Question

put the following in numerical order from most to least 1 3/7, 1 4/14, 1 1/4

Answer 1

To order the fractions \(1 \frac{3}{7}\), \(1 \frac{4}{14}\), and \(1 \frac{1}{4}\) from most to least, we first convert them to improper fractions:

1. \(1 \frac{3}{7} = \frac{7 \cdot 1 + 3}{7} = \frac{10}{7}\)
2. \(1 \frac{4}{14} = 1 \frac{2}{7} = \frac{14 \cdot 1 + 4}{14} = \frac{18}{14} = \frac{9}{7}\)
3. \(1 \frac{1}{4} = \frac{4 \cdot 1 + 1}{4} = \frac{5}{4} = \frac{35}{28}\)

Next, we need to compare these values. To do this conveniently, we can find a common denominator.

The fractions simplify as follows:

- \(1 \frac{3}{7} = \frac{10}{7}\)
- \(1 \frac{4}{14} = \frac{9}{7}\)
- \(1 \frac{1}{4} = \frac{5}{4} = \frac{35}{28}\)

In terms of a common denominator, \(1 \frac{3}{7} = \frac{40}{28}\) and \(1 \frac{4}{14} = \frac{36}{28}\):

Converting \( \frac{5}{4} \) to a fraction with 28 as the denominator, we get:

- \( \frac{5}{4} = \frac{5 \cdot 7}{4 \cdot 7} = \frac{35}{28} \)

Now we can list the fractions with a common denominator of 28:

- \(1 \frac{3}{7} = \frac{40}{28}\)
- \(1 \frac{4}{14} = \frac{36}{28}\)
- \(1 \frac{1}{4} = \frac{35}{28}\)

Now, we can order them:

1. \(1 \frac{3}{7} = \frac{40}{28}\)
2. \(1 \frac{4}{14} = \frac{36}{28}\)
3. \(1 \frac{1}{4} = \frac{35}{28}\)

Therefore, in numerical order from most to least, the fractions are:

1. \(1 \frac{3}{7}\)
2. \(1 \frac{4}{14}\)
3. \(1 \frac{1}{4}\)