Question

NO LINKS!!

Make and test a conjecture about the given quantity. Test at least three sets of numbers. (NOT MULTIPLE CHOICE)

a. product of any two odd integers

b. the sum of two negative integers

Answer 1

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.

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