To solve the sum of these mixed fractions:

\[
1 \frac{3}{20} + 2 \frac{7}{16}
\]

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

   - \(1 \frac{3}{20} = \frac{1 \times 20 + 3}{20} = \frac{23}{20}\)
   - \(2 \frac{7}{16} = \frac{2 \times 16 + 7}{16} = \frac{39}{16}\)

2. **Find a common denominator for the fractions:**
   The least common denominator (LCD) of 20 and 16 is 80.

   - Convert \(\frac{23}{20}\) to have a denominator of 80:
     \[
     \frac{23}{20} = \frac{23 \times 4}{20 \times 4} = \frac{92}{80}
     \]

   - Convert \(\frac{39}{16}\) to have a denominator of 80:
     \[
     \frac{39}{16} = \frac{39 \times 5}{16 \times 5} = \frac{195}{80}
     \]

3. **Add the two fractions:**
   \[
   \frac{92}{80} + \frac{195}{80} = \frac{92 + 195}{80} = \frac{287}{80}
   \]

4. **Simplify the improper fraction:**
   Divide 287 by 80 to convert it to a mixed number:
   \[
   \frac{287}{80} = 3 \frac{47}{80}
   \]

Thus, the sum is:

\[
3 \frac{47}{80}
\]

Would you like further clarification on any of these steps?

Here are 5 related questions:
1. How do you subtract mixed fractions?
2. Can you multiply mixed numbers directly, or do you need to convert them first?
3. What is the least common denominator (LCD) and why is it important?
4. How do you convert improper fractions back to mixed numbers?
5. What is the process for adding or subtracting improper fractions?

**Tip:** Always simplify fractions at the end of a calculation to give the most concise result.

Learn how to add mixed fractions with this detailed example of solving 1 3/20 + 2 7/16. The solution covers converting mixed numbers to improper fractions, finding the least common denominator, and simplifying the final result. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation