Evaluating the Expression: $2\frac{1}{4} \times 4 + 2\frac{1}{4} \times 3 + 2\frac{1}{4} \times 2 + 2\frac{1}{4} \times 1$
To evaluate this expression, we need to follow the order of operations (PEMDAS):
Step 1: Convert mixed numbers to improper fractions
$2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$
Step 2: Multiply each fraction by the corresponding integer
$\frac{9}{4} \times 4 = \frac{36}{4} = 9$
$\frac{9}{4} \times 3 = \frac{27}{4}$
$\frac{9}{4} \times 2 = \frac{18}{4} = \frac{9}{2}$
$\frac{9}{4} \times 1 = \frac{9}{4}$
Step 3: Add up the results
$9 + \frac{27}{4} + \frac{9}{2} + \frac{9}{4}$
To add these fractions, we need to find a common denominator, which is 4. We can rewrite each fraction with a denominator of 4:
$9 = \frac{36}{4}$
$\frac{27}{4} = \frac{27}{4}$
$\frac{9}{2} = \frac{18}{4}$
Now, we can add the fractions:
$\frac{36}{4} + \frac{27}{4} + \frac{18}{4} + \frac{9}{4} = \frac{90}{4} = \frac{45}{2} = 22.5$
Therefore, the final answer is:
$2\frac{1}{4} \times 4 + 2\frac{1}{4} \times 3 + 2\frac{1}{4} \times 2 + 2\frac{1}{4} \times 1 = \frac{45}{2} = 22.5$
