Alright, let's divide the length 7 yards, 1 foot, and 9 inches by 3 step by step.
### Step 1: Convert the entire initial length into inches
First, convert the given lengths into inches:
- 1 yard = 36 inches
- 1 foot = 12 inches
So, we have:
- Yards to inches: [tex]\( 7 \text{ yd} \times 36 \text{ inches/yd} = 252 \text{ inches} \)[/tex]
- Feet to inches: [tex]\( 1 \text{ ft} \times 12 \text{ inches/ft} = 12 \text{ inches} \)[/tex]
- Inches: [tex]\( 9 \text{ inches} \)[/tex]
Adding these all together:
[tex]\[ 252 \text{ inches} + 12 \text{ inches} + 9 \text{ inches} = 273 \text{ inches} \][/tex]
### Step 2: Divide the total inches by 3
Next, divide the total inches by 3:
[tex]\[ \frac{273 \text{ inches}}{3} = 91 \text{ inches} \][/tex]
### Step 3: Convert inches back into yards, feet, and inches
Now, convert 91 inches back into yards, feet, and inches:
- Yards to inches: [tex]\( 1 \text{ yd} = 36 \text{ inches} \)[/tex]
Determine how many whole yards 91 inches contains:
[tex]\[ \left\lfloor \frac{91 \text{ inches}}{36 \text{ inches/yd}} \right\rfloor = 2 \text{ yd} \][/tex]
[tex]\[ 2 \text{ yd} \times 36 \text{ inches/yd} = 72 \text{ inches} \][/tex]
Subtract the inches taken by the yards:
[tex]\[ 91 \text{ inches} - 72 \text{ inches} = 19 \text{ inches} \][/tex]
Now, let's convert the remaining 19 inches into feet and inches:
- Feet to inches: [tex]\( 1 \text{ ft} = 12 \text{ inches} \)[/tex]
Determine how many whole feet 19 inches contains:
[tex]\[ \left\lfloor \frac{19 \text{ inches}}{12 \text{ inches/ft}} \right\rfloor = 1 \text{ ft} \][/tex]
[tex]\[ 1 \text{ ft} \times 12 \text{ inches/ft} = 12 \text{ inches} \][/tex]
Subtract the inches taken by the feet:
[tex]\[ 19 \text{ inches} - 12 \text{ inches} = 7 \text{ inches} \][/tex]
### Step 4: Express the result
Finally, we have:
[tex]\[ 91 \text{ inches} = 2 \text{ yd}, 1 \text{ ft}, 7 \text{ in} \][/tex]
Therefore, after dividing 7 yards, 1 foot, and 9 inches by 3, the result is:
[tex]\[ 2 \text{ yd}, 1 \text{ ft}, 7 \text{ in} \][/tex]
So, the answer is:
[tex]\[ 7 \text{ yd 1 ft 9 in} \div 3 = 2 \text{ yd 1 ft 7 in} \][/tex]
