The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 31 large cakes are needed for the party so \( \frac{31}{10} \) = 3\(\frac{1}{10}\) 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 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 150 small cakes are needed for the party so \( \frac{150}{26} \) = 5\(\frac{10}{13}\) 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 + 6 = 10 cooks.

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.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.