To add a fraction and a whole number, you can convert the whole number into a fraction or use a shortcut method. Here's how:
Method 1: Converting the Whole Number to a Fraction
- Express the whole number as a fraction: Put the whole number over a denominator of 1. For example, if you have the whole number 2, express it as 2/1.
- Find a Common Denominator: If the fraction you're adding already has a denominator, find the least common multiple (LCM) of 1 (from the whole number fraction) and the other fraction's denominator. This will be your common denominator. If the other fraction's denominator is 3, the common denominator is 3.
- Convert the Whole Number Fraction: Multiply both the numerator and the denominator of the whole number fraction by whatever number makes the denominator equal to the common denominator. For example, to convert 2/1 to have a denominator of 3, multiply both the numerator and denominator by 3: (2*3)/(1*3) = 6/3.
- Add the Fractions: Add the numerators, keeping the common denominator the same. For example, if you are adding 6/3 + 1/3, you would add 6 + 1 = 7. The answer is 7/3.
- Simplify (if needed): If the resulting fraction is improper (numerator is larger than the denominator), convert it to a mixed number. 7/3 becomes 2 1/3.
Method 2: Shortcut Method
Based on the reference video, you can use this shortcut (0:11-1:52):
- Multiply the denominator by the whole number.
- Add this result to the numerator. The result becomes the new numerator, keeping the original denominator.
Example: 2 + 1/3
- Multiply: 3 * 2 = 6
- Add: 6 + 1 = 7
- The result is 7/3
This can then be converted to the mixed number 2 1/3.
