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Multiplying by 0, 1, 10 and 100
Some numbers follow special rules when you multiply by them. These rules are so reliable that once you learn them, you will never get these facts wrong. In this lesson you will learn what happens when you multiply by 0, 1, 10 and 100.
Multiplying by 0
Any number times 0 equals 0.
Think about it with groups. 5 × 0 means 5 groups of nothing. If you have 5 empty boxes, you have 0 things! And 0 × 5 means zero groups of 5, which is also nothing.
- 8 × 0 = 0
- 0 × 100 = 0
- 1,000 × 0 = 0
Multiplying by 1
Any number times 1 equals the same number.
6 × 1 means 6 groups of 1 thing, which is 6. And 1 × 6 means 1 group of 6, which is still 6.
- 9 × 1 = 9
- 1 × 47 = 47
Do not mix them up
A common mistake is to think 7 × 0 = 7. Remember: multiplying by 0 gives 0, and multiplying by 1 keeps the number the same.
Multiplying by 10
When you multiply a whole number by 10, each digit moves one place to the left, and a 0 fills the ones place.
| Number | × 10 | Why |
|---|---|---|
| 4 | 40 | 4 ones become 4 tens |
| 12 | 120 | 1 ten becomes 1 hundred, 2 ones become 2 tens |
| 35 | 350 | 3 tens become 3 hundreds, 5 ones become 5 tens |
Multiplying by 100
When you multiply a whole number by 100, each digit moves two places to the left, and two 0s fill the empty places.
- 3 × 100 = 300
- 25 × 100 = 2,500
- 60 × 100 = 6,000
Using tens to multiply bigger numbers
You can use these rules with facts you know. For 4 × 30: 30 is 3 tens, so 4 × 30 is 4 × 3 tens = 12 tens = 120.
- 6 × 20 = 6 × 2 tens = 12 tens = 120
- 5 × 70 = 5 × 7 tens = 35 tens = 350
Patterns with zeros
Look at this pattern: 4 × 2 = 8, 4 × 20 = 80, 4 × 200 = 800. Each time one factor is ten times bigger, the product is ten times bigger too. Spotting patterns like this makes big multiplication feel easy.
Example
A school orders 8 boxes of pencils. Each box holds 100 pencils. How many pencils is that? 8 × 100 = 800 pencils. Then the school orders 3 boxes of 40 rulers. That is 3 × 4 tens = 12 tens = 120 rulers.
Key takeaways
- Any number times 0 is 0.
- Any number times 1 stays the same.
- Multiplying by 10 moves digits one place left and adds a 0.
- Multiplying by 100 moves digits two places left; use tens to multiply numbers like 4 × 30.
Practice
- 15 × 0
- 1 × 89
- 23 × 10
- 7 × 100
- 6 × 40
Answers: 1 is 0. 2 is 89. 3 is 230. 4 is 700. 5 is 240 (6 × 4 tens = 24 tens).