Question

order each set of measures from least to greatest.

1. 8 ft; 2 yd; 60 in.
2. 5 qt; 2 gal; 12 pt; 8 c
3. \\(\frac{1}{2}\\) ton; 8,000 oz; 430 lb
4. 2.5 mi; 12,000 ft; 5,000 yd
5. 63 fl oz; 7 c; 1.5 qt
6. 9.5 yd; 32.5 ft; 380 in.

Explanation:

Let's solve each problem one by one by converting all units to a common unit and then ordering them.

Problem 30: 8 ft; 2 yd; 60 in.

Step 1: Convert all to inches.

• 1 ft = 12 in, so 8 ft = \( 8 \times 12 = 96 \) in.
• 1 yd = 36 in, so 2 yd = \( 2 \times 36 = 72 \) in.
• 60 in remains as 60 in.

Step 2: Order from least to greatest.

60 in, 72 in (2 yd), 96 in (8 ft)

So the order is: 60 in, 2 yd, 8 ft

Problem 31: 5 qt; 2 gal; 12 pt; 8 c

Step 1: Convert all to cups (c).

• 1 qt = 4 c, so 5 qt = \( 5 \times 4 = 20 \) c.
• 1 gal = 16 c, so 2 gal = \( 2 \times 16 = 32 \) c.
• 1 pt = 2 c, so 12 pt = \( 12 \times 2 = 24 \) c.
• 8 c remains as 8 c.

Step 2: Order from least to greatest.

8 c, 20 c (5 qt), 24 c (12 pt), 32 c (2 gal)

So the order is: 8 c, 5 qt, 12 pt, 2 gal

Problem 32: \( \frac{1}{2} \) ton; 8,000 oz; 430 lb

Step 1: Convert all to pounds (lb).

• 1 ton = 2000 lb, so \( \frac{1}{2} \) ton = \( \frac{1}{2} \times 2000 = 1000 \) lb.
• 1 lb = 16 oz, so 8000 oz = \( \frac{8000}{16} = 500 \) lb.
• 430 lb remains as 430 lb.

Step 2: Order from least to greatest.

430 lb, 500 lb (8000 oz), 1000 lb (\( \frac{1}{2} \) ton)

So the order is: 430 lb, 8,000 oz, \( \frac{1}{2} \) ton

Problem 33: 2.5 mi; 12,000 ft; 5,000 yd

Step 1: Convert all to feet (ft).

• 1 mi = 5280 ft, so 2.5 mi = \( 2.5 \times 5280 = 13200 \) ft.
• 1 yd = 3 ft, so 5000 yd = \( 5000 \times 3 = 15000 \) ft.
• 12,000 ft remains as 12,000 ft.

Step 2: Order from least to greatest.

12,000 ft, 13200 ft (2.5 mi), 15000 ft (5,000 yd)

So the order is: 12,000 ft, 2.5 mi, 5,000 yd

Problem 34: 63 fl oz; 7 c; 1.5 qt

Step 1: Convert all to fluid ounces (fl oz).

• 1 c = 8 fl oz, so 7 c = \( 7 \times 8 = 56 \) fl oz.
• 1 qt = 32 fl oz, so 1.5 qt = \( 1.5 \times 32 = 48 \) fl oz.
• 63 fl oz remains as 63 fl oz. Wait, no, wait: Wait, 1 qt is 32 fl oz, so 1.5 qt is 48 fl oz? Wait, no, 1 cup is 8 fl oz, so 7 cups is 56 fl oz. 1 quart is 32 fl oz, so 1.5 quarts is 48 fl oz? Wait, but 63 fl oz is more than 56 and 48? Wait, no, let's check again. Wait, 1 cup = 8 fl oz, so 7 c = 56 fl oz. 1 qt = 32 fl oz, so 1.5 qt = 48 fl oz. Then 63 fl oz is 63. So the order would be 1.5 qt (48 fl oz), 7 c (56 fl oz), 63 fl oz? Wait, no, wait: Wait, 1.5 qt is 48 fl oz, 7 c is 56 fl oz, 63 fl oz is 63. So from least to greatest: 1.5 qt, 7 c, 63 fl oz. Wait, but let's confirm:

1.5 qt = 1.5 * 32 = 48 fl oz

7 c = 7 * 8 = 56 fl oz

63 fl oz = 63 fl oz

So 48 < 56 < 63. So order: 1.5 qt, 7 c, 63 fl oz

Problem 35: 9.5 yd; 32.5 ft; 380 in

Step 1: Convert all to inches (in).

• 1 yd = 36 in, so 9.5 yd = \( 9.5 \times 36 = 342 \) in.
• 1 ft = 12 in, so 32.5 ft = \( 32.5 \times 12 = 390 \) in.
• 380 in remains as 380 in.

Step 2: Order from least to greatest.

342 in (9.5 yd), 380 in, 390 in (32.5 ft)

So the order is: 9.5 yd, 380 in, 32.5 ft

Final Answers:

1. 60 in, 2 yd, 8 ft
2. 8 c, 5 qt, 12 pt, 2 gal
3. 430 lb, 8,000 oz, \( \frac{1}{2} \) ton
4. 12,000 ft, 2.5 mi, 5,000 yd
5. 1.5 qt, 7 c, 63 fl oz
6. 9.5 yd, 380 in, 32.5 ft

Answer:

Let's solve each problem one by one by converting all units to a common unit and then ordering them.

