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NUMBER · GRADE 6 · ALBERTAOUTCOME AB-MAT6-N7

F10 · Unit Fractions and Fraction of a Quantity

Learning goal

“I can multiply by a unit fraction by dividing. I can find a fraction of a quantity. I can split a quantity into equal groups, then take the groups I need.”

Unit fraction — a fraction with numerator 1, like 1/4 or 1/7. It names one equal part.
Quantity — an amount you can count or measure, like 24 counters or 30 litres.
Fraction of a quantity — a part of that amount, like 3/4 of 24 counters.
Worked example

6 × 1/3. Repeated addition: 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 = 6/3 = 2. Six jumps of 1/3 land exactly on 2, a whole number. Notice the twin: 6 ÷ 3 = 2. Multiplying by 1/3 gives the same answer as dividing by 3. Rule: multiplying by a unit fraction 1/d is the same as dividing by d. Model both ways: a bar of 6 thirds shaded whole (6/3 = 2 wholes), AND the jumps on the 0–2 number line landing on 2.

Check yourself — explain it

Why does 6 × 1/3 equal 6 ÷ 3?

Paired problem — example still visible

8 × 1/4 → 8/4 = 2, and 8 ÷ 4 = 2. Same answer.

Faded completion — last step is yours

9 × 1/3 = 9/3 = ___ , and the matching division is 9 ÷ ___ . Finish both steps. → 3; 3

Ready to practise?

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

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