Question

which list shows the absolute values in order from least to greatest select each correct answer A -5/14 -4/7 6/7, B -2/3 -5/9 2/9, C -1/10 -4/5 7/10, D -3/8 3/4 -7/8

Answer 1

To order the absolute values from least to greatest, we first need to calculate the absolute value of each number in the lists provided:

1. **A:**
- \(-5/14\) → \(5/14\)
- \(-4/7\) → \(4/7\)
- \(6/7\) → \(6/7\)

Absolute values: \(5/14\), \(4/7\), \(6/7\)

2. **B:**
- \(-2/3\) → \(2/3\)
- \(-5/9\) → \(5/9\)
- \(2/9\) → \(2/9\)

Absolute values: \(2/3\), \(5/9\), \(2/9\)

3. **C:**
- \(-1/10\) → \(1/10\)
- \(-4/5\) → \(4/5\)
- \(7/10\) → \(7/10\)

Absolute values: \(1/10\), \(4/5\), \(7/10\)

4. **D:**
- \(-3/8\) → \(3/8\)
- \(3/4\) → \(3/4\)
- \(-7/8\) → \(7/8\)

Absolute values: \(3/8\), \(3/4\), \(7/8\)

Now let's order the absolute values from least to greatest in each list:

- **List A:** \(5/14\), \(4/7\), \(6/7\)
- **List B:** \(2/9\), \(5/9\), \(2/3\)
- **List C:** \(1/10\), \(4/5\), \(7/10\)
- **List D:** \(3/8\), \(3/4\), \(7/8\)

Next, we'll find the decimal approximations to compare the absolute values more easily:

- \(5/14 ≈ 0.357\)
- \(4/7 ≈ 0.571\)
- \(6/7 ≈ 0.857\)

- \(2/9 ≈ 0.222\)
- \(5/9 ≈ 0.556\)
- \(2/3 ≈ 0.667\)

- \(1/10 = 0.1\)
- \(4/5 = 0.8\)
- \(7/10 = 0.7\)

- \(3/8 = 0.375\)
- \(3/4 = 0.75\)
- \(7/8 = 0.875\)

Now, let's order the values from the lists:

- **A:** \(5/14 (0.357), 4/7 (0.571), 6/7 (0.857)\) → Correctly ordered: \(5/14 < 4/7 < 6/7\)
- **B:** \(2/9 (0.222), 5/9 (0.556), 2/3 (0.667)\) → Correctly ordered: \(2/9 < 5/9 < 2/3\)
- **C:** \(1/10 (0.1), 7/10 (0.7), 4/5 (0.8)\) → Not correctly ordered (should be \(1/10 < 7/10 < 4/5\))
- **D:** \(3/8 (0.375), 3/4 (0.75), 7/8 (0.875)\) → Correctly ordered: \(3/8 < 3/4 < 7/8\)

Thus, the lists that show absolute values in order from least to greatest are:

- **A**
- **B**
- **D**