Integers Algebra

The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French) are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}.

Source – Wikipedia.


Addition of Integers:

The followings are some of the examples for addition of integers in algebra.

Find two consecutive integers whose sum is equal 225.

Solution:

We can take in this as x and x + 1 are the two numbers. Then we can use the fact in their sum is equal to 225 to write the equation as
x + (x + 1) = 225

2x + 1 = 225

We can solve for x to obtain
x = 112

Therefore, two numbers are
x = 112 and x + 1 = 113 is the solution of the given sum of two consecutive integers.

Find two consecutive integers whose sum is equal 147.

Solution:

We can take in this as x and x + 1 are the two numbers. Then we can use the fact in their sum is equal to 147 to write the equation as
x + (x + 1) = 147

2x + 1 = 147

We can solve for x to obtain
x = 73

Therefore, two numbers are
x = 73 and x + 1 = 74 is the solution of the given sum of two consecutive integers.

Multiplication of Integers:

The followings are some of the examples for multiplication of integers in algebra.

Find the multiplication of integers 6 * 4.

Solution:

6 * 4 = six four

= 6 + 6 + 6 + 6

= 24

Likewise, we have 6 * (-4) = four minus six

= (-6) + (-6) + (-6) + (-6)

= -24 `rArr` (1)

By commutative property, you know that

6 * 4 = 6 * 4 and 6 * 4 = four six = 6 + 6 + 6 + 6

You can also write, 4 * 6 = 6 + 6 + 6 + 6

Likewise, (- 4) * 6 = (- 6) + (- 6) + (- 6) + (- 6)

= - 24 `rArr` (2)

Hence, from (1) and (2), 4 * (- 6) = (-4)* 6 + (-24) = (4 * 6) is the solution for the given multiplication of the integers.

Find the Multiplication of the given integers: 8 x 5.

Solution:

Given integers are (8) × (5)

= |8| × |5|

= 8 × 5

= 40 is the solution for the given integers.


Find the Multiplication of the integers: 7 x (-5).

Solution:

Given integers are 7 x (-5)

= | 7 | × | -5 |

= 7 × -5

= -35 is the solution for the given integers.