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