Let's solve the expression step by step:

Expression:  
\[
30 \frac{1}{4} - 14 + 20 \div 3 \frac{1}{5}
\]

### Step 1: Convert mixed numbers to improper fractions

- \(30 \frac{1}{4} = \frac{121}{4}\)
- \(3 \frac{1}{5} = \frac{16}{5}\)

### Step 2: Perform the division
We now have:
\[
30 \frac{1}{4} - 14 + 20 \div \frac{16}{5}
\]
Dividing 20 by \(\frac{16}{5}\) is the same as multiplying 20 by \(\frac{5}{16}\):
\[
20 \times \frac{5}{16} = \frac{100}{16} = \frac{25}{4}
\]

### Step 3: Substitute the result back into the expression
Now the expression is:
\[
\frac{121}{4} - 14 + \frac{25}{4}
\]

### Step 4: Combine the fractions
First, combine the fractions \(\frac{121}{4}\) and \(\frac{25}{4}\):
\[
\frac{121 + 25}{4} = \frac{146}{4} = 36 \frac{1}{2}
\]

### Step 5: Subtract 14 from \(36 \frac{1}{2}\):
\[
36 \frac{1}{2} - 14 = 22 \frac{1}{2}
\]

So, the final result is:
\[
22 \frac{1}{2}
\]

Do you need any further details on these steps?

Here are 5 related questions for practice:
1. Simplify \(45 \frac{2}{3} + 12 - 6 \frac{1}{4}\).
2. What is \(25 \div 2 \frac{1}{3}\)?
3. Solve \(18 \frac{3}{5} - 10 \frac{1}{4}\).
4. Simplify \(40 - 15 \div 3 \frac{2}{5}\).
5. Evaluate \(50 \frac{1}{6} + 10 - 5 \frac{1}{3}\).

**Tip:** When dividing by a mixed number, it's often easier to convert it to an improper fraction first!

Learn how to solve the mixed number expression 30 1/4 - 14 + 20 ÷ 3 1/5 step-by-step. This guide covers converting mixed numbers to improper fractions, dividing fractions, and combining results. Suitable for students in Grades 6-8.

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