The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 have in common.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-3b⁶ - 4b⁶
(-3 - 4)b⁶
-7b⁶

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.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{53}{9} \) = 5\(\frac{8}{9}\)

So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.

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

\( \frac{4}{9} \) ÷ \( \frac{3}{5} \) = \( \frac{4}{9} \) x \( \frac{5}{3} \)

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

\( \frac{4}{9} \) x \( \frac{5}{3} \) = \( \frac{4 x 5}{9 x 3} \) = \( \frac{20}{27} \) = \(\frac{20}{27}\)