If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{4} \) = 5\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 15 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 15 x 2 = 30 small cakes during that time. 490 small cakes are needed for the party so \( \frac{490}{30} \) = 16\(\frac{1}{3}\) 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 6 + 17 = 23 cooks.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{7 x 5}{3 x 5} \) - \( \frac{9 x 3}{5 x 3} \)

\( \frac{35}{15} \) - \( \frac{27}{15} \)

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

\( \frac{35 - 27}{15} \) = \( \frac{8}{15} \) = \(\frac{8}{15}\)

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{72} \) = \( \frac{\frac{40}{8}}{\frac{72}{8}} \) = \( \frac{5}{9} \)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{25}} \)
\( \frac{\sqrt{16}}{\sqrt{25}} \)
\( \frac{\sqrt{4^2}}{\sqrt{5^2}} \)
\(\frac{4}{5}\)

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