Simplify`3 1/5+2 1/10-1 1/2-1/4`

Answer

To simplify the expression \(3 \frac{1}{5} + 2 \frac{1}{10} - 1 \frac{1}{2} - \frac{1}{4}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. **Convert \(3 \frac{1}{5}\)**:
\[ 3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5} \]

2. **Convert \(2 \frac{1}{10}\)**:
\[ 2 \frac{1}{10} = \frac{2 \times 10 + 1}{10} = \frac{20 + 1}{10} = \frac{21}{10} \]

3. **Convert \(1 \frac{1}{2}\)**:
\[ 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]

Now we can rewrite the expression:
\[ \frac{16}{5} + \frac{21}{10} - \frac{3}{2} - \frac{1}{4} \]

### Step 2: Find a Common Denominator
Next, we need to find a common denominator for the fractions. The denominators are 5, 10, 2, and 4. The least common multiple (LCM) of these numbers is 20.

### Step 3: Convert Each Fraction to Have the Common Denominator
Now we convert each fraction to have a denominator of 20:

1. **Convert \(\frac{16}{5}\)**:
\[ \frac{16}{5} = \frac{16 \times 4}{5 \times 4} = \frac{64}{20} \]

2. **Convert \(\frac{21}{10}\)**:
\[ \frac{21}{10} = \frac{21 \times 2}{10 \times 2} = \frac{42}{20} \]

3. **Convert \(\frac{3}{2}\)**:
\[ \frac{3}{2} = \frac{3 \times 10}{2 \times 10} = \frac{30}{20} \]

4. **Convert \(\frac{1}{4}\)**:
\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \]

Now we can rewrite the expression:
\[ \frac{64}{20} + \frac{42}{20} - \frac{30}{20} - \frac{5}{20} \]

### Step 4: Combine the Fractions
Now we can combine the fractions:
\[ \frac{64 + 42 - 30 - 5}{20} = \frac{64 + 42 = 106}{20} - \frac{30 + 5 = 35}{20} = \frac{106 - 35}{20} = \frac{71}{20} \]

### Step 5: Convert Back to Mixed Number
Finally, we convert \(\frac{71}{20}\) back to a mixed number:
\[ 71 \div 20 = 3 \quad \text{(whole number)} \quad \text{remainder } 11 \]
So,
\[ \frac{71}{20} = 3 \frac{11}{20} \]

### Final Answer
The simplified form of \(3 \frac{1}{5} + 2 \frac{1}{10} - 1 \frac{1}{2} - \frac{1}{4}\) is:
\[ 3 \frac{11}{20} \]