Adding Fractions Adding fractions is a way to combine fractions with different denominators. A denominator is the bottom number of a fraction, and the...
Adding fractions is a way to combine fractions with different denominators. A denominator is the bottom number of a fraction, and the numerator is the top number. Adding fractions with the same denominator is straightforward, as they essentially add the fractions on top of each other.
However, when adding fractions with different denominators, we need to rewrite them in a common denominator. This means finding the least common multiple of the denominators, which is the smallest number that is divisible by both the numerator and denominator. Once the fractions are in the same denominator, addition can be performed as usual.
Here's how to add fractions with different denominators:
Find the Least Common Multiple (LCM) of the denominators. This is the smallest number that is divisible by both the numerator and denominator.
Convert the fractions to equivalent fractions with the same denominator. This means finding a multiple of the denominator that is equal to both the numerator and denominator.
Add the fractions as usual. This is simply adding the numerators together.
Reduce the answer to its simplest form. This means finding the greatest common factor of the numerator and denominator and dividing it out.
Examples:
Adding 1/3 and 1/4:
Convert 1/3 and 1/4 to 4/12 and 3/12, respectively.
4/12 + 3/12 = 7/12.
Adding 3/5 and 2/5:
Convert 3/5 and 2/5 to 6/10 and 4/10, respectively.
6/10 + 4/10 = 10/10, which simplifies to 1