Adding Fractions
Adding fractions can seem tricky at first, but with a little practice, it becomes straightforward. Here's a step-by-step guide on how to add fractions:
1. Understanding the Basics
- Fractions represent parts of a whole. The bottom number (denominator) tells you how many equal parts the whole is divided into, and the top number (numerator) tells you how many of those parts you have.
- To add fractions, they must have the same denominator. This means the whole is divided into the same number of equal parts.
2. Finding a Common Denominator
If the fractions you're adding don't have the same denominator, you need to find a common one:
- Find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators divide into evenly.
- Multiply each fraction by a fraction that equals 1. This will change the denominator without changing the value of the fraction. The number you multiply by is determined by how many times the LCM is bigger than the original denominator.
Example:
Add 1/3 + 1/4
- LCM of 3 and 4 is 12.
- Multiply 1/3 by 4/4 (which equals 1) to get 4/12.
- Multiply 1/4 by 3/3 (which equals 1) to get 3/12.
3. Adding the Fractions
Once you have the same denominator, simply add the numerators. Keep the denominator the same.
Example (continued):
- 4/12 + 3/12 = 7/12
4. Simplifying the Answer
If possible, simplify the fraction by finding the greatest common factor (GCD) of the numerator and denominator and dividing both by it.
Example (continued):
- 7/12 cannot be simplified further.
5. Adding Mixed Numbers
To add mixed numbers, add the whole numbers and the fractions separately. If the fraction part adds up to more than one, simplify it and add the whole number part to the original whole number.
Example:
- 2 1/2 + 3 1/3 =
- Add the whole numbers: 2 + 3 = 5
- Find a common denominator for the fractions: 1/2 = 3/6 and 1/3 = 2/6
- Add the fractions: 3/6 + 2/6 = 5/6
- Combine the results: 5 + 5/6 = 5 5/6
Practice Makes Perfect!
Adding fractions can be a bit challenging at first, but with regular practice and understanding the steps, you'll soon be a pro!
