To add a fraction and a whole number, you can convert the whole number into an improper fraction with the same denominator as the fraction, then add the numerators. Alternatively, you can rewrite the whole number and fraction as a mixed number.
Here's a breakdown of the two primary methods:
Method 1: Converting the Whole Number to a Fraction
- Express the whole number as a fraction: Place the whole number over a denominator of 1 (e.g., 2 becomes 2/1).
- Find a common denominator: Multiply the numerator and denominator of the whole number fraction by the denominator of the other fraction (the one you're adding to). This ensures both fractions have the same denominator.
- Add the numerators: Once both fractions have the same denominator, add their numerators together. Keep the denominator the same.
- Simplify (if needed): Simplify the resulting fraction if possible, either by reducing it to its lowest terms or converting an improper fraction into a mixed number.
Example: 2 + 1/3
- 2 = 2/1
- 2/1 * (3/3) = 6/3 (Now both fractions have a denominator of 3)
- 6/3 + 1/3 = 7/3
- 7/3 = 2 1/3 (Converting the improper fraction to a mixed number)
Method 2: Rewriting as a Mixed Number
- Combine the whole number and fraction: Simply write the whole number followed by the fraction. This automatically creates a mixed number.
- Simplify (if needed): If the fraction part of the mixed number is improper (numerator is greater than or equal to the denominator), you can convert the improper fraction part to a mixed number itself, and add the whole number parts together.
Example: 2 + 1/3
- 2 + 1/3 = 2 1/3
- No further simplification needed in this case.
In summary: When adding a whole number and a fraction, you can either rewrite the whole number as a fraction with a common denominator or directly combine the whole number and fraction to form a mixed number.
