Question

question 5:
what is the solution to \\(\frac{5}{8} \div \frac{3}{4}\\)?
a \\(\frac{15}{32}\\)
b \\(\frac{2}{3}\\)
c \\(\frac{9}{11}\\)
d \\(\frac{5}{6}\\)

Explanation:

Step1: Recall division of fractions rule

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{5}{8} \div \frac{3}{4}=\frac{5}{8}\times\frac{4}{3}\).

Step2: Simplify and multiply

Simplify the fractions before multiplying. The 4 in the numerator and 8 in the denominator have a common factor of 4. Divide 4 by 4 (gives 1) and 8 by 4 (gives 2). Now we have \(\frac{5}{2}\times\frac{1}{3}\). Multiply the numerators: \(5\times1 = 5\) and multiply the denominators: \(2\times3=6\)? Wait, no, wait. Wait, original after reciprocal: \(\frac{5}{8}\times\frac{4}{3}\). 4 and 8: 4 is 4, 8 is \(2\times4\), so cancel 4, get \(\frac{5}{2}\times\frac{1}{3}\)? No, wait, \(\frac{5}{8}\times\frac{4}{3}=\frac{5\times4}{8\times3}=\frac{20}{24}\). Simplify \(\frac{20}{24}\) by dividing numerator and denominator by 4: \(\frac{5}{6}\). Wait, let's do it again. \(\frac{5}{8}\div\frac{3}{4}=\frac{5}{8}\times\frac{4}{3}\). 4 and 8: 4 is 4, 8 is 8, so 4/8 = 1/2. So \(\frac{5}{8}\times\frac{4}{3}=\frac{5\times1}{2\times3}=\frac{5}{6}\). Wait, but let's check the options. Option D is \(\frac{5}{6}\)? Wait, no, the options: A is 15/32, B is 2/3, C is 9/11, D is 5/6? Wait, maybe I made a mistake. Wait, \(\frac{5}{8}\div\frac{3}{4}=\frac{5}{8}\times\frac{4}{3}=\frac{5\times4}{8\times3}=\frac{20}{24}=\frac{5}{6}\). Yes, so the answer is D? Wait, but let's check the options again. Wait, the user's image: the options are A:15/32, B:2/3, C:9/11, D:5/6? Wait, maybe the original problem was \(\frac{5}{8}\div\frac{3}{4}\). Let's recalculate: \(\frac{5}{8}\times\frac{4}{3}=\frac{5\times4}{8\times3}=\frac{20}{24}=\frac{5}{6}\). So the correct option is D. \(\frac{5}{6}\).

Answer:

D. \(\frac{5}{6}\)