:
Dividing fractions follows a systematic approach: convert the operation into multiplication by using the reciprocal of the divisor. The reciprocal of \\frac{3}{4}\ is \\frac{4}{3}\. Thus, the original problem transforms into:
58×43\frac{5}{8} \times \frac{4}{3}
Multiplying the numerators and denominators separately:
5×48×3=2024\frac{5 \times 4}{8 \times 3} = \frac{20}{24}
Simplifying \\frac{20}{24}\ requires finding the greatest common divisor (GCD) of 20 and 24, which is 4:
20÷424÷4=56\frac{20 \div 4}{24 \div 4} = \frac{5}{6}
Thus, the correct answer is \\frac{5}{6}\.
Fraction division is essential in various mathematical contexts, including ratio analysis, probability calculations, and measurements. The reciprocal method allows the problem to be expressed in terms of multiplication, which is often simpler than direct division. The simplification step ensures the result is expressed in its most reduced form, making it more meaningful in practical applications.
In the given multiple-choice options—\\frac{1}{8}\, \\frac{5}{6}\, \\frac{3}{4}\, and \1\frac{1}{2}\—the only correct answer is \\frac{5}{6}\. Misinterpretation of fraction division can lead to errors, such as mistakenly multiplying both denominators instead of using the reciprocal. Recognizing and applying the correct method is essential for solving similar problems efficiently and accurately. This principle holds significance in algebra, physics calculations, and real-world problem-solving scenarios.
