If the tiger has consumed 154 pounds of food in 11 days that's \( \frac{154}{11} \) = 14 pounds of food per day. The tiger needs to consume 196 - 154 = 42 more pounds of food to reach 196 pounds total. At 14 pounds of food per day that's \( \frac{42}{14} \) = 3 more days.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

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

\( \frac{6 x 2}{4 x 2} \) + \( \frac{3 x 1}{8 x 1} \)

\( \frac{12}{8} \) + \( \frac{3}{8} \)

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

\( \frac{12 + 3}{8} \) = \( \frac{15}{8} \) = 1\(\frac{7}{8}\)

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

\( \frac{8}{100} \) x 10 = \( \frac{8 \times 10}{100} \) = \( \frac{80}{100} \) = 0.8 errors per hour

So, in an average hour, the machine will produce 10 - 0.8 = 9.2 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 9.2 = 174.8 error free parts were produced yesterday.

1

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{6} \) ÷ \( \frac{3}{6} \) = \( \frac{4}{6} \) x \( \frac{6}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{6} \) x \( \frac{6}{3} \) = \( \frac{4 x 6}{6 x 3} \) = \( \frac{24}{18} \) = 1\(\frac{1}{3}\)