L4 · Subtracting mixed numbers, including regrouping (common denominators)

Learning goal

“I can subtract mixed numbers with common denominators - by wholes and parts, or by converting to improper fractions - and when the fraction part is too small to subtract, I regroup by trading 1 whole for its parts without changing the amount. I check by adding the answer back.”

Regroup — trade 1 whole for denominator-many unit parts (3 1/4 becomes 2 5/4) so a subtraction becomes possible. The amount does not change; only its dress does. (Deepening the L3 term.)

Trade — the concrete move inside regrouping: hand over 1 whole, receive its parts in return.

Difference — the result of a subtraction; check it by adding it back to the number subtracted. (Review from L2.)

Improper fraction — the conversion strategy's form: every mixed number can be unpacked into unit parts and subtracted as a single count. (Review from G5U05.)

Worked example

4 5/7 - 2 2/7. Wholes and parts: wholes 4 - 2 = 2. Parts: 5/7 - 2/7 = 3/7. Difference: 2 3/7. Convert strategy: 4 5/7 = 33/7 and 2 2/7 = 16/7. 33/7 - 16/7 = 17/7 = 2 3/7. The strategies agree, as they must - and adding back checks it too: 2 3/7 + 2 2/7 = 4 5/7. Model both ways: bars in sevenths with 2 wholes and 2 sevenths crossed out, AND a number line in sevenths (extended to 5): start at 4 5/7, jump back 2 wholes, then back 2/7, land on 2 3/7.

Check yourself — explain it

Why do both strategies give 2 3/7?

Paired problem — example still visible

5 6/8 - 3 2/8 -> wholes 2, parts 4/8 -> 2 1/2

Faded completion — last step is yours

"6 4/5 - 2 1/5: wholes 4, parts 3/5, so the difference is ___." -> 4 3/5

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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