Carl has three lengths of cable, 5/6 yard long, 1/4 yard long, and 2/3 yard long. He needs at least 1 yard of cable. Which two pieces together make a length at least 1 yard and closest to 1 yard?
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26/24
To determine which two pieces of cable will make a length at least 1 yard and closest to 1 yard, we need to compare the sum of the lengths with 1 yard.
Let's add the lengths of the cables:
5/6 + 1/4 + 2/3
To find a common denominator, we can multiply the fractions by the product of the denominators, which in this case is 6:
(5/6) * (6/6) + (1/4) * (6/6) + (2/3) * (6/6)
This simplifies to:
(5/6) + (3/6) + (4/6)
Next, add the numerators:
(5 + 3 + 4)/6
This yields:
12/6
Now, simplify the fraction:
12/6 = 2
Therefore, the sum of the three cable lengths is 2 yards.
Since Carl needs at least 1 yard of cable, we can eliminate the shortest cable length (1/4 yard), as it is not sufficient on its own. Now we need to determine which two pieces of cable, combined, will get as close to 1 yard as possible.
Comparing the remaining two lengths:
5/6 yard and 2/3 yard
If we add these two fractions together:
(5/6) + (2/3)
To find a common denominator, we multiply the fractions by the product of the denominators, which is 6:
(5/6) * (6/6) + (2/3) * (6/6)
This simplifies to:
(5/6) + (4/6)
Next, add the numerators:
(5 + 4)/6
Which results in:
9/6
Now, simplify the fraction:
9/6 = 1 1/2
Therefore, combining the lengths of the cables that are 5/6 yard and 2/3 yard together will give Carl a length of cable that is closest to 1 yard (1 1/2 yards or 1.5 yards).