Question

identify the numeric order of these fractions and mixed numbers from smallest to largest 1 3/6 2 3/5, 7/9 1 7/8 A 2 3/5, 1 7/8, 1 3/6, 7/9 B 7/9, 10/6, 16/18, 13/5 C 7/9, 1 3/6, 1 7/8, 2 3/5 D 13/15, 15/8, 9/6, 7/9

Answer 1

To compare the fractions and mixed numbers, let's convert everything to improper fractions or decimal form for easier comparison.

1. **Convert mixed numbers and fractions:**
- \( 1 \frac{3}{6} = 1 + \frac{3}{6} = 1 + 0.5 = 1.5 \)
- \( 2 \frac{3}{5} = 2 + \frac{3}{5} = 2 + 0.6 = 2.6 \)
- \( 7/9 \approx 0.777 \)
- \( 1 \frac{7}{8} = 1 + \frac{7}{8} = 1 + 0.875 = 1.875 \)

2. **For mixed numbers in option D:**
- \( 13/15 \approx 0.867 \)
- \( 15/8 = 1.875 \)
- \( 9/6 = 1.5 \)
- \( 7/9 \approx 0.777 \)

Now let's list down the values we have computed:

- \( 1 \frac{3}{6} = 1.5 \)
- \( 2 \frac{3}{5} = 2.6 \)
- \( 7/9 \approx 0.777 \)
- \( 1 \frac{7}{8} = 1.875 \)
- \( 13/15 \approx 0.867 \)
- \( 15/8 = 1.875 \)
- \( 9/6 = 1.5 \)

Now, let's compare all these values:

1. \( 7/9 \approx 0.777 \) (smallest)
2. \( 13/15 \approx 0.867 \)
3. \( 1 \frac{3}{6} (= 1.5) \)
4. \( 9/6 (= 1.5) \)
5. \( 1 \frac{7}{8} (= 1.875) \)
6. \( 15/8 (= 1.875) \)
7. \( 2 \frac{3}{5} (= 2.6) \) (largest)

So for the correct order:

- \( 7/9 \)
- \( 13/15 \)
- \( 1 \frac{3}{6} = 9/6\) (They are essentially equal)
- \( 1 \frac{7}{8} = 15/8 \) (They are equal as well)
- \( 2 \frac{3}{5} \)

Next, let's sort through the provided options:

A) **\( 2 \frac{3}{5}, 1 \frac{7}{8}, 1 \frac{3}{6}, 7/9 \)** - Incorrect order

B) **\( 7/9, 10/6, 16/18, 13/5 \)** - Incorrect order; several wrong numbers (10/6 is equal to 5/3, not comparable to this set)

C) **\( 7/9, 1 \frac{3}{6}, 1 \frac{7}{8}, 2 \frac{3}{5} \)** - Correct order.

D) **\( 13/15, 15/8, 9/6, 7/9 \)** - Incorrect order.

Thus, the correct sequence from smallest to largest is found in **option C**: **\( 7/9, 1 \frac{3}{6}, 1 \frac{7}{8}, 2 \frac{3}{5} \)**.