Question

n7 2, n7 3, & n7 4

1. use a number line to order each set of numbers from least to greatest.

a) \\( \frac{7}{8}, \frac{5}{8}, \frac{3}{8}, \frac{10}{8} \\)

from least to greatest:

b) \\( \frac{4}{10}, \frac{12}{10}, \frac{9}{10}, 1\frac{4}{10} \\)

from least to greatest:

Explanation:

Part a)

Step1: Analyze the fractions

All fractions have the same denominator (8). For fractions with the same denominator, the one with the smaller numerator is smaller. The numerators are 3, 5, 7, 10. So we order them by numerator size.

Step2: Order the fractions

Since \(3 < 5 < 7 < 10\), the fractions from least to greatest are \(\frac{3}{8}\), \(\frac{5}{8}\), \(\frac{7}{8}\), \(\frac{10}{8}\).

Part b)

Step1: Analyze the numbers

We have three proper fractions with denominator 10 (\(\frac{4}{10}\), \(\frac{9}{10}\), \(\frac{12}{10}\)) and a mixed number \(1\frac{4}{10}\) (which is greater than 1, while the proper fractions are less than or equal to 1 since \(\frac{12}{10}=1.2\) and \(1\frac{4}{10} = 1.4\)). For the proper fractions with denominator 10, order by numerator: 4 < 9 < 12. Then compare with the mixed number.

Step2: Order the numbers

First, order the proper fractions: \(\frac{4}{10}<\frac{9}{10}<\frac{12}{10}\). Then, \(1\frac{4}{10}\) is greater than \(\frac{12}{10}\) (since \(1\frac{4}{10}=\frac{14}{10}\) and \(14>12\)). So the order from least to greatest is \(\frac{4}{10}\), \(\frac{9}{10}\), \(\frac{12}{10}\), \(1\frac{4}{10}\).

Answer:

a) \(\frac{3}{8}\), \(\frac{5}{8}\), \(\frac{7}{8}\), \(\frac{10}{8}\)
b) \(\frac{4}{10}\), \(\frac{9}{10}\), \(\frac{12}{10}\), \(1\frac{4}{10}\)