Adding Fractions with Different Denominators
Adding fractions with different denominators is a core Grade 7 skill in Big Ideas Math, Course 2, Chapter 2 on Rational Numbers. The process requires finding the least common denominator (LCD)—the least common multiple of both denominators—then rewriting each fraction as an equivalent fraction with that LCD. For example, 3/10 + 7/15 uses LCD 30, becoming 9/30 + 14/30 = 23/30. Similarly, 1/6 + 3/8 uses LCD 24: 4/24 + 9/24 = 13/24. Once fractions share a denominator, only the numerators are added. This method also extends to algebraic fractions like 4/9 + x/2, where LCD 18 gives (8 + 9x)/18.
Key Concepts
To add fractions with different denominators, first find the least common denominator (LCD). The LCD is the least common multiple (LCM) of the denominators. Then, convert each fraction into an equivalent fraction with the LCD. Finally, add the numerators and place the result over the common denominator. Do not simplify the equivalent fractions before combining them, or you will lose the common denominator.
Common Questions
What is the first step when adding fractions with different denominators?
Find the least common denominator (LCD), which is the least common multiple (LCM) of the two denominators.
How do you add 3/10 + 7/15?
The LCD of 10 and 15 is 30. Rewrite: 3/10 = 9/30 and 7/15 = 14/30. Then 9/30 + 14/30 = 23/30.
How do you add 1/6 + 3/8?
The LCD of 6 and 8 is 24. Rewrite: 1/6 = 4/24 and 3/8 = 9/24. Then 4/24 + 9/24 = 13/24.
Why can't you add fractions with different denominators directly?
The denominators represent different-sized pieces. Adding numerators directly would be like adding halves and thirds without converting them to the same size unit first.
Does this method work with algebraic fractions?
Yes. For 4/9 + x/2, the LCD is 18. Rewrite as 8/18 + 9x/18, giving the sum (8 + 9x)/18.
Should you simplify fractions before finding the LCD?
No—do not simplify the individual fractions before combining them, or you may lose the common denominator. Simplify the final answer after adding.