Question

do you expect the quotient to be less than 1 or greater than 1? why? the fraction \\(\frac{3}{5}\\) fits into \\(1\frac{2}{5}\\) ? 1 time. that means the quotient is ? 1.

Explanation:

Step 1: Analyze the dividend and divisor

The dividend is \(1\frac{2}{5}\) (which is \(\frac{7}{5}\)) and the divisor is \(\frac{3}{5}\). When dividing, if the dividend (in fraction form) is greater than the divisor, the quotient is greater than 1. Here, \(\frac{7}{5}>\frac{3}{5}\). Also, we check how many times \(\frac{3}{5}\) fits into \(1\frac{2}{5}\). Since \(1\frac{2}{5}=\frac{7}{5}\), and \(\frac{3}{5}\times2=\frac{6}{5}\), \(\frac{3}{5}\times3=\frac{9}{5}\) (too big), but actually \(\frac{7}{5}\div\frac{3}{5}=\frac{7}{3}\approx2.33\), but more simply, since \(1\frac{2}{5}\) is greater than \(\frac{3}{5}\), and when we see how many times \(\frac{3}{5}\) fits into \(1\frac{2}{5}\), \(1\) time of \(\frac{3}{5}\) is \(\frac{3}{5}\), and \(1\frac{2}{5}-\frac{3}{5}=\frac{4}{5}\), so there's still more, meaning it fits more than 1 time.

Step 2: Determine the quotient's relation to 1

Since the dividend (\(1\frac{2}{5}\)) is greater than the divisor (\(\frac{3}{5}\)), and the fraction \(\frac{3}{5}\) fits into \(1\frac{2}{5}\) more than 1 time (because \(1\frac{2}{5}>\frac{3}{5}\)), the quotient (which is \(1\frac{2}{5}\div\frac{3}{5}\)) will be greater than 1.

Answer:

The fraction \(\frac{3}{5}\) fits into \(1\frac{2}{5}\) \(\boldsymbol{\text{more than}}\) 1 time. That means the quotient is \(\boldsymbol{\text{greater than}}\) 1.