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:

• $5/14\approx 0.357$

• $4/7\approx 0.571$

• $6/7\approx 0.857$

• $2/9\approx 0.222$

• $5/9\approx 0.556$

• $2/3\approx 0.667$

• $1/10=0.1$

• $4/5=0.8$

• $7/10=0.7$

• $3/8=0.375$

• $3/4=0.75$

• $7/8=0.875$

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