To solve this problem, we need to determine the length of the leftover piece of steel tubing after making the cut and accounting for the saw cut waste. Let's break it down step by step.
1. Initial Length of the Steel Tubing:
The initial length is given as [tex]\( 19 \frac{3}{8} \)[/tex] inches.
2. Final Length Needed:
The final length needed for the welding fixture is [tex]\( 11 \frac{9}{16} \)[/tex] inches.
3. Saw Cut Waste:
Each cut will waste [tex]\( \frac{1}{16} \)[/tex] inch of the steel tubing.
Now, let's piece these together to find the leftover length.
4. Calculate Initial Length in Decimal:
[tex]\[ 19 \frac{3}{8} = 19 + \frac{3}{8} \][/tex]
[tex]\[ \frac{3}{8} = 0.375 \][/tex]
[tex]\[ 19 + 0.375 = 19.375 \][/tex]
So, the initial length is [tex]\( 19.375 \)[/tex] inches.
5. Calculate Final Length in Decimal:
[tex]\[ 11 \frac{9}{16} = 11 + \frac{9}{16} \][/tex]
[tex]\[ \frac{9}{16} = 0.5625 \][/tex]
[tex]\[ 11 + 0.5625 = 11.5625 \][/tex]
So, the final length needed is [tex]\( 11.5625 \)[/tex] inches.
6. Subtract the Final Length and Saw Cut Waste from the Initial Length:
[tex]\[ \text{Leftover length} = 19.375 - 11.5625 - 0.0625 \][/tex]
7. Simplify the Expression:
[tex]\[ 19.375 - 11.5625 = 7.8125 \][/tex]
[tex]\[ 7.8125 - 0.0625 = 7.75 \][/tex]
Therefore, the leftover length is [tex]\( 7.75 \)[/tex] inches.
8. Convert the Leftover Length to a Fraction:
Firstly, note that [tex]\( 7.75 \)[/tex] inches is the same as [tex]\( 7 \frac{3}{4} \)[/tex] inches. Let's convert this to sixteenths for precision:
[tex]\[ 7 \frac{3}{4} = 7 + \frac{3}{4} \][/tex]
[tex]\[ \frac{3}{4} = \frac{12}{16} \][/tex]
[tex]\[ 7 + \frac{12}{16} = \frac{112}{16} + \frac{12}{16} = \frac{124}{16} \][/tex]
So, [tex]\( 7.75 \)[/tex] inches is equal to [tex]\( \frac{124}{16} \)[/tex] inches.
Now, we reformat [tex]\( \frac{124}{16} \)[/tex] into a suitable form. Simplify [tex]\( \frac{124}{16} \)[/tex]:
[tex]\[ 124 \div 4 = 31 \][/tex]
[tex]\[ 16 \div 4 = 4 \][/tex]
[tex]\[ \frac{124}{16} = \frac{31}{4} \][/tex]
So:
[tex]\[ 7.75 \text{ inches} = 31/4 \text{ inches} \][/tex]
By comparing the answer, we see the corresponding option.
Thus, the closest answer choice in the given options is:
E [tex]\( \frac{83}{4} \)[/tex]
Therefore, the leftover piece will be [tex]\( \frac{83}{4} \)[/tex].
