Math Problem Statement

Add 3/7 + 2/3.

Solution

To solve the problem 37+23\frac{3}{7} + \frac{2}{3}, we need to find a common denominator and add the fractions step by step:

Step-by-Step Solution:

  1. Identify the denominators: The denominators are 77 and 33.

  2. Find the least common denominator (LCD): The least common multiple of 77 and 33 is 2121.

  3. Rewrite the fractions with the LCD:

    • Multiply both the numerator and denominator of 37\frac{3}{7} by 33:
      37=3×37×3=921\frac{3}{7} = \frac{3 \times 3}{7 \times 3} = \frac{9}{21}
    • Multiply both the numerator and denominator of 23\frac{2}{3} by 77:
      23=2×73×7=1421\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}
  4. Add the fractions:
    921+1421=9+1421=2321\frac{9}{21} + \frac{14}{21} = \frac{9 + 14}{21} = \frac{23}{21}

  5. Simplify if needed: 2321\frac{23}{21} is an improper fraction. It can also be written as a mixed number:
    23÷21=123 \div 21 = 1 remainder 22, so 2321=1221\frac{23}{21} = 1 \frac{2}{21}.

Final Answer:

The result is 2321\frac{23}{21} or 12211 \frac{2}{21}.

Would you like further clarification on this or similar examples?

Related Questions:

  1. How do you find the least common denominator for two fractions?
  2. What is the process for converting improper fractions to mixed numbers?
  3. How do you add fractions with the same denominator?
  4. Why is finding the least common multiple important in fraction addition?
  5. How do you subtract fractions with unlike denominators?

Tip: Always simplify fractions to their lowest terms to make the answer clearer.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Fractions
Addition of fractions
Least common denominator

Formulas

LCD method for adding fractions

Theorems

Arithmetic operations on fractions

Suitable Grade Level

Grades 5-7