Question

unit 6 review (measurement)
score: 10/52 10/52 answered
question 7
195 in. to yards, feet, and inches
yds ft 6 in
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Explanation:

Step1: Recall conversion factors

We know that \( 1 \text{ yard} = 3 \text{ feet} \) and \( 1 \text{ foot} = 12 \text{ inches} \), so \( 1 \text{ yard} = 3\times12 = 36 \text{ inches} \). First, we subtract the given inches (6 inches) from the total inches to convert the remaining inches to feet and yards. So, \( 195 - 6=189 \) inches left to convert to yards and feet.

Step2: Convert inches to yards

To convert inches to yards, we divide the number of inches by 36 (since 1 yard = 36 inches). So, \( \frac{189}{36}=5.25 \) yards? Wait, no, wait. Wait, we can also convert inches to feet first. Wait, let's correct. Wait, first, let's find how many feet are in 195 inches, then convert feet to yards. Wait, total inches is 195. We know that 1 foot = 12 inches, so number of feet is \( 195\div12 = 16.25 \) feet. But we know that the inches part is 6, so the feet and yards come from \( 195 - 6 = 189 \) inches. Now, 189 inches to feet: \( 189\div12 = 15.75 \) feet? No, wait, no. Wait, the problem is to express 195 inches as yards, feet, inches. Let's do it step by step.

First, convert inches to yards: \( 195 \div 36 \). Let's compute \( 36\times5 = 180 \), so \( 195 - 180 = 15 \) inches? Wait, no, the given inches is 6, so maybe I made a mistake. Wait, the problem has a box with 6 inches filled. So we need to find yards and feet such that total inches is \( 36\times\text{yards} + 12\times\text{feet} + 6 = 195 \). So \( 36y + 12f + 6 = 195 \). Subtract 6: \( 36y + 12f = 189 \). Divide both sides by 3: \( 12y + 4f = 63 \). Wait, maybe better to first find total feet: \( 195 \div 12 = 16.25 \) feet. So 16 feet and 0.25 feet, but 0.25 feet is 3 inches, but the given inches is 6, so maybe the initial approach is wrong. Wait, no, the problem is to convert 195 inches to yards, feet, inches. Let's do it properly.

1. First, find how many yards are in 195 inches. Since 1 yard = 36 inches, divide 195 by 36: \( 195 \div 36 = 5 \) yards with a remainder. \( 36\times5 = 180 \), so \( 195 - 180 = 15 \) inches. But 15 inches can be converted to feet and inches: 15 inches = 1 foot (12 inches) + 3 inches. Wait, but the problem has 6 inches filled. Wait, maybe the problem is that we have to express 195 inches as y yds, f ft, 6 in. So \( 36y + 12f + 6 = 195 \). So \( 36y + 12f = 189 \). Divide both sides by 3: \( 12y + 4f = 63 \). Wait, 12y + 4f = 63. Let's factor out 4: 4(3y + f) = 63. But 63 is not divisible by 4. Wait, maybe the filled 6 inches is correct, so we need to find y and f such that \( 36y + 12f = 195 - 6 = 189 \). Let's divide 189 by 12 to get feet: \( 189 \div 12 = 15.75 \) feet. So 15 feet and 0.75 feet. 0.75 feet is 9 inches? No, that's not matching. Wait, maybe I messed up the conversion. Wait, 1 yard = 3 feet, 1 foot = 12 inches. So 1 yard = 36 inches. Let's start over.

Total inches: 195. We need to write this as \( y \times 36 + f \times 12 + i = 195 \), where \( i \) is the inches part (0 ≤ i < 12), \( f \) is the feet part (0 ≤ f < 3), and \( y \) is the yards part. Wait, because 3 feet = 1 yard, so feet should be less than 3. Ah! That's the key. So feet must be between 0 and 2 (since 3 feet make a yard). So let's correct.

So, first, find the inches part: i = 195 % 12. 195 divided by 12: 12*16=192, so 195-192=3. Wait, but the problem has 6 in the inches box. So maybe the problem is that we have to have 6 inches, so we adjust. So if we want i=6, then the remaining inches is 195-6=189. Now, 189 inches to feet: 189 / 12 = 15.75 feet. But feet must be less than 3 (since 3 feet = 1 yard), so we take the number of yards from the feet. Wait, no: yards = total feet / 3, and feet = total feet % 3. So total feet from 189 inches: 189 / 12 = 15.75 feet. Wait, that can't be. Wait, no, 1 foot = 12 inches, so 189 inches is 15 feet and 9 inches? Wait, 12*15=180, 189-180=9. So 189 inches is 15 feet 9 inches. But 15 feet is 5 yards (since 3 feet = 1 yard, 15/3=5). So 5 yards, 15 feet? No, wait, 5 yards is 15 feet, but then 15 feet + 0 feet (wait, no). Wait, I think the mistake is in the problem's pre-filled 6 inches. Wait, maybe the pre-filled 6 is wrong, but we have to go with the problem. Wait, no, let's do it correctly.

Correct method:

To convert 195 inches to yards, feet, inches:

1. Find the number of inches: i = 195 % 12. 195 ÷ 12 = 16*12=192, remainder 3. So i=3. Then the remaining inches: 195 - 3 = 192 inches.

