Question

# Make and test a conjecture about the sign of the product of any two negative integers.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

## The correct answer is: Hence, we conclude that the product of any two negative integers is a positive integer and we have proved this conjecture by deductive reasoning.

### Let’s create a conjecture for the pairs (-1,-2), (-9,-20) and (-35, -10). We are asked to make a conjecture about the sign of the product of any two negative integers.

So first, do the product of the assumed pair of negative integers. We got

-1 (-2) = +2

-9 (-20) = +180

-35 (-10) = +350

So, we conclude that the product of any two negative integers a positive integer and this is the conjecture.

Now, let’s see if the conjecture is true or not by deductive reasoning. Let’s say the pair is (-x,-y). Taking the product.

-x (-y) = +xy

So, we can see that the result is a positive integer.

Final Answer:

Hence, we conclude that the product of any two negative integers is a positive integer and we have proved this conjecture by deductive reasoning.

### Related Questions to study

### Classify the equation 6(x + 2)= 5(x + 7) as having one solution , no solution or infinitely many solutions ?

### Classify the equation 6(x + 2)= 5(x + 7) as having one solution , no solution or infinitely many solutions ?

### Does the diagram provide necessary information to prove that the triangles ABC and ACD are congruent by AAS-congruence postulate? If not, mention the required condition.

### Does the diagram provide necessary information to prove that the triangles ABC and ACD are congruent by AAS-congruence postulate? If not, mention the required condition.

### Given 6 collinear points, make a conjecture about the number of ways to connect different pairs of points.

### Given 6 collinear points, make a conjecture about the number of ways to connect different pairs of points.

### Prove that the triangles ABC and XYZ are congruent.

### Prove that the triangles ABC and XYZ are congruent.

### Describe the pattern in the numbers 9.001, 9.010, 9.019, 9.028, ... and write the next three numbers in the pattern.

### Describe the pattern in the numbers 9.001, 9.010, 9.019, 9.028, ... and write the next three numbers in the pattern.

### Solve 49x + 9= 49x + 83

a)Does the equation have one solution , no solution or infinitely many solutions ?

b) Write two equations in one variable that have the same number of solutions as this equation

### Solve 49x + 9= 49x + 83

a)Does the equation have one solution , no solution or infinitely many solutions ?

b) Write two equations in one variable that have the same number of solutions as this equation

### Describe the pattern in the numbers 5, -15, 45, -215, ... and write the next three numbers in the pattern.

### Describe the pattern in the numbers 5, -15, 45, -215, ... and write the next three numbers in the pattern.

### – State and prove the AAS congruence postulate using the ASA congruence postulate.

### – State and prove the AAS congruence postulate using the ASA congruence postulate.

### Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?

### Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?

### Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.

Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.

¶**Types of Expression**

1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.

¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.

### Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.

Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.

¶**Types of Expression**

1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.

¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.