If a fact family has only 2 multiplication and divison sentences , what do you know about the product and diviend?

How many fact families with a diviend under 100 contain only odd numbers? You can use a multiplication table to help you.

If a fact family has only 2 multiplication and division sentences, we can infer the following about the product and dividend:

1. The product is the result of multiplying two numbers together. For example, in the fact family (2, 4, 8), the product is 8 (2 x 4 = 8).

2. The dividend is the number being divided. For example, in the fact family (4 ÷ 2 = 2), the dividend is 4.

Regarding the second question, to find out how many fact families with a dividend under 100 contain only odd numbers, we can use a multiplication table to see which products fall within the range of 1 to 100.

First, let us find out the odd numbers from 1 to 100:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

Now, we can use these odd numbers as possible dividends and cross-reference them with the multiplication table to find fact families with a dividend under 100 containing only odd numbers.

For example, let's consider the odd number 3. In the multiplication table, we check which products are less than 100 when one of the factors is 3:

3 x 1 = 3 (valid)
3 x 2 = 6 (valid)
3 x 3 = 9 (valid)
3 x 4 = 12 (not valid - over 100)
...

By continuing this process for each odd number, we can count the number of fact families that satisfy the given criteria.

When a fact family has only 2 multiplication and division sentences, it means that there are only 2 related facts involved. One fact will be a multiplication sentence where two numbers are being multiplied to get the product, and the other fact will be a division sentence where the product is divided by one of the numbers to get the other number (dividend).

For example, if we have the fact family {4, 2, 8}, we can form the following multiplication and division sentences:
- 4 x 2 = 8
- 8 ÷ 4 = 2

From these sentences, we can deduce that the product of the multiplication sentence is 8, and the dividend of the division sentence is also 8.

Regarding the second question, to determine how many fact families with a dividend under 100 contain only odd numbers, we can use a multiplication table. The multiplication table will help us identify which products can be obtained by multiplying two odd numbers.

1. Create a multiplication table up to 10 x 10 (or higher if needed).
2. Look at each cell in the table and identify the products that have both factors as odd numbers.
3. For each unique product, create a fact family using the product and its corresponding odd factors. Count the number of fact families that have a dividend under 100.

For example, using a multiplication table up to 10 x 10:

| 1 2 3 4 5 6 7 8 9 10
---------------------------------
1 | 1 2 3 4 5 6 7 8 9 10
2 | 2 4 6 8 10 12 14 16 18 20
3 | 3 6 9 12 15 18 21 24 27 30
4 | 4 8 12 16 20 24 28 32 36 40
5 | 5 10 15 20 25 30 35 40 45 50
6 | 6 12 18 24 30 36 42 48 54 60
7 | 7 14 21 28 35 42 49 56 63 70
8 | 8 16 24 32 40 48 56 64 72 80
9 | 9 18 27 36 45 54 63 72 81 90
10| 10 20 30 40 50 60 70 80 90100

From the table, we can identify the following unique products that result from multiplying two odd numbers: 3, 5, 9, 15, 21, 35, 45, 63, 105, and 315.

Next, we create fact families using these products and their corresponding odd factors, making sure that the dividend is under 100. Counting the fact families will give us the answer to how many fact families with a dividend under 100 contain only odd numbers.