Question

1. how many groups of \\(\frac{5}{7}\\) are in 1? \\(\square\\) groups 2. evaluate. \\(8 \div \frac{5}{7} = \square\\)

Explanation:

Step1: Solve the first sub - question

To find how many groups of \(\frac{5}{7}\) are in \(1\), we use the division operation. The formula for finding the number of groups of a number \(a\) in a number \(b\) is \(b\div a\). Here, \(b = 1\) and \(a=\frac{5}{7}\). So we calculate \(1\div\frac{5}{7}\). When dividing by a fraction, we multiply by its reciprocal. So \(1\div\frac{5}{7}=1\times\frac{7}{5}=\frac{7}{5} = 1.4\) or in fraction form \(\frac{7}{5}\) (or \(1\frac{2}{5}\)). But we can also think about it in terms of the number line or the rectangle model. From the number line, we can see that the length of \(1\) is divided into segments of length \(\frac{5}{7}\). The number of such segments is \(1\div\frac{5}{7}=\frac{7}{5}\).

Step2: Solve the second sub - question

To evaluate \(8\div\frac{5}{7}\), we use the rule of dividing by a fraction, which is multiplying by the reciprocal. So \(8\div\frac{5}{7}=8\times\frac{7}{5}=\frac{56}{5}=11.2\) or \(11\frac{1}{5}\).

Answer:

1. \(\frac{7}{5}\) (or \(1\frac{2}{5}\) or \(1.4\))
2. \(\frac{56}{5}\) (or \(11\frac{1}{5}\) or \(11.2\))