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

To fill a 4 gallon tank exactly halfway you'll need 2 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{2 \text{ gallons}}{1 \text{ gallons}} \) = 2

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

5 + (5 + 4) ÷ 4 x 2 - 3²
P: 5 + (9) ÷ 4 x 2 - 3²
E: 5 + 9 ÷ 4 x 2 - 9
MD: 5 + \( \frac{9}{4} \) x 2 - 9
MD: 5 + \( \frac{18}{4} \) - 9
AS: \( \frac{20}{4} \) + \( \frac{18}{4} \) - 9
AS: \( \frac{38}{4} \) - 9
AS: \( \frac{38 - 36}{4} \)
\( \frac{2}{4} \)
\(\frac{1}{2}\)

The equation for this sequence is:

a_n = a_n-1 + 3

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3
a₆ = 13 + 3
a₆ = 16

44% of the water consumption is industrial use and 27% is personal use so (44% - 27%) = 17% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 10,000 gallons = 1,700 gallons.