Make and test a conjecture about the following and provide your examples. (10pts each)
1. Make and test a conjecture about the product of two even numbers
2. Make and test a conjecture about the product of two odd numbers.
3. Make and test a conjecture about the quotient of two integers with different sign.
1. Make and test a conjecture about the product of two even numbers
2. Make and test a conjecture about the product of two odd numbers.
3. Make and test a conjecture about the quotient of two integers with different sign.
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Answer:
1. Conjecture: The product of two even numbers is always even.
Testing: Let's take two even numbers, 4 and 6.
4 x 6 = 24, which is an even number.
Let's take two other even numbers, 8 and 10.
8 x 10 = 80, which is an even number.
These results support the conjecture that the product of two even numbers is always even.
2. Conjecture: The product of two odd numbers is always odd.
Testing: Let's take two odd numbers, 3 and 5.
3 x 5 = 15, which is an odd number.
Let's take two other odd numbers, 7 and 9.
7 x 9 = 63, which is an odd number.
These results support the conjecture that the product of two odd numbers is always odd.
3. Conjecture: The quotient of two integers with different sign is always negative.
Testing: Let's take two integers with different signs, 4 and -2.
4 ÷ -2 = -2, which is a negative number.
Let's take two other integers with different signs, -6 and 2.
-6 ÷ 2 = -3, which is also a negative number.
These results support the conjecture that the quotient of two integers with different sign is always negative.