Question

Identify the numeric order of these fractions and mixed numbers from smallest to largest: 1 and 3/6
, 2 and 3/5
, 7/9
, 1 and 7/8
.(1 point)
Responses

Answer 1

To compare the fractions and mixed numbers, we first convert all of them to improper fractions:

1. \( 1 \frac{3}{6} = \frac{6}{6} + \frac{3}{6} = \frac{9}{6} = \frac{3}{2} \)
2. \( 2 \frac{3}{5} = \frac{10}{5} + \frac{3}{5} = \frac{13}{5} \)
3. \( 7/9 \) remains the same.
4. \( 1 \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \)

Next, we compare these improper fractions:

- \( \frac{3}{2} = \frac{12}{8} \)
- \( \frac{13}{5} = \frac{26.0}{10} = \frac{52}{20} = \frac{104}{40} \) (for comparison it’s easier to view as decimals)
- \( \frac{15}{8} = 1.875 \)
- \( \frac{7}{9} \approx 0.777 \)

Now we will convert them into decimal form for easier comparison:

1. \( \frac{3}{2} = 1.5 \)
2. \( \frac{13}{5} = 2.6 \)
3. \( \frac{7}{9} \approx 0.777 \)
4. \( \frac{15}{8} = 1.875 \)

Ordering them from smallest to largest:

1. \( \frac{7}{9} \approx 0.777 \)
2. \( 1 \frac{3}{6} = 1.5 \)
3. \( 1 \frac{7}{8} = 1.875 \)
4. \( 2 \frac{3}{5} = 2.6 \)

Thus, the order from smallest to largest is:
- \( 7/9 \)
- \( 1 \frac{3}{6} \)
- \( 1 \frac{7}{8} \)
- \( 2 \frac{3}{5} \)