Adding Fractions with Different Denominators
Add fractions with different denominators in Grade 6 math by finding the least common denominator, converting each fraction, adding numerators, and simplifying the result.
Key Concepts
Property To add or subtract fractions with different denominators, you must first rename them to have a common denominator. For example, to solve $\frac{1}{2} + \frac{1}{3}$, you first find equivalent fractions with a denominator of 6.
Examples Add $\frac{1}{2} + \frac{1}{3}$: Rename to $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ Add $\frac{1}{3} + \frac{2}{3}$ after renaming to a denominator of 6: $\frac{2}{6} + \frac{4}{6} = \frac{6}{6} = 1$ Subtract $\frac{5}{12} \frac{1}{6}$: Rename to $\frac{5}{12} \frac{2}{12} = \frac{3}{12}$.
Explanation You can't add fractions with different denominators, just like you can't add cats and dogs. You first need a common name, or 'common denominator'! We use multiplication to give each fraction a new name so they can finally be added together properly.
Common Questions
How do you add fractions with different denominators?
Find the least common denominator of the two fractions. Convert each fraction to an equivalent form with that denominator. Then add the numerators and keep the denominator the same, simplifying if possible.
How do you find the least common denominator?
The least common denominator is the least common multiple of the denominators. For one-third plus one-fourth, the LCM of 3 and 4 is 12, so convert to four-twelfths plus three-twelfths to get seven-twelfths.
Can you add fractions without finding the LCD?
Yes, you can multiply the denominators to get a common denominator, but you will likely need to simplify more at the end. Using the LCD keeps numbers smaller and makes the final simplification step easier.
What mistake do students make when adding unlike fractions?
The most common mistake is adding both numerators AND both denominators. For example, one-third plus one-fourth does not equal two-sevenths. You must never add denominators — only numerators after finding a common denominator.