Question

plot $1\frac{7}{10}$ and $2\frac{2}{5}$.

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{7}{10}\) to an improper fraction: \(1\frac{7}{10}=\frac{1\times10 + 7}{10}=\frac{17}{10}\).
Then, convert \(2\frac{2}{5}\) to an improper fraction: \(2\frac{2}{5}=\frac{2\times5+2}{5}=\frac{12}{5}\), and to have the same denominator as \(\frac{17}{10}\), we rewrite \(\frac{12}{5}\) as \(\frac{24}{10}\).

Step2: Analyze the number line

Assuming the number line has intervals of \(\frac{1}{10}\) (since we are dealing with tenths). The position of \(1\frac{7}{10}=\frac{17}{10}\) is at the 17th tenth - mark (starting from 0). The position of \(2\frac{2}{5}=\frac{24}{10}\) is at the 24th tenth - mark. But since the problem is a bit unclear in the image, if we assume we need to find a number between them or mark them, but based on the conversion, \(1\frac{7}{10}=\frac{17}{10} = 1.7\) and \(2\frac{2}{5}=\frac{12}{5}=2.4\). If we are to find a common operation or mark, but maybe the question is to compare or find a mid - point? Wait, maybe the original question is to plot \(1\frac{7}{10}\) and \(2\frac{2}{5}\) on the number line. Let's check the number line: from the image, the number line has marks. Let's assume each small mark is \(\frac{1}{10}\). So \(1\frac{7}{10}\) is 7 marks after 1, and \(2\frac{2}{5}=2\frac{4}{10}\) is 4 marks after 2.

Answer:

To plot \(1\frac{7}{10}\) (which is \(1.7\)) and \(2\frac{2}{5}\) (which is \(2.4\)) on the number line:

• For \(1\frac{7}{10}\), start at 1 and move 7 tenths (small intervals) to the right.
• For \(2\frac{2}{5}\), start at 2 and move 4 tenths (since \(\frac{2}{5}=\frac{4}{10}\)) to the right.

If the question was to find a relation, but based on the given, the plotted points would be at those positions. If you meant to find a sum or difference, let's calculate the sum: \(1\frac{7}{10}+2\frac{2}{5}=\frac{17}{10}+\frac{12}{5}=\frac{17 + 24}{10}=\frac{41}{10}=4\frac{1}{10}\), or difference: \(2\frac{2}{5}-1\frac{7}{10}=\frac{12}{5}-\frac{17}{10}=\frac{24 - 17}{10}=\frac{7}{10}\). But since the image is a bit unclear, the main task is plotting the two mixed numbers on the number line with \(1\frac{7}{10}\) at \(1.7\) and \(2\frac{2}{5}\) at \(2.4\) on the number line.