Grade 6 Math: Adding Fractions with Unlike Denominators

Grade 6 focus: Adding fractions is straightforward when the denominators match. When they do not, you rewrite each fraction as an equivalent fraction so they share a common denominator—usually the least common denominator (LCD), which is the least common multiple (LCM) of the denominators.

Video lesson: Watch this Khan Academy tutorial to see the ideas explained step by step.

Step-by-step method

1. Identify denominators. For example, in \(\frac{2}{3} + \frac{1}{4}\), the denominators are \(3\) and \(4\).
2. Find the LCD. \(\mathrm{LCM}(3,4)=12\).
3. Build equivalent fractions. \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{1}{4} = \frac{3}{12}\).
4. Add the numerators and keep the denominator: \(\frac{8}{12} + \frac{3}{12} = \frac{11}{12}\).
5. Simplify if possible. Here \(\frac{11}{12}\) is already in simplest form.

Worked example

Add \(\frac{5}{6} + \frac{1}{8}\).

\(\mathrm{LCM}(6,8)=24\). Then \(\frac{5}{6} = \frac{20}{24}\) and \(\frac{1}{8} = \frac{3}{24}\). Sum: \(\frac{23}{24}\).

Why the LCD helps

Equivalent fractions let you express both amounts using the same-sized parts, so addition means counting parts of the same whole—exactly what “common denominator” is for.

Common mistakes

• Adding numerators and denominators directly (e.g., \(\frac{1}{2} + \frac{1}{3} \neq \frac{2}{5}\)).
• Forgetting to change both fractions when rewriting.
• Stopping before simplifying (e.g., writing \(\frac{4}{8}\) instead of \(\frac{1}{2}\)).

Practice tip

Always ask: “Do my denominators match?” If not, find the LCD before you add.