Skill: Subtract mixed numbers without regrouping

To subtract mixed numbers without regrouping, subtract the whole numbers and fractional parts separately. This works when the fractional part of the first number is at least as large as the fractional part of the second number.

Example:

$$5\frac{3}{8}-2\frac{1}{8}$$

1. Check the fractional parts. Since $\frac{3}{8}\geq\frac{1}{8}$, no regrouping is needed.

2. Subtract the whole numbers:

$$5-2=3$$

3. Subtract the fractional parts. The denominators are already the same:

$$\frac{3}{8}-\frac{1}{8}=\frac{2}{8}$$

4. Put the results together:

$$3\frac{2}{8}$$

5. Simplify the fraction:

$$\frac{2}{8}=\frac{1}{4}$$

Therefore,

$$5\frac{3}{8}-2\frac{1}{8}=3\frac{1}{4}$$

If the denominators are different, first rewrite the fractions as equivalent fractions with a common denominator. If the first fractional part is smaller, regrouping is needed, so it is not a subtraction-without-regrouping problem.