We are tasked with solving the following expression:

\[
25\% \times \frac{2}{5} + 2\frac{1}{4}
\]

### Step 1: Convert percentages to fractions
First, convert \( 25\% \) into a fraction. Since \( 25\% = \frac{25}{100} \), simplify:

\[
\frac{25}{100} = \frac{1}{4}
\]

Now the expression becomes:

\[
\frac{1}{4} \times \frac{2}{5} + 2\frac{1}{4}
\]

### Step 2: Multiply the fractions
Multiply \( \frac{1}{4} \times \frac{2}{5} \):

\[
\frac{1}{4} \times \frac{2}{5} = \frac{1 \times 2}{4 \times 5} = \frac{2}{20} = \frac{1}{10}
\]

### Step 3: Convert the mixed number to an improper fraction
Now, convert \( 2\frac{1}{4} \) into an improper fraction. To do this, multiply the whole number \( 2 \) by the denominator \( 4 \), then add the numerator \( 1 \):

\[
2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}
\]

### Step 4: Add the fractions
Now, we add \( \frac{1}{10} + \frac{9}{4} \). First, find a common denominator. The least common denominator between \( 10 \) and \( 4 \) is \( 20 \).

Convert each fraction:

\[
\frac{1}{10} = \frac{2}{20}, \quad \frac{9}{4} = \frac{45}{20}
\]

Now, add the fractions:

\[
\frac{2}{20} + \frac{45}{20} = \frac{47}{20}
\]

### Step 5: Convert back to a mixed number
Convert \( \frac{47}{20} \) into a mixed number:

\[
\frac{47}{20} = 2 \frac{7}{20}
\]

So, the final answer is:

\[
2 \frac{7}{20}
\]

Let me know if you need more details or have any questions!

Here are 5 related questions to expand your understanding:
1. How do you simplify percentages in other calculations?
2. How do you convert a mixed number into an improper fraction?
3. How would the solution change if we were asked to subtract instead of add?
4. Can you show the process of finding a common denominator for two fractions?
5. How do you simplify complex fractions involving both percentages and decimals?

**Tip:** When adding fractions with different denominators, always find the least common denominator to simplify your calculations!

Explore the solution to 25% x 2/5 + 2 1/4 with a clear, step-by-step breakdown. This guide covers converting percentages to fractions, multiplying fractions, and adding mixed numbers. Suitable for Grades 5-7.

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