Question

Four people have found the distance in kilometers across a small bridge using different methods. Their results are given in the table. Order the distances from least to greatest. Mindy 5.5 Aaron 23/4 Tanya 28−−√, harld 5 1/2 Responses 5 1/2, 28−−√, 5.5¯¯¯, 23/4 5 1/2, 28−−√, 5.5¯¯¯, 23/4 - 28−−√, 5 1/2, 5.5¯¯¯, 23/4 28−−√, 5 1/2, 5.5¯¯¯, 23/4 - 28−−√, 5.5¯¯¯, 23/4, 5 1/2 28−−√, 5.5¯¯¯, 23/4, 5 1/2 23/4 , 5.5¯¯¯, 28−−√, 5 1/2

Answer 1

To order the distances from least to greatest based on the values given by Mindy, Aaron, Tanya, and Harold, we first need to convert all values into a comparable format (decimals or fractions).

1. Mindy: 5.5 km - This is already in decimal format.

2. Aaron: 23/4 km - Converting this to decimal:
   \[ 23 \div 4 = 5.75 \text{ km} \]

3. Tanya: \( \sqrt{28} \) km - We can calculate this as:
   \[ \sqrt{28} \approx 5.2915 \text{ km} \] (The exact value of \( \sqrt{28} \) is approximately 5.291502622129181.)

4. Harold: \( 5 \frac{1}{2} \) km - Converting this into decimal:
   \[ 5 + 0.5 = 5.5 \text{ km} \]

Now we have the following distances in decimal form:

• Mindy: 5.5 km
• Aaron: 5.75 km
• Tanya: 5.2915 km
• Harold: 5.5 km

Next, we will list these values in order:

1. Tanya: 5.2915 km
2. Mindy: 5.5 km
3. Harold: 5.5 km
4. Aaron: 5.75 km

When ordering, note that both Mindy and Harold report the same distance (5.5 km). Therefore, we can note that they are equivalent.

So the ordered distances from least to greatest are:

• \( \sqrt{28} \) (Tanya)
• \( 5.5 \) (Mindy and Harold)
• \( 23/4 \) (Aaron)

Thus a possible correct response is:

• 28−−√, 5 1/2, 5.5¯¯¯, 23/4

If formatting allows, we can clarify the distances with the names too:

• Tanya: \( \sqrt{28} \), Mindy: 5.5, Harold: 5.5, Aaron: 5.75.

In a general response format:

• 28−−√, 5 1/2, 5.5, 23/4.