Question

complex fractions and unit rates
simplify.

1. \\(\frac{\frac{1}{3}}{4}\\)
2. \\(\frac{\frac{3}{4}}{8}\\)
3. \\(\frac{\frac{3}{2}}{3}\\)
4. \\(\frac{\frac{4}{1}}{3}\\)
5. \\(\frac{\frac{5}{6}}{3}\\)
6. \\(\frac{\frac{3}{5}}{4}\\)
7. \\(\frac{\frac{3}{4}}{\frac{6}{7}}\\)
8. \\(\frac{\frac{4}{15}}{\frac{2}{5}}\\)
9. \\(\frac{\frac{6}{7}}{\frac{9}{14}}\\)

Explanation:

Step1: Recall the rule for dividing fractions

To simplify a complex fraction \(\frac{\frac{a}{b}}{\frac{c}{d}}\), we use the rule \(\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}\) (multiply by the reciprocal of the denominator fraction).

Step2: Simplify each complex fraction

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Answer:

Step1: Recall the rule for dividing fractions

To simplify a complex fraction \(\frac{\frac{a}{b}}{\frac{c}{d}}\), we use the rule \(\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}\) (multiply by the reciprocal of the denominator fraction).

Step2: Simplify each complex fraction

1. \(\frac{\frac{1}{3}}{\frac{4}{1}}\) (wait, original is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, the first problem is \(\frac{\frac{1}{3}}{4}\)? Wait, the user wrote: "1. \(\frac{1}{3}\) over \(\frac{4}{1}\)? Wait, no, looking at the image: 1. \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first problem is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first problem is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, let's check again. The first problem is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? Wait, no, the first is \(\frac{\frac{1}{3}}{4}\)? 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