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What is the product of 2 positive integers?

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  • Last Updated : 07 Dec, 2021

Algebra is a branch of mathematics that deals with numbers and symbols. The equations of algebra are composed of constants, variables, and coefficients of variables with are associated with the means of various mathematical operations. Algebra is conducted with some mathematical operations like summation, subtraction, multiplication, and division.

Positive and negative numbers

The numerical values represented on a number line can be determined as a positive or negative numbers. As any standard numerical figure less than zero is considered a negative number that carries a minus (-) sign. For example: -5, -7, -10, etc. Whereas, any standard numerical figure greater than zero is considered a positive number that carries a plus (+) sign. For example: +5, +7, +10, etc.

Sign Rules

There are sign rules defined for addition, subtraction, multiplication, and division. These rules are mentioned below for various sign numbers. For instance, positive numbers adding positive numbers or negative numbers, etc. Let’s take a look at these,

  • For addition

The addition is the operation of combining numbers. It is denoted by using the plus sign ‘+’.

  1. (Positive number) + (Positive number) = Positive number [(+) + (+) = (+)]
  2. (Negative number) + (Negative number) = Negative number [(-) + (-) = (-)]

The result of operation during adding two numbers with different signs is based on the greater term involved in the operation.

  1. If the sign of the larger value has a positive (+) sign then, the result will also have a positive sign.
  2. If the sign of the larger value has a negative (-) sign then, the result will have a negative sign.
  1. (Positive number) + (Negative number) = Positive number [(+) + (-) = (+)]
  2. (Negative number) + (Positive number) = Negative number [(-) + (+) = (-)]
  • For subtraction

Subtraction is the operation of removing the value from the collection. It is denoted by using the minus sign ‘-‘. In the operations of subtraction, the signs of numbers are changed which is needed to be subtracted. And, then follow the same sign rules of addition. For example, (10) – (+8) = (10) + (-8) = 2. Here, +8 is changed into -8, and then, sign rules of addition are followed.

  1. (Positive number) + (Positive number) = Positive number [(+) + (+) = (+)]
  2. (Negative number) + (Negative number) = Negative number [(-) + (-) = (-)]

The result of operation during adding two numbers with different signs is based on the greater term involved in the operation.

  1. If the sign of the larger value has a positive (+) sign then, the result will also have a positive sign.
  2. If the sign of the larger value has a negative (-) sign then, the result will have a negative sign.
  1. (Positive number) + (Negative number) = Positive number [(+) + (-) = (+)]
  2. (Negative number) + (Positive number) = Negative number [(-) + (+) = (-)]
  • For multiplication

Multiplication is an operation in which the number can be added to it by a certain time. It is denoted by the multiplication sign ‘x’.

While dealing with numbers having the same signs the result is always positive.

  1. (Positive number) × (Positive number) = Positive number [(+) × (+) = (+)]
  2. (Negative number) × (Negative number) = Positive number [(-) × (-) = (+)]

While dealing with numbers having the same signs the result is always negative.

  1. (Positive number) × (Negative number) = Negative number [(+) × (-) = (-)]
  2. (Negative number) × (Positive number) = Negative number [(-) × (+) = (-)]
  • For division

The division is an operation in which a large collection of numbers is splitter into smaller values. It is denoted by the division sign’÷’. Division also follows the same sign rules as multiplication. If the signs are the same divide and put a positive sign. And, if the signs are different divide and put a negative sign.

While dealing with numbers having the same signs the result is always positive.

  1. (Positive number) ÷ (Positive number) = Positive number [(+) ÷  (+) = (+)]
  2. (Negative number) ÷  (Negative number) = Positive number [(-) ÷  (-) = (+)]

While dealing with numbers having the same signs the result is always negative.

  1. (Positive number) ÷ (Negative number) = Negative number [(+) ÷ (-) = (-)]
  2. (Negative number) ÷ (Positive number) = Negative number [(-) ÷ (+) = (-)]

What is the product of 2 positive integers?

Answer:

While dealing with two positive signs of the numbers the result would be positive according to the sign rule. While multiplying or dividing two positive numbers, firstly we have to simplify the numbers and then look into the signs carried by them. Once, the numerical value of the two numbers having the same positive signs is determined, the sign rule can be applied. That is, 

Positive (+) × Positive (+) = Positive (+)  

Sample Questions

Question 1: What do 2 negatives make?

Answer:

While dealing with two negative signs of the numbers the result would be positive according to the sign rule.

(negative number) × (negative number) = positive number

Question 2: What do positive and negative numbers make?

Answer:

While dealing with a negative sign and a positive sign of the numbers the result would be negative according to the sign rule.

(positive number) × (negative number) = negative number

Question 3: What is 5 × 15?

Answer:

5 × 15 equals 75. As both numbers are positive numbers the result is also positive as per the sign rule.

Question 4: What is 12÷ 2?

Answer:

12 ÷ 2 equals 6. As both the numbers in the division are positive the result is also positive as per the sign rule.

Question 5: What is -10 ÷ 5?

Answer:

-10 ÷ 5 equals -2. As the numbers in the division are one positive and one negative the result will be negative as per the sign rule.

Question 6: What is 2 x 4?

Answer:

2 ×  4 equals 8. As both, the numbers in the multiplication are positive the result is also positive as per the sign rule.

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