How it works
Free 0 and 1 multiplication worksheets teach two rules, and Make a new sheet changes the numbers. The first mixes 40 lines such as 0 × 9 and 9 × 1. Sheet type adds 347 × 1, 5,000 × 0 and true or false.
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Two rules, and why each one is true
Read 6 × 1 as 6 groups of 1 and the answer has to be 6. Read 6 × 0 as 6 groups of nothing and it has to be 0. The first is the identity property, the second the zero property of multiplication. Neither cares how large the number is, so the sheets climb from 2 × 1 to 9,999 × 1.
Where pupils slip with 0 and 1
The common slip is to answer 7 × 0 with 7, a habit carried over from 7 + 0. The sheet × 0, × 1, + 0 and − 0: read the sign sets all four side by side. The other slip is to answer 7 × 1 with 1. True or false with × 0 and × 1 prints both mistakes as finished lines for pupils to catch.
- Ask for 1,000,000 × 0 out loud. A class that answers without a pause owns the rule, not a list.
- In a chain like 6 × 3 × 0 × 8, hunt for a 0 first. Find one and the line is finished.
- Set Problems to 12 on the opening sheet for an exit ticket. Two rules do not need 40 lines.
Questions and answers
Why is any number times 0 equal to 0?
Multiplication counts equal groups. 5 × 0 is 5 groups with nothing in them, and 0 × 5 is no groups at all, so either way there is nothing to count. Bags of 1 and empty bags: 6 bags of 0 apples puts that picture into words.
Can you divide by 0 or by 1?
By 1, yes: 8 ÷ 1 = 8, and Divide by 1 drills it. Zero can be divided: 0 ÷ 6 = 0. But 6 ÷ 0 asks for a number that gives 6 when multiplied by 0, and none does. No sheet here prints a division by 0.
When do schools teach multiplying by 0 and 1?
England lists multiplying by 0 and 1, and dividing by 1, among Year 4's mental methods. In the United States they are third grade facts: 0 and 1 are one-digit numbers, so 0 × 8 and 1 × 9 sit on the Common Core's memory list.