The factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 the greatest factor 72 and 52 have in common.

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

\( \frac{3}{6} \) ÷ \( \frac{4}{9} \) = \( \frac{3}{6} \) x \( \frac{9}{4} \)

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

\( \frac{3}{6} \) x \( \frac{9}{4} \) = \( \frac{3 x 9}{6 x 4} \) = \( \frac{27}{24} \) = 1\(\frac{1}{8}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{2 x 2}{2 x 2} \) - \( \frac{4 x 1}{4 x 1} \)

\( \frac{4}{4} \) - \( \frac{4}{4} \)

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

\( \frac{4 - 4}{4} \) = \( \frac{0}{4} \) =

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

7\( \sqrt{18} \) + 6\( \sqrt{2} \)
7\( \sqrt{9 \times 2} \) + 6\( \sqrt{2} \)
7\( \sqrt{3^2 \times 2} \) + 6\( \sqrt{2} \)
(7)(3)\( \sqrt{2} \) + 6\( \sqrt{2} \)
21\( \sqrt{2} \) + 6\( \sqrt{2} \)

Now that the radicands are identical, you can add them together:

If the tiger has consumed 40 pounds of food in 5 days that's \( \frac{40}{5} \) = 8 pounds of food per day. The tiger needs to consume 80 - 40 = 40 more pounds of food to reach 80 pounds total. At 8 pounds of food per day that's \( \frac{40}{8} \) = 5 more days.