Adding Fractions, Set 2
Fractions can only be added when they have the same denominator. The easiest way to find the lowest common denominator is to list multiples. List out the multiples of each denominator until you find the first number that appears in both lists. For example, if you have fractions with denominators 3 and 4, you would list their multiples:
- Multiples of 3: 3, 6, 9, 12, 15...
- Multiples of 4: 4, 8, 12, 16...
Notice that 12 is the first number that appears in both lists, making it the least common multiple (LCM) and thus the lowest common denominator.
Once the fractions have the same denominator, add the numerators while keeping the denominator unchanged. For instance, 1/4 + 2/4 equals 3/4.
Consider another example: 1/3 + 1/2. Using the LCD method, you'd first determine the lowest common denominator (which is 6), then convert each fraction: 1/3 becomes 2/6, and 1/2 becomes 3/6. Now you can easily add 2/6 + 3/6, which equals 5/6.
Adding mixed numbers requires an extra step. First, convert the mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator, then placing this sum over the original denominator. For example, 2 1/4 becomes 9/4. Then proceed with adding as you would with other fractions.
A few practical tips will help you master fraction addition: Always check that your final fraction is in its simplest form by dividing both the numerator and denominator by their greatest common factor. Take your time with each step, and don't rush the process of finding the common denominator.