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

\( \frac{4}{5} \) ÷ \( \frac{1}{7} \) = \( \frac{4}{5} \) x \( \frac{7}{1} \)

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

\( \frac{4}{5} \) x \( \frac{7}{1} \) = \( \frac{4 x 7}{5 x 1} \) = \( \frac{28}{5} \) = 5\(\frac{3}{5}\)

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:

\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
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An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

If the tiger has consumed 56 pounds of food in 4 days that's \( \frac{56}{4} \) = 14 pounds of food per day. The tiger needs to consume 126 - 56 = 70 more pounds of food to reach 126 pounds total. At 14 pounds of food per day that's \( \frac{70}{14} \) = 5 more days.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{6 x 5}{8 x 5} \) + \( \frac{8 x 4}{10 x 4} \)

\( \frac{30}{40} \) + \( \frac{32}{40} \)

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

\( \frac{30 + 32}{40} \) = \( \frac{62}{40} \) = 1\(\frac{5}{9}\)