Question

think about the division expression $1\frac{2}{5}\div\frac{3}{5}$. 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:

Step1: Convert mixed number to improper fraction

$$1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5}$$

Step2: Divide fractions

Dividing by a fraction is multiplying by its reciprocal. So, $$\frac{7}{5}\div\frac{3}{5}=\frac{7}{5}\times\frac{5}{3}$$
Cancel out the common factor of \(5\): $$\frac{7}{5}\times\frac{5}{3}=\frac{7}{3}$$
Since \(\frac{7}{3}\approx2.33>1\)

Answer:

The quotient is greater than \(1\) because when we calculate \(1\frac{2}{5}\div\frac{3}{5}=\frac{7}{3}\approx2.33\) which is greater than \(1\). Also, \(\frac{3}{5}\) fits into \(1\frac{2}{5}\) (i.e., \(\frac{7}{5}\)) more than \(1\) time.