L4 · Subtracting mixed numbers (regrouping)

Learning goal

“I can subtract mixed numbers - and when the fractional part I start with is too small, I regroup one whole into parts before subtracting.”

Regroup — trade one whole for an equal set of parts (1 = 4/4), so a too-small fractional part becomes big enough to subtract from; the value does not change.

Difference — the result of a subtraction.

Fractional part — the fraction piece of a mixed number.

Whole-number part — the whole piece of a mixed number (in 5 1/4, the whole-number part is 5).

Worked example

Subtract 4 7/8 - 1 3/8. Step 1: Compare the fractional parts first: 7/8 is bigger than 3/8, so no trade is needed. Step 2: Wholes: 4 - 1 = 3. Fractions: 7/8 - 3/8 = 4/8. Step 3: The difference is 3 4/8 = 3 1/2. Both models agree: 4 whole bars + an eighths bar with 7 parts shaded, 3 crossed out, and a 0-5 number line in eighths - start at 4 7/8, jump back 1 whole, then back 3/8, land on 3 1/2. Say it plainly: like parts leave like parts - wholes from wholes, eighths from eighths.

Check yourself — explain it

Why do we compare the fractional parts before subtracting anything?

Paired problem — example still visible

5 5/6 - 2 1/4 -> in twelfths: 5 10/12 - 2 3/12 = 3 7/12

Faded completion — last step is yours

"6 4/5 - 3 2/5 = 3 ___" -> 2/5 (the difference is 3 2/5)

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