L2 · Adding mixed numbers

Learning goal

“I can add two mixed numbers by adding the whole-number parts and the fractional parts - and when the fractional parts add to more than 1, I regroup the extra whole.”

Mixed number — a number made of a whole-number part and a fractional part, like 2 3/5.

Fractional part — the fraction piece of a mixed number (in 2 3/5, the fractional part is 3/5).

Regroup — trade one whole for an equal set of parts (1 = 6/6), or trade a set of parts equal to 1 for a whole, without changing the value.

Simplify — rewrite a fraction in lowest terms.

Worked example

Add 2 3/5 + 1 1/5. Step 1: A mixed number is a sum: 2 3/5 means 2 + 3/5. So whole parts can join whole parts and fractional parts can join fractional parts. Step 2: Wholes: 2 + 1 = 3. Fractions: 3/5 + 1/5 = 4/5. Step 3: The sum is 3 4/5. Both models agree: two whole bars + a fifths bar with 3 + 1 parts shaded, and a 0-4 number line in fifths - start at 2 3/5, jump 1 whole, then jump 1/5 more, land on 3 4/5. Say it plainly: like parts join like parts - wholes with wholes, fifths with fifths.

Check yourself — explain it

Why can the whole-number parts and the fractional parts be added separately?

Paired problem — example still visible

3 1/4 + 2 5/8 -> in eighths: 3 2/8 + 2 5/8 = 5 7/8

Faded completion — last step is yours

"4 2/3 + 1 1/6: in sixths, 4 4/6 + 1 1/6 = 5 ___" -> 5/6 (the sum is 5 5/6)

Ready to practise?

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

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