The fact families 2*3=6 and 2*10=20 both contain exactly three different digits . How many other fact families with dividends under 100 contain exactly three different digits? Name one multiplication fact in each of these families?
To find the other fact families with dividends under 100 that contain exactly three different digits, we can go through each possible dividend and divisor combination and check if their product has exactly three different digits.
Here's how we can do it:
Step 1: Go through each dividend from 1 to 99 (inclusive).
Step 2: For each dividend, go through each divisor from 1 to 9 (inclusive).
Step 3: Calculate the product of the dividend and divisor.
Step 4: Check if the product has exactly three different digits.
Step 5: If it does, record the multiplication fact in that fact family.
Let's apply this process to find the fact families:
1. Start with the first dividend, which is 1. Calculate 1 * 1 = 1. Since the product contains only one digit, we skip it.
2. Move to the next dividend, which is 2. Calculate all possible products for divisors from 1 to 9: 2 * 1=2, 2 * 2=4, 2 * 3=6, ..., 2 * 9=18. Among these, 2 * 3 = 6 satisfies the condition of having exactly three different digits.
- Fact family: 2 * 3 = 6
3. Continue this process for the remaining dividends from 3 to 99. After going through all the dividends, we find the following fact families:
- Fact family: 2 * 3 = 6
- Fact family: 2 * 10 = 20
- Fact family: 3 * 4 = 12
- Fact family: 4 * 6 = 24
- Fact family: 4 * 8 = 32
- Fact family: 5 * 9 = 45
- Fact family: 6 * 7 = 42
- Fact family: 6 * 8 = 48
- Fact family: 7 * 8 = 56
- Fact family: 8 * 9 = 72
Therefore, there are a total of 10 fact families with dividends under 100 that contain exactly three different digits.