Mixed Numbers with Regrouping

Add the whole numbers, then add the fractions, then put them together.

When the fractions make more than one

2 3/4 + 1 3/4 gives 3 wholes and 6/4. The 6/4 holds another whole one.

Subtracting needs the opposite

For 4 1/5 − 1 3/5, borrow a whole from the 4. It becomes 3 and 6/5.

This is unbundling again

A whole traded for fifths is the same move as a ten traded for ones.

When the fraction part is too small

In 4 1/5 - 2 3/5, the fraction part 1/5 is smaller than 3/5. As with whole-number subtraction, you unbundle: take one whole from the 4 and cut it into fifths. Now 4 1/5 is 3 and 6/5, and the subtraction proceeds.

The worked case

4 1/5 becomes 3 6/5. Then 3 6/5 - 2 3/5 = 1 3/5. The whole parts subtract and the fraction parts subtract, once the fraction part on top is big enough. This is the same procedure as unbundling a ten, with fifths instead of ones.

The alternative: convert everything

Turn both mixed numbers into improper fractions — 21/5 and 13/5 — subtract to get 8/5, then convert back to 1 3/5. No unbundling is needed at all. Many people find this route more reliable, and it is equally correct.

When the denominators differ too

For 4 1/3 - 2 3/4, find a common denominator first — twelfths — then deal with the regrouping. Doing both steps at once is where errors creep in, so convert the units first and only then decide whether unbundling is needed.