To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 5}{4 x 5} \) - \( \frac{3 x 2}{10 x 2} \)

\( \frac{25}{20} \) - \( \frac{6}{20} \)

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

\( \frac{25 - 6}{20} \) = \( \frac{19}{20} \) = \(\frac{19}{20}\)

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.

57% of the water consumption is industrial use and 30% is personal use so (57% - 30%) = 27% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 10,000 gallons = 2,700 gallons.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{75mph} \)
1 hour

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{25}} \)
\( \frac{\sqrt{16}}{\sqrt{25}} \)
\( \frac{\sqrt{4^2}}{\sqrt{5^2}} \)
\(\frac{4}{5}\)