Problem 30: 8 ft; 2 yd; 60 in.

Step 1: Convert all to inches.

• 1 ft = 12 in, so 8 ft = \( 8 \times 12 = 96 \) in.
• 1 yd = 36 in, so 2 yd = \( 2 \times 36 = 72 \) in.
• 60 in remains as 60 in.

Step 2: Order from least to greatest.

60 in, 72 in (2 yd), 96 in (8 ft)

So the order is: 60 in, 2 yd, 8 ft

Problem 31: 5 qt; 2 gal; 12 pt; 8 c

Step 1: Convert all to cups (c).

• 1 qt = 4 c, so 5 qt = \( 5 \times 4 = 20 \) c.
• 1 gal = 16 c, so 2 gal = \( 2 \times 16 = 32 \) c.
• 1 pt = 2 c, so 12 pt = \( 12 \times 2 = 24 \) c.
• 8 c remains as 8 c.

Step 2: Order from least to greatest.

8 c, 20 c (5 qt), 24 c (12 pt), 32 c (2 gal)

So the order is: 8 c, 5 qt, 12 pt, 2 gal

Problem 32: \( \frac{1}{2} \) ton; 8,000 oz; 430 lb

Step 1: Convert all to pounds (lb).

• 1 ton = 2000 lb, so \( \frac{1}{2} \) ton = \( \frac{1}{2} \times 2000 = 1000 \) lb.
• 1 lb = 16 oz, so 8000 oz = \( \frac{8000}{16} = 500 \) lb.
• 430 lb remains as 430 lb.

Step 2: Order from least to greatest.

430 lb, 500 lb (8000 oz), 1000 lb (\( \frac{1}{2} \) ton)

So the order is: 430 lb, 8,000 oz, \( \frac{1}{2} \) ton

Problem 33: 2.5 mi; 12,000 ft; 5,000 yd

Step 1: Convert all to feet (ft).

• 1 mi = 5280 ft, so 2.5 mi = \( 2.5 \times 5280 = 13200 \) ft.
• 1 yd = 3 ft, so 5000 yd = \( 5000 \times 3 = 15000 \) ft.
• 12,000 ft remains as 12,000 ft.

Step 2: Order from least to greatest.

12,000 ft, 13200 ft (2.5 mi), 15000 ft (5,000 yd)

So the order is: 12,000 ft, 2.5 mi, 5,000 yd

Problem 34: 63 fl oz; 7 c; 1.5 qt

Step 1: Convert all to fluid ounces (fl oz).

• 1 c = 8 fl oz, so 7 c = \( 7 \times 8 = 56 \) fl oz.
• 1 qt = 32 fl oz, so 1.5 qt = \( 1.5 \times 32 = 48 \) fl oz.
• 63 fl oz remains as 63 fl oz. Wait, no, wait: Wait, 1 qt is 32 fl oz, so 1.5 qt is 48 fl oz? Wait, no, 1 cup is 8 fl oz, so 7 cups is 56 fl oz. 1 quart is 32 fl oz, so 1.5 quarts is 48 fl oz? Wait, but 63 fl oz is more than 56 and 48? Wait, no, let's check again. Wait, 1 cup = 8 fl oz, so 7 c = 56 fl oz. 1 qt = 32 fl oz, so 1.5 qt = 48 fl oz. Then 63 fl oz is 63. So the order would be 1.5 qt (48 fl oz), 7 c (56 fl oz), 63 fl oz? Wait, no, wait: Wait, 1.5 qt is 48 fl oz, 7 c is 56 fl oz, 63 fl oz is 63. So from least to greatest: 1.5 qt, 7 c, 63 fl oz. Wait, but let's confirm:

1.5 qt = 1.5 * 32 = 48 fl oz

7 c = 7 * 8 = 56 fl oz

63 fl oz = 63 fl oz

So 48 < 56 < 63. So order: 1.5 qt, 7 c, 63 fl oz

Problem 35: 9.5 yd; 32.5 ft; 380 in

Step 1: Convert all to inches (in).

• 1 yd = 36 in, so 9.5 yd = \( 9.5 \times 36 = 342 \) in.
• 1 ft = 12 in, so 32.5 ft = \( 32.5 \times 12 = 390 \) in.
• 380 in remains as 380 in.

Step 2: Order from least to greatest.

342 in (9.5 yd), 380 in, 390 in (32.5 ft)

So the order is: 9.5 yd, 380 in, 32.5 ft

Final Answers:

1. 60 in, 2 yd, 8 ft
2. 8 c, 5 qt, 12 pt, 2 gal
3. 430 lb, 8,000 oz, \( \frac{1}{2} \) ton
4. 12,000 ft, 2.5 mi, 5,000 yd
5. 1.5 qt, 7 c, 63 fl oz
6. 9.5 yd, 380 in, 32.5 ft