L3 · Adding mixed numbers (common denominators)

Learning goal

“I can add mixed numbers with common denominators in two ways - wholes and parts separately, or by converting both to improper fractions - I can say why the two ways must agree, and I finish with simplest form, trading a whole out of the fraction part when the parts overflow.”

Regroup — trade between wholes and parts without changing the amount: when the fraction parts add to a whole or more, trade each whole (denominator-many parts) into the whole-number part.

Strategy — a planned way of computing. This lesson compares two strategies that must agree, because both count the same total.

Mixed number — a whole number and a fraction written together, naming one amount. (Review from G5U05.)

Improper fraction — a fraction with numerator greater than denominator; the other dress a mixed number can wear. (Review from G5U05.)

Worked example

2 1/4 + 1 2/4. Strategy 1 - wholes and parts separately: Wholes: 2 + 1 = 3. Parts: 1/4 + 2/4 = 3/4. Total: 3 3/4. Strategy 2 - convert to improper fractions: 2 1/4 = 9/4 and 1 2/4 = 6/4. Add: 9/4 + 6/4 = 15/4. Convert back: 15/4 = 3 3/4. Say it plainly: the strategies MUST agree - both count the same total amount, just grouped differently. If they ever disagree, one of them has a counting error, and the other strategy is your built-in check. Model both ways: bars showing 2 wholes + 1 quarter beside 1 whole + 2 quarters, AND a number line in quarters (extended to 4): start at 2 1/4, jump 1 whole, then jump 2/4, land on 3 3/4.

Check yourself — explain it

Why must Strategy 1 and Strategy 2 give the same answer?

Paired problem — example still visible

1 1/6 + 2 3/6, wholes and parts -> wholes 3, parts 4/6 -> 3 4/6 = 3 2/3

Faded completion — last step is yours

"2 2/5 + 1 1/5: wholes 3, parts 3/5, so the sum is 3 and ___ fifths." -> 3 (3 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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