Lesson 63: Subtracting Mixed Numbers with Regrouping, Part 2

New Concept

When subtracting mixed numbers, it is sometimes necessary to regroup. We rewrite the fractions with common denominators before regrouping.

What’s next

This is the foundation for handling complex fractions. Next, you'll tackle worked examples that show how to find common denominators and regroup in one problem.

Property

To subtract mixed numbers, first rewrite the fractions to have common denominators. If the top fraction is smaller than the bottom fraction, you must regroup by borrowing 1 from the whole number and adding it to the fraction part.

Examples

• $5\frac{1}{2} - 1\frac{2}{3} \rightarrow 5\frac{3}{6} - 1\frac{4}{6} \rightarrow 4\frac{9}{6} - 1\frac{4}{6} = 3\frac{5}{6}$
• $6\frac{1}{4} - 2\frac{3}{4} \rightarrow 5\frac{5}{4} - 2\frac{3}{4} = 3\frac{2}{4} = 3\frac{1}{2}$
• $7\frac{1}{3} - 3\frac{5}{6} \rightarrow 7\frac{2}{6} - 3\frac{5}{6} \rightarrow 6\frac{8}{6} - 3\frac{5}{6} = 3\frac{3}{6} = 3\frac{1}{2}$

Explanation

Think of it as a pizza problem! You can't give away more slices than you have. So, you trade one whole pizza for more slices, making sure all slices are the same size (common denominators). Now you have a big pile of slices, making it easy to subtract and see what's left for a midnight snack.