If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 40 large cakes are needed for the party so \( \frac{40}{12} \) = 3\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 13 x 3 = 39 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{39} \) = 12\(\frac{2}{39}\) 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 4 + 13 = 17 cooks.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

1

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 have in common.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (3 + 2) ÷ 2 x 3 - 3²
P: 3 + (5) ÷ 2 x 3 - 3²
E: 3 + 5 ÷ 2 x 3 - 9
MD: 3 + \( \frac{5}{2} \) x 3 - 9
MD: 3 + \( \frac{15}{2} \) - 9
AS: \( \frac{6}{2} \) + \( \frac{15}{2} \) - 9
AS: \( \frac{21}{2} \) - 9
AS: \( \frac{21 - 18}{2} \)
\( \frac{3}{2} \)
1\(\frac{1}{2}\)