Convert the mixed number 5 1/2 to an improper fraction.

Question

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Here are the solutions to the problems:

20.

Convert the mixed number $5 \frac{1}{2}$ to an improper fraction.
$5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}$
Find the reciprocal of $\frac{11}{2}$ .
The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$ .
$\text{Reciprocal of } \frac{11}{2} = \frac{2}{11}$
The reciprocal is \boxed{\textbf{\frac{2}{11}}}.

21.
Perform the subtraction.
$2 - 3 = -1$
Find the equivalent value of $-1$ modulo 5.
To do this, add multiples of 5 until the result is positive and less than 5.
$-1 + 5 = 4$
So, $-1 \equiv 4 \pmod 5$ .
The result is $\boxed{\textbf{4}}$ .

22.
Recall the formula for the area of a square.
$\text{Area} = \text{side} \times \text{side} = \text{side}^2$
Substitute the given side length, $5 \text{ cm}$ , into the formula.
$\text{Area} = (5 \text{ cm})^2 = 25 \text{ cm}^2$
The area is $\boxed{\textbf{25 cm}^2}$ .

23.
Identify the value of $n$ for the eleventh triangular number.
For the eleventh triangular number, $n = 11$ .
Substitute $n=11$ into the given formula $\frac{n(n+1)}{2}$ .
$\text{Triangular number} = \frac{11(11+1)}{2}$
Perform the operations.
$\frac{11(12)}{2} = \frac{132}{2} = 66$
The eleventh triangular number is $\boxed{\textbf{66}}$ .

24.
Determine the number of 'O' symbols shown.
There are 3 'O' symbols.
Multiply the number of symbols by the value each symbol represents.
$3 \text{ symbols} \times 10 \text{ pots/symbol} = 30 \text{ pots}$
The number of pots represented is $\boxed{\textbf{30 pots}}$ .

Convert the mixed number 5 (1)/(2) to an improper fraction.