Solve for the following expression    5 2/7 + -1  1/2
 
 
 


To solve the expression \( 5 \frac{2}{7} + (-1 \frac{1}{2}) \), we first need to convert the mixed numbers into improper fractions, then perform the addition.

### Step 1: Convert mixed numbers to improper fractions.
- \( 5 \frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{35 + 2}{7} = \frac{37}{7} \)
- \( -1 \frac{1}{2} = -\frac{1 \times 2 + 1}{2} = -\frac{2 + 1}{2} = -\frac{3}{2} \)

### Step 2: Find a common denominator.
The least common denominator (LCD) of 7 and 2 is 14.

- Convert \( \frac{37}{7} \) to have a denominator of 14: 
  \[
  \frac{37}{7} = \frac{37 \times 2}{7 \times 2} = \frac{74}{14}
  \]
- Convert \( -\frac{3}{2} \) to have a denominator of 14: 
  \[
  -\frac{3}{2} = \frac{-3 \times 7}{2 \times 7} = \frac{-21}{14}
  \]

### Step 3: Add the fractions.
\[
\frac{74}{14} + \frac{-21}{14} = \frac{74 - 21}{14} = \frac{53}{14}
\]

### Step 4: Convert the improper fraction back to a mixed number.
\[
\frac{53}{14} = 3 \frac{11}{14}
\]

So, \( 5 \frac{2}{7} + (-1 \frac{1}{2}) = 3 \frac{11}{14} \).

Would you like more details on any step, or do you have any questions? 

Here are 5 related questions you might find interesting:
1. How do you subtract two mixed numbers?
2. What is the process to multiply mixed numbers?
3. Can you convert improper fractions to decimals?
4. How do you find the least common denominator (LCD) between three fractions?
5. What happens when you add fractions with different denominators?

**Tip:** When dealing with mixed numbers, always convert them to improper fractions first to simplify operations like addition and subtraction.

Learn how to solve the expression 5 2/7 + -1 1/2 step-by-step with detailed explanations. This problem involves adding mixed numbers and converting them into improper fractions. Suitable for students in Grades 6-8.

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