To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{44} \) = \( \frac{\frac{32}{4}}{\frac{44}{4}} \) = \( \frac{8}{11} \)

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

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

vans = \( \frac{78}{7} \) = 11\(\frac{1}{7}\)

So, it will take 11 full vans and one partially full van to transport the entire team making a total of 12 vans.

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

\( \frac{4}{6} \) ÷ \( \frac{2}{6} \) = \( \frac{4}{6} \) x \( \frac{6}{2} \)

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

\( \frac{4}{6} \) x \( \frac{6}{2} \) = \( \frac{4 x 6}{6 x 2} \) = \( \frac{24}{12} \) = 2

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

2 + (4 + 2) ÷ 5 x 5 - 5²
P: 2 + (6) ÷ 5 x 5 - 5²
E: 2 + 6 ÷ 5 x 5 - 25
MD: 2 + \( \frac{6}{5} \) x 5 - 25
MD: 2 + \( \frac{30}{5} \) - 25
AS: \( \frac{10}{5} \) + \( \frac{30}{5} \) - 25
AS: \( \frac{40}{5} \) - 25
AS: \( \frac{40 - 125}{5} \)
\( \frac{-85}{5} \)
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