4 1/5 + 2 1/3 - 3 1/2 how to solve problems

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

### Step 1: Convert the mixed numbers into improper fractions.
- \( 4 \frac{1}{5} = \frac{21}{5} \)
  - \( 4 \times 5 = 20 \), and \( 20 + 1 = 21 \), so \( 4 \frac{1}{5} = \frac{21}{5} \)
- \( 2 \frac{1}{3} = \frac{7}{3} \)
  - \( 2 \times 3 = 6 \), and \( 6 + 1 = 7 \), so \( 2 \frac{1}{3} = \frac{7}{3} \)
- \( 3 \frac{1}{2} = \frac{7}{2} \)
  - \( 3 \times 2 = 6 \), and \( 6 + 1 = 7 \), so \( 3 \frac{1}{2} = \frac{7}{2} \)

### Step 2: Find a common denominator.
The denominators are 5, 3, and 2. The least common denominator (LCD) is 30.

### Step 3: Convert each fraction to have a denominator of 30.
- \( \frac{21}{5} = \frac{126}{30} \) (since \( 21 \times 6 = 126 \))
- \( \frac{7}{3} = \frac{70}{30} \) (since \( 7 \times 10 = 70 \))
- \( \frac{7}{2} = \frac{105}{30} \) (since \( 7 \times 15 = 105 \))

### Step 4: Perform the addition and subtraction.
Now add and subtract the fractions:
\[
\frac{126}{30} + \frac{70}{30} - \frac{105}{30} = \frac{126 + 70 - 105}{30} = \frac{91}{30}
\]

### Step 5: Simplify if necessary.
The result \( \frac{91}{30} \) is an improper fraction. Converting it back to a mixed number:
\[
91 \div 30 = 3 \text{ remainder } 1
\]
Thus, \( \frac{91}{30} = 3 \frac{1}{30} \).

So, the final answer is **3 \(\frac{1}{30}\)**.

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Would you like more details on any step?

Here are some related questions:
1. How do you find the least common denominator (LCD)?
2. What is the process for converting mixed numbers to improper fractions?
3. How can you simplify fractions further after addition or subtraction?
4. How do you convert an improper fraction back to a mixed number?
5. How does borrowing work in subtraction with fractions?

**Tip**: Always ensure that the denominators are the same before adding or subtracting fractions!

Learn how to solve 4 1/5 + 2 1/3 - 3 1/2 step-by-step by converting mixed numbers into improper fractions, finding a common denominator, and performing addition and subtraction. Suitable for students in Grades 6-8.

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