a plumber bought 2 lengths of pipes, L and M as shown below 3/1/2 and 2/2/5 what is the combined length of pipes L and M

The lengths of pipes \( L \) and \( M \) are given as mixed numbers:

- \( L = 3 \frac{1}{2} \)
- \( M = 2 \frac{2}{5} \)

To find the combined length of pipes \( L \) and \( M \), we need to add these two mixed numbers.

1. **Convert the mixed numbers to improper fractions:**

   \[
   L = 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}
   \]
   \[
   M = 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}
   \]

2. **Find a common denominator for the fractions:**

   The denominators are 2 and 5. The least common denominator (LCD) is 10.

   \[
   L = \frac{7}{2} = \frac{7 \times 5}{2 \times 5} = \frac{35}{10}
   \]
   \[
   M = \frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10}
   \]

3. **Add the fractions:**

   \[
   L + M = \frac{35}{10} + \frac{24}{10} = \frac{35 + 24}{10} = \frac{59}{10}
   \]

4. **Convert the improper fraction back to a mixed number:**

   \[
   \frac{59}{10} = 5 \frac{9}{10}
   \]

So, the combined length of pipes \( L \) and \( M \) is \( 5 \frac{9}{10} \) units.

Would you like more details or have any questions?

Here are five related questions:

1. How do you add mixed numbers directly without converting to improper fractions?
2. What is the least common denominator, and how is it determined?
3. How can you simplify fractions after adding them?
4. What is the process for converting an improper fraction to a mixed number?
5. How do you subtract mixed numbers?

**Tip:** When adding or subtracting mixed numbers, it's often easier to convert them to improper fractions first.

A plumber bought 2 lengths of pipes, L and M, as shown below: 3 1/2 and 2 2/5. What is the combined length of pipes L and M?

Learn how to find the combined length of two mixed numbers, 3 1/2 and 2 2/5, by converting them into improper fractions and adding them together. This step-by-step guide is ideal for students in Grades 5-7.

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