Lesson 6: Subtract mixed numbers.

Property

To subtract a fraction from a mixed number where the fraction part of the mixed number is smaller than the fraction being subtracted, you must regroup. Convert one whole from the mixed number into a fraction and add it to the existing fraction part.
$A \frac{b}{c} - \frac{d}{c} = (A-1) + \frac{c}{c} + \frac{b}{c} - \frac{d}{c} = (A-1) \frac{b+c-d}{c}$, for $b < d$.

Examples

• $5 \frac{1}{4} - \frac{3}{4} = 4 \frac{5}{4} - \frac{3}{4} = 4 \frac{2}{4} = 4 \frac{1}{2}$
• $3 \frac{2}{8} - \frac{5}{8} = 2 \frac{10}{8} - \frac{5}{8} = 2 \frac{5}{8}$

Explanation

When subtracting a fraction from a mixed number, you may need to regroup if the fractional part of the mixed number is too small. To do this, "take" one whole from the whole number part and rewrite it as a fraction with the same denominator. Add this new fraction to the original fraction part of the mixed number. Finally, you can subtract the fractions and keep the new whole number.

Property

To regroup a mixed number $W \frac{a}{b}$ to get a larger numerator in the fraction part, you can rewrite it as an equivalent mixed number by taking 1 from the whole number and adding it to the fraction:

Examples