Grade 5 › G5U03 Divisibility

Grade 5 › G5U03 Divisibility › L3
GRADE 5 · ALBERTAOUTCOME AB-G5-5N3

L3 · Why division by zero is impossible; divisibility clinic

Learning goal

“I can explain, using multiplication, why dividing by zero is impossible - and I can use the generalized tests for 2, 3 and 5 to find factors of a number.”

Dividend — the number being divided. In 12 / 3 = 4, the dividend is 12.
Divisor — the number you divide by. In 12 / 3 = 4, the divisor is 3.
Quotient — the answer to a division. In 12 / 3 = 4, the quotient is 4.
Impossible (undefined) — a calculation with no possible answer. Division by zero is impossible: no quotient exists.
Worked example

What is 6 / 0? Step 1: Division is multiplication turned around. 12 / 3 = 4 because 4 x 3 = 12. So 6 / 0 asks: "what number x 0 = 6?" Step 2: Try candidates. 5 x 0 = 0. 100 x 0 = 0. EVERY number times 0 equals 0. Step 3: No number times 0 can ever give 6. The multiplication question has no answer, so 6 / 0 is impossible - we say it is undefined. Say it plainly: zero groups is not "a very small share." Sharing 6 cookies among 0 people does not make smaller pieces - there are no groups at all, so there is nothing to count. And be careful not to flip it: 0 / 6 = 0 is perfectly fine, because 0 x 6 = 0 checks out.

Check yourself — explain it

Why is 5 / 0 impossible, but 0 / 5 allowed?

Paired problem — example still visible

Compute if possible: 9 / 0. -> Impossible - it asks "what x 0 = 9?", and every number x 0 = 0.

Faded completion — last step is yours

"14 / 0 asks: what x 0 = ___? Since every number x 0 = ___, the division is ___" -> 14; 0; impossible

Ready to practise?

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

Start practice →Take the unit quiz