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!