The ratio of the number of watermelons to the number of greengrocers is ${\color{blue}27}:{\color{red}3}.$ So we start with the ratio $27:3$ and write it as a fraction:

\[ \dfrac{{\color{blue}27}}{{\color{red}3}} \]

We can make a denominator of $1$ by dividing the numerator and denominator by $3$:

\[ \dfrac{27 \div 3}{3 \div 3} = \dfrac{9}{1} = 9 \]

So, $27$ watermelons in $3$ greengrocers $ = 9$ watermelons per greengrocer.

The ratio of the number of rabbits to hats is ${\color{blue}12}:{\color{red}4}.$ So we start with the ratio $12:4$ and write it as a fraction:

\[ \dfrac{{\color{blue}12}}{{\color{red}4}} \]

We can make a denominator of $1$ by dividing the numerator and denominator by $4$:

\[ \dfrac{12\div 4}{4\div 4} = \dfrac{3}{1} =3 \]

So, $12$ rabbits in $4$ hats $= 3$ rabbits per hat.

The ratio of meters to minutes that Alexander ran is ${\color{blue}800}:{\color{red}5}.$ So we start with the ratio $800:5$ and write it as a fraction:

\[ \dfrac{{\color{blue}800}}{{\color{red}5}} \]

We can make a denominator of $1$ by dividing the numerator and denominator by $5$:

\[ \dfrac{{\color{blue}800}\div 5}{{\color{red}5}\div 5} = \dfrac{{\color{blue}160}}{{\color{red}1}} \]

Hence, Alexander ran at a rate of $160$ meters per minute.

The ratio of the number of plants to the number of gardens is ${\color{blue}15}:{\color{red}3}.$ So we start with the ratio $15:3$ and write it as a fraction:

\[ \dfrac{{\color{blue}15}}{{\color{red}3}} \]

We can make a denominator of $1$ by dividing the numerator and denominator by $3$:

\[ \dfrac{{\color{blue}15} \div 3}{{\color{red}3} \div 3} = \dfrac{{\color{blue}5}}{{\color{red}1}} \]

Consequently, Lisbeth will plant $5$ plants per garden.

The ratio of the number of pizzas to the number of friends is ${\color{blue}36}:{\color{red}15}.$ Expressing this as a fraction, we have:

\[ \dfrac{{\color{blue}36}}{{\color{red}15}} \]

We can reduce this fraction to its lowest terms by dividing the numerator and denominator by $3{:}$

\[ \dfrac{36 \div 3}{15 \div 3} = \dfrac{12}{5} \]

Hence, Alexander must distribute the pizzas at a rate of $\dfrac{12}{5}$ pizzas per friend.

The ratio of lawns to hours is ${\color{blue}4}:{\color{red}8}.$ Expressing this as a fraction, we have:

\[ \dfrac{{\color{blue}4}}{{\color{red}8}} \]

We can reduce this fraction to its lowest terms by dividing the numerator and denominator by $4{:}$

\[ \dfrac{4\div 4}{8\div 4} = \dfrac{1}{2} \]

Consequently, the lawns are being mowed at a rate of $\dfrac{1}{2}$ lawns per hour.

The ratio of the number of cakes to the number of friends is ${\color{blue}11}:{\color{red}5}.$ Expressing this as a fraction, we have:

\[ \dfrac{{\color{blue}11}}{{\color{red}5}} \]

We can convert this fraction to a decimal by multiplying the numerator and denominator by $2{:}$

\[ \dfrac{11 \times 2}{5 \times 2} = \dfrac{22}{10} = 2.2 \]

Thus, Melissa must distribute the cakes at a rate of $2.2$ cakes per friend.

The ratio of treats to children is ${\color{blue}13}:{\color{red}2}.$ Expressing this as a fraction, we have:

\[ \dfrac{{\color{blue}13}}{{\color{red}2}} \]

We can convert this fraction to a decimal by multiplying the numerator and denominator by $5{:}$

\[ \dfrac{13 \times 5}{2 \times 5} = \dfrac{65}{10} = 6.5 \]

Hence, Monica must distribute the treats at a rate of $6.5$ treats per child.