If a b has a remainder of zero, then a is divisible by b.
The even counting numbers are divisible by 2.
They are 2, 4, 6, 8,… .
The odd counting numbers are not divisible by
2. They are 1, 3, 5, 7,… .
The process of reasoning to a general conclusion through observations of specific cases. Also called induction.
Often used by mathematicians and scientists to predict answers to complicated problems.
In testing a hypothesis, if a special case is found that satisfies the conditions of the conjecture but produces a different result, that case is called a counterexample.
Only one exception is necessary to prove a hypothesis false.
If a counterexample cannot be found, the conjecture is neither proven nor disproven.
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).
7, 11, 15, 19, 23, 27, 31,…
Solution:
We can see that four is added to each term to get the following term.
31 + 4 = 35,
35 + 4 = 39,
39 + 4 = 43
Therefore, the next three numbers in the sequence are 35, 39, and 43.
Read the problem carefully at least twice.
Try to make a sketch of the problem. Label the information given.
Make a list of the given facts that are pertinent to the problem.
Decide if you have enough information to solve the problem.
