To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

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

\( \frac{3 x 9}{5 x 9} \) + \( \frac{2 x 5}{9 x 5} \)

\( \frac{27}{45} \) + \( \frac{10}{45} \)

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

\( \frac{27 + 10}{45} \) = \( \frac{37}{45} \) = \(\frac{37}{45}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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

2\( \sqrt{125} \) + 5\( \sqrt{5} \)
2\( \sqrt{25 \times 5} \) + 5\( \sqrt{5} \)
2\( \sqrt{5^2 \times 5} \) + 5\( \sqrt{5} \)
(2)(5)\( \sqrt{5} \) + 5\( \sqrt{5} \)
10\( \sqrt{5} \) + 5\( \sqrt{5} \)

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

If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{20} \) = 1\(\frac{13}{20}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{76} \) = 3\(\frac{18}{19}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 4 = 6 cooks.