Answer:
Carl has 3/4 yard of cable left after using 1 yard.
Explanation:
To find out how much cable Carl has left after using 1 yard, we need to add up the lengths of the three cables and subtract 1 from the sum.
Step 1: Add up the lengths of the three cables
5/6 yard + 1/4 yard + 2/3 yard
To add these fractions, we need to find a common denominator. The least common multiple of 6, 4, and 3 is 12.
5/6 yard = 10/12 yard (multiply the numerator and denominator by 2)
1/4 yard = 3/12 yard (multiply the numerator and denominator by 3)
2/3 yard = 8/12 yard (multiply the numerator and denominator by 4)
So we have:
10/12 yard + 3/12 yard + 8/12 yard = 21/12 yard
Step 2: Subtract 1 yard from the sum of the three cables
21/12 yard - 1 yard
To subtract these quantities, we need a common unit. We can convert 1 yard to 12/12 yard.
21/12 yard - 12/12 yard = 9/12 yard
Step 3: Simplify the result
9/12 yard can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3.
9/12 yard = (9 ÷ 3) / (12 ÷ 3) yard = 3/4 yard
So Carl has 3/4 yard of cable left after using 1 yard.