Answer:
a) The product of any two odd integers is an odd integer.
b) The sum of two negative integers is always smaller than the smallest negative integer.
Step-by-step explanation:
Part a
Given:
- The product of any two odd integers.
Carry out a few examples to find a pattern:
- 1 × 3 = 3
- 3 × 5 = 15
- 5 × 7 = 35
Pattern:
- The solution is always odd.
Write the conjecture based on the found pattern.
Conjecture:
- The product of any two odd integers is an odd integer.
Test the conjecture for accuracy using at least three sets of numbers.
Test:
- 277 × 109 = 30193
- 15 × 23 = 345
- 9 × 61 = 549
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Part b
Given:
- The sum of two negative integers.
Carry out a few examples to find a pattern:
- -1 + -2 = -3
- -10 + -3 = -13
- -20 + -1 = -21
Pattern:
- The solution is always smaller than the smallest number.
Write the conjecture based on the found pattern.
Conjecture:
- The sum of two negative integers is always smaller than the smallest negative integer.
Test the conjecture for accuracy using at least three sets of numbers.
Test:
- -5 + -5 = -10
- -40 + -52 = -92
- -13 + -14 = -27
