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.

45% of the water consumption is industrial use and 34% is personal use so (45% - 34%) = 11% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{11}{100} \) x 25,000 gallons = 2,750 gallons.

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

The amount of flour you need is (2\(\frac{7}{8}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{23}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{21}{8} \) cups
2\(\frac{5}{8}\) cups

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{5} \) ÷ \( \frac{1}{7} \) = \( \frac{3}{5} \) x \( \frac{7}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{5} \) x \( \frac{7}{1} \) = \( \frac{3 x 7}{5 x 1} \) = \( \frac{21}{5} \) = 4\(\frac{1}{5}\)