To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{5 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 2

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{3}{100} \) x 6 = \( \frac{3 \times 6}{100} \) = \( \frac{18}{100} \) = 0.18 errors per hour

So, in an average hour, the machine will produce 6 - 0.18 = 5.82 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 5.82 = 93.1 error free parts were produced yesterday.

The greatest common factor (GCF) is the greatest factor that divides two integers.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)