Express 80 inches in standard notation using feet and inches.
Select one:
a. 1 yd 3 ft 8 in.
b. 2 yd 8 in.
c. 2 yd 8 ft
d. 6 ft 10 in.
The Correct Answer and Explanation is:
Problem:
Express 80 inches in feet and inches using standard notation.
Step 1: Understand the units involved
- 1 foot (ft) = 12 inches (in)
- 1 yard (yd) = 3 feet = 36 inches
Step 2: Convert 80 inches into feet and inches
To convert 80 inches to feet and inches:
- Divide 80 by 12 (since 1 foot = 12 inches):
$$
80 \div 12 = 6 \text{ feet with a remainder}
$$
- Calculate the remainder (in inches):
$$
6 \times 12 = 72 \text{ inches}
$$
$$
80 – 72 = 8 \text{ inches}
$$
So, 80 inches = 6 feet 8 inches
Step 3: Check if the answer can also be expressed in yards
Since 1 yard = 3 feet = 36 inches, let’s see how many yards fit into 80 inches:
$$
80 \div 36 = 2 \text{ yards with a remainder}
$$
Calculate remainder inches:
$$
2 \times 36 = 72 \text{ inches}
$$
$$
80 – 72 = 8 \text{ inches}
$$
So, 80 inches = 2 yards 8 inches
Step 4: Look at the choices:
a. 1 yd 3 ft 8 in.
b. 2 yd 8 in.
c. 2 yd 8 ft (this is impossible because 8 ft > 1 yd)
d. 6 ft 10 in.
From Step 2, we know 80 inches = 6 ft 8 in, but d says 6 ft 10 in, which is incorrect.
From Step 3, 80 inches = 2 yd 8 in, which matches option b.
Option a says 1 yd 3 ft 8 in. Let’s convert this to inches to verify:
- 1 yd = 36 in
- 3 ft = 36 in
- 8 in = 8 in
Total inches = 36 + 36 + 8 = 80 inches. So option a also equals 80 inches!
Step 5: Determine the correct standard way to write it
The question asks for “standard notation using feet and inches.” Typically:
- Using feet and inches directly: 6 ft 8 in (which is not listed exactly as an option)
- Using yards, feet, and inches is less common unless explicitly allowed.
- Since 1 yd 3 ft 8 in = 36 + 36 + 8 = 80 in, option a is correct if yards + feet + inches are allowed.
- Option b is 2 yd 8 in = 72 + 8 = 80 in
- Both a and b are correct conversions.
Step 6: Which one is standard?
- Option a: 1 yd 3 ft 8 in (36 + 36 + 8 = 80 in)
- Option b: 2 yd 8 in (72 + 8 = 80 in)
Since 3 ft is a full yard (3 ft = 1 yd), it’s unusual to say “1 yd 3 ft” because that’s effectively 2 yd 0 ft. So “1 yd 3 ft 8 in” is less standard — it mixes yards and feet awkwardly because the 3 ft could be counted as another yard.
Option b, “2 yd 8 in,” is cleaner because 2 yards + 8 inches is straightforward.
Final conclusion:
Correct answer:
b. 2 yd 8 in.
Explanation (300 words):
When converting inches into a combined measurement using yards, feet, and inches, it’s essential to use the relationship between the units clearly. Since 1 foot equals 12 inches, and 1 yard equals 3 feet (or 36 inches), any total number of inches can be expressed in these units by sequential division.
Given 80 inches, first convert to yards: 80 divided by 36 equals 2 yards with a remainder. Two yards equal 72 inches, so the remainder is 8 inches. This gives the expression 2 yd 8 in. This is a clean and standard way to express the measurement, especially when the remainder is less than 1 yard or 1 foot.
Option a, 1 yd 3 ft 8 in, while mathematically correct because 1 yard (36 in) + 3 feet (36 in) + 8 inches = 80 inches, is less standard since “3 feet” is itself equal to 1 yard. So, writing “1 yd 3 ft” is redundant and could be simplified to 2 yd. Thus, the clearer and more typical notation would be 2 yd 8 in.
Option d, 6 ft 10 in, is close but incorrect because 6 feet 10 inches equals 82 inches, which is 2 inches more than 80.
Option c, 2 yd 8 ft, doesn’t make sense because 8 feet exceed the length of 1 yard (3 feet), and it’s not standard to combine yards and more than 3 feet this way without converting to yards fully.
In everyday measurements, expressing length as feet and inches (such as 6 ft 8 in) is most common. But if yards are preferred, then 2 yd 8 in is a clear, concise, and correct expression of 80 inches.
