Carl has three lengths of cable,5/6 yard long,1/4 yard long and 2/3 yard long.he needs at least one yard of cable. Which two pieces together
Make a k
Length at least 1 yard and closest to one yard
Add the first two.
5/6 + 1/4 = 10/12 + 3/12= 13/12
To find the two lengths of cable that, when combined, have a length closest to one yard, follow these steps:
1. Convert the given lengths to a common unit. Since we are looking for a length closest to one yard, let's convert all lengths to yards.
a) The first length is 5/6 yard.
b) The second length is 1/4 yard.
c) The third length is 2/3 yard.
2. Find the sum of each pair of lengths:
a) Combining the first and second length: (5/6) + (1/4) = (20/24) + (6/24) = 26/24 yards.
b) Combining the first and third length: (5/6) + (2/3) = 15/18 + 12/18 = 27/18 yards.
c) Combining the second and third length: (1/4) + (2/3) = 3/12 + 8/12 = 11/12 yards.
3. Compare the sums to one yard:
a) 26/24 yards is approximately 1.083 yards, which is over one yard.
b) 27/18 yards is approximately 1.5 yards, which is over one yard.
c) 11/12 yards is approximately 0.917 yards, which is under one yard.
4. Since the combined length of 11/12 yards is closest to one yard, the two pieces of cable that should be used together are the second length (1/4 yard) and the third length (2/3 yard).
To find the two lengths that, when combined, have a length closest to one yard, you can follow these steps:
1. Start by listing the lengths of the cables:
- Length 1: 5/6 yard
- Length 2: 1/4 yard
- Length 3: 2/3 yard
2. Convert the lengths to a common denominator to make them easier to compare:
- Length 1: 5/6 yard
- Length 2: 3/12 yard (1/4 yard is equivalent to 3/12 yard)
- Length 3: 8/12 yard (2/3 yard is equivalent to 8/12 yard)
3. Calculate the total length of each pair of cables:
- Length 1 + Length 2 = 5/6 + 3/12 = 10/12 + 3/12 = 13/12 yard
- Length 1 + Length 3 = 5/6 + 8/12 = 10/12 + 8/12 = 18/12 yard
- Length 2 + Length 3 = 3/12 + 8/12 = 11/12 yard
4. Determine which combination is closest to one yard:
- Length 1 + Length 2 = 13/12 yard (greater than one yard)
- Length 1 + Length 3 = 18/12 yard (greater than one yard)
- Length 2 + Length 3 = 11/12 yard (less than one yard)
From the calculations, we can see that the combination of Length 2 (1/4 yard) and Length 3 (2/3 yard) has a total length of 11/12 yard, which is the closest to one yard without exceeding it. Therefore, Carl should use the 1/4 yard and 2/3 yard cables together to get a length closest to one yard.