To find the shortest length of conduit needed to cut the given pieces with allowances for saw cuts, let's go through the steps one by one:
1. **Calculate the total length of all given pieces.**
- First piece: 7 7/8 inches = 7 + 7/8 inches
- Second piece: 3 1/4 inches = 3 + 1/4 inches
- Third piece: 6 1/2 inches = 6 + 1/2 inches
- Fourth piece: 12 1/8 inches = 12 + 1/8 inches
- Fifth piece: 24 3/16 inches = 24 + 3/16 inches
Add all these lengths together:
Total length = (7 + 7/8) + (3 + 1/4) + (6 + 1/2) + (12 + 1/8) + (24 + 3/16) inches
To simplify, let's add whole numbers and fractions separately:
Whole numbers: 7 + 3 + 6 + 12 + 24 = 52 inches
Fractions: 7/8 + 1/4 + 1/2 + 1/8 + 3/16
To add the fractions, we need a common denominator. The smallest common denominator for 8, 4, 2, and 16 is 16. Convert all fractions to have a denominator of 16:
(7/8) = (14/16)
(1/4) = (4/16)
(1/2) = (8/16)
(1/8) = (2/16)
(3/16) = (3/16)
Now add them together:
Fractions: (14/16) + (4/16) + (8/16) + (2/16) + (3/16) = (31/16) inches
But 31/16 inches is the same as 1 + 15/16 inches, because 31/16 = 16/16 + 15/16.
Total fractions' length: 1 + 15/16 inches
Now, combine the whole numbers with the total fractions' length:
Total length = 52 + (1 + 15/16) inches
Total length = 53 + 15/16 inches
2. **Calculate the total saw cut length allowances.**
There are 4 cuts needed since after the last cut there is no need for an additional saw cut:
Saw cut allowances = 4 cuts * 1/16 inch/cut
= 4/16 inches
= 1/4 inches
3. **Add the total length of the pieces to the saw cut allowances.**
Grand total length required = Total length + Saw cut allowances
= (53 + 15/16) + 1/4 inches
To combine 15/16 inches and 1/4 inches, convert 1/4 inches to 16ths to get a common denominator:
1/4 inches = 4/16 inches
Now add them:
15/16 + 4/16 = 19/16 inches
But 19/16 inches is the same as 1 + 3/16 inches, because 19/16 = 16/16 + 3/16.
Grand total length required = 53 + (1 + 3/16) inches
= 54 + 3/16 inches
The shortest length of 1/2 inch conduit needed to cut the given pieces with allowances for saw cuts is 54 and 3/16 inches.
Therefore, the correct option is:
Od. 54 3/16th inches.
