Grade 6 Math: Adding and Subtracting Mixed Numbers

Grade 6 focus: Mixed numbers combine a whole number and a proper fraction (e.g., \(2\frac{1}{3}\)). To add or subtract, you can either convert to improper fractions or add/subtract whole parts and fraction parts separately—then handle regrouping if needed.

Video lesson: Watch this Math with Mr. J lesson on adding and subtracting mixed numbers when denominators differ.

Strategy A: Improper fractions

1. Rewrite each mixed number as an improper fraction.
2. Add or subtract using fraction rules (LCD if denominators differ).
3. Convert the answer back to a mixed number if appropriate.

Strategy B: Wholes + fractions

1. Add or subtract the whole-number parts.
2. Add or subtract the fractional parts (common denominator).
3. If the fractional part is negative or “too small,” regroup from the whole.

Worked example (addition)

\(1\frac{2}{5} + 2\frac{1}{4}\). LCD of \(5\) and \(4\) is \(20\).

Wholes: \(1 + 2 = 3\). Fractions: \(\frac{2}{5} + \frac{1}{4} = \frac{8}{20} + \frac{5}{20} = \frac{13}{20}\). Result: \(3\frac{13}{20}\).

Regrouping reminder

Subtracting \(3\frac{1}{6} – 1\frac{5}{6}\) may require borrowing: rewrite \(3\frac{1}{6}\) as \(2\frac{7}{6}\), then subtract to get \(1\frac{2}{6} = 1\frac{1}{3}\) after simplifying.

Practice tip

Show each step—especially regrouping—so errors are easy to spot.