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

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 5}{6 x 5} \) - \( \frac{5 x 3}{10 x 3} \)

\( \frac{25}{30} \) - \( \frac{15}{30} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{25 - 15}{30} \) = \( \frac{10}{30} \) = \(\frac{1}{3}\)

To subtract these radicals together their radicands must be the same:

4\( \sqrt{18} \) - 5\( \sqrt{2} \)
4\( \sqrt{9 \times 2} \) - 5\( \sqrt{2} \)
4\( \sqrt{3^2 \times 2} \) - 5\( \sqrt{2} \)
(4)(3)\( \sqrt{2} \) - 5\( \sqrt{2} \)
12\( \sqrt{2} \) - 5\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

If the tiger has consumed 112 pounds of food in 8 days that's \( \frac{112}{8} \) = 14 pounds of food per day. The tiger needs to consume 154 - 112 = 42 more pounds of food to reach 154 pounds total. At 14 pounds of food per day that's \( \frac{42}{14} \) = 3 more days.

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 8 = \( \frac{3 \times 8}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour

So, in an average hour, the machine will produce 8 - 0.24 = 7.76 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.76 = 124.2 error free parts were produced yesterday.