2. Convert 192 inches to feet: 192 ÷ 12 = 16 feet.

3. Convert 16 feet to yards: 16 ÷ 3 = 5 yards with a remainder of 1 foot (since 3*5=15, 16-15=1).

So 195 inches = 5 yards, 1 foot, 3 inches. But the problem has 6 in the inches box, so maybe there's a mistake, but let's check the problem again. Wait, the problem says "195 in. to yards, feet, and inches" with a box for inches filled with 6. So we need to find yards and feet such that 36y + 12f + 6 = 195. So 36y + 12f = 189. Divide both sides by 3: 12y + 4f = 63. Wait, 12y + 4f = 63. Let's factor 4: 4(3y + f) = 63. 63 is not divisible by 4, so that's impossible. So maybe the pre-filled 6 is wrong. But assuming that the inches part is 6, let's see: 195 - 6 = 189 inches. Now, 189 inches to feet: 189 / 12 = 15.75 feet. 15.75 feet to yards: 15.75 / 3 = 5.25 yards. But that's not integer. Wait, maybe the problem is to first convert to feet, then to yards. Wait, 195 inches = 195 / 12 feet = 16.25 feet. 16.25 feet = 5 yards (5*3=15 feet) and 1.25 feet. 1.25 feet = 1.25*12=15 inches. But that's 5 yards, 1 foot, 15 inches? No, that's wrong because 1 foot is 12 inches, so 1.25 feet is 1 foot and 3 inches. So 16.25 feet = 5 yards, 1 foot, 3 inches. So total inches: 5*36 + 1*12 + 3 = 180 + 12 + 3 = 195. So the correct inches part is 3, not 6. But the problem has 6 filled. Maybe it's a typo, but let's proceed with the correct method. Wait, maybe the problem is to have 6 inches, so we need to adjust. Let's see: if inches is 6, then total inches from yards and feet is 195 - 6 = 189. Now, 189 inches. Let's find how many yards: 189 / 36 = 5.25 yards. But 0.25 yards is 0.25*3=0.75 feet, and 0.75 feet is 9 inches. No, that's not matching. Wait, maybe the problem is to convert 195 inches to yards, feet, inches, ignoring the pre-filled 6. Let's do that.

Correct steps:

1. Inches to feet: \( 195 \div 12 = 16 \) feet with a remainder of \( 195 - 16\times12 = 195 - 192 = 3 \) inches. So 16 feet, 3 inches.

2. Feet to yards: \( 16 \div 3 = 5 \) yards with a remainder of \( 16 - 5\times3 = 16 - 15 = 1 \) foot.

So putting it together: 5 yards, 1 foot, 3 inches.

But the problem has 6 in the inches box, so maybe there's a mistake. But assuming that we have to work with the pre-filled 6, let's see:

If inches is 6, then the remaining inches is 195 - 6 = 189.

189 inches to feet: 189 / 12 = 15.75 feet.

15.75 feet to yards: 15.75 / 3 = 5.25 yards. But that's not integer. So maybe the pre-filled 6 is wrong. But the problem is likely expecting us to use the correct conversion. Let's do it correctly.

So:

- Total inches: 195

- Inches part: 195 % 12 = 3 (since 12*16=192, 195-192=3)

- Remaining inches: 195 - 3 = 192

- Feet from remaining inches: 192 / 12 = 16 feet

- Yards from feet: 16 / 3 = 5 yards (3*5=15), remaining feet: 16 - 15 = 1 foot

So the correct values are 5 yards, 1 foot, 3 inches. But the problem has 6 in the inches box, so maybe it's a mistake. But perhaps the problem is to convert 195 inches to yards, feet, inches, and the 6 is a distractor. Wait, no, the user provided the image with 6 in the inches box. Maybe the problem is to find yards and feet such that 36y + 12f + 6 = 195. So 36y + 12f = 189. Divide both sides by 3: 12y + 4f = 63. Let's solve for y and f. 12y = 63 - 4f. So 63 - 4f must be divisible by 12. Let's try f=0: 63, not divisible by 12. f=1: 59, no. f=2: 55, no. f=3: 51, no. f=4: 47, no. f=5: 43, no. f=6: 39, no. f=7: 35, no. f=8: 31, no. f=9: 27, no. f=10: 23, no. f=11: 19, no. f=12: 15, no. f=13: 11, no. f=14: 7, no. f=15: 3, no. So no solution. Therefore, the pre-filled 6 is incorrect. The correct inches part is 3. So let's proceed with the correct method.

So:

Step1: Find inches

Inches = 195 % 12 = 3 (since 12*16=192, 195-192=3)

Step2: Find remaining inches for feet and yards

Remaining inches = 195 - 3 = 192

Step3: Convert remaining inches to feet

Feet = 192 / 12 = 16

Step4: Convert feet to yards

Yards = 16 // 3 = 5 (integer division), remaining feet = 16 % 3 = 1

So the correct values are 5 yards, 1 foot, 3 inches. But the problem has 6 in the inches box, so maybe there's a mistake. But assuming that we have to use the pre-filled 6, perhaps the problem is different. Wait, maybe the original problem was 198 inches? No, the user provided 195. Alternatively, maybe the conversion is different. Wait, 1 yard = 3 feet, 1 foot = 12 inches, so 1 yard = 36 inches. Let's check 5 yards, 1 foot, 6 inches: 5*36 + 1*12 + 6 = 180 + 12 + 6 = 198, which is more than 195. 4 yards, 2 feet, 6 inches: 4*36 + 2*12 + 6 = 144 + 24 + 6 = 174, less than 195. 5 yards, 0 feet, 6 inches: 5*36 + 0 + 6 = 186, less than 195. 5 yards, 1 foot, 6 inches: 198, as above. So the pre-filled 6 is incorrect. Therefore, the correct inches is 3, feet is 1, yards is 5.

Answer:

5 yds, 1 ft, 3 in (but since the problem has 6 in the inches box, there might be a typo, but the correct conversion gives 5, 1, 3)