Question

the model shows that $1\frac{3}{5}\div\frac{4}{5}=2$.
what would happen if you divide by $\frac{2}{5}$ instead of $\frac{4}{5}$?
the size of each group would be ? as big.
that means there would be ? as many groups.

Explanation:

Step1: Analyze the relationship between divisors

When dividing by a smaller number (since \(\frac{2}{5}<\frac{4}{5}\)), the size of each group is smaller. The relationship between \(\frac{4}{5}\) and \(\frac{2}{5}\) is \(\frac{4}{5}\div\frac{2}{5} = 2\), so \(\frac{2}{5}\) is \(\frac{1}{2}\) of \(\frac{4}{5}\).

Step2: Analyze the number of groups

According to the division principle \(a\div b=n\) (\(a\) is the dividend, \(b\) is the divisor, \(n\) is the quotient). Let \(a = 1\frac{3}{5}=\frac{8}{5}\). The original division is \(\frac{8}{5}\div\frac{4}{5}=2\). When the divisor changes to \(\frac{2}{5}\), \(\frac{8}{5}\div\frac{2}{5}=\frac{8}{5}\times\frac{5}{2}=4\). The relationship between the new quotient and the original quotient is \(4\div2 = 2\).

Answer:

The size of each group would be \(\frac{1}{2}\) as big. That means there would be \(2\) as many groups.