If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 29 large cakes are needed for the party so \( \frac{29}{12} \) = 2\(\frac{5}{12}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 290 small cakes are needed for the party so \( \frac{290}{80} \) = 3\(\frac{5}{8}\) 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 3 + 4 = 7 cooks.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-3a^6}{9a^4} \)
\( \frac{-3}{9} \) a^{(6 - 4)}
-\(\frac{1}{3}\)a²

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{30}{100} \) = \( \frac{30 x 15}{100} \) = \( \frac{450}{100} \) = 4 shots

The center makes 25% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{4}{\frac{25}{100}} \) = 4 x \( \frac{100}{25} \) = \( \frac{4 x 100}{25} \) = \( \frac{400}{25} \) = 16 shots

to make the same number of shots as the guard and thus score the same number of points.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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:

\( \frac{9 x 9}{5 x 9} \) + \( \frac{7 x 5}{9 x 5} \)

\( \frac{81}{45} \) + \( \frac{35}{45} \)

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

\( \frac{81 + 35}{45} \) = \( \frac{116}{45} \) = 2\(\frac{26}{45}\)