Math Problem Statement
Solution
Let's solve the given fraction addition problem:
Step 1: Find the least common denominator (LCD)
The denominators are 21 and 14. The least common denominator of 21 and 14 is their least common multiple (LCM).
- Prime factorization of 21:
- Prime factorization of 14:
The LCM is .
Step 2: Convert each fraction to have the LCD
Now, we will express both fractions with a denominator of 42.
Step 3: Add the fractions
Now that the fractions have the same denominator, we can add them:
Step 4: Simplify the result
Since 13 is a prime number and does not divide 42, the fraction is already in its simplest form.
Thus, the answer is:
Would you like more details or have any questions? Here are five related problems for practice:
- Add and simplify.
- Subtract and simplify.
- Add and simplify.
- Subtract and simplify.
- Add and simplify.
Tip: When adding fractions, always find the least common denominator (LCD) before performing the addition!
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Math Problem Analysis
Mathematical Concepts
Fractions
Addition of Fractions
Least Common Denominator (LCD)
Formulas
LCM (Least Common Multiple) to find the common denominator
Addition of fractions: (a/b) + (c/d) = (ad + bc) / bd
Theorems
The principle of adding fractions by finding a common denominator
Suitable Grade Level
Grades 5-7