Meaning of Integer

Introduction to Meaning of integer:

              The integers are the combination of negative number and non negative numbers. The integers are formed with the help of the natural numbers. The integer set is formed countable infinite set. The integer numbers are denoted with the help of alphabetic letter Z. the natural numbers including the 0. Denoted by 0,1,2,3,….

              Here we are going to understand the meaning of integer by solving some example problems.

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Basic properties of an integers:


Now we see about the some basic properties of an integers.

1) Commutative property of addition of integer:

The commutative property is one of the property of integer addition .it tells that we can add numbers in any order.

For example: -7 + 8 = 8+ (-7)

2) Commutative property of multiplication of integer:

       The commutative property of multiplication is also one of the properties of an onteger that tells  we can multiply numbers in any order doesn’t change result.

For example: -8 x 5 = 5 x (-8).

3) Associative property of addition of integer:

       The associative property of Addition is one of the properties of an integer that tells  we can group together then we get the same result.

For example : (-4 + 3) + 2 = -4 + (3 + 2)

4) Associative property of multiplication of integer:

       The associative property of multiplication is fourth property of an integers that tells we can group together in a product then we get the same answer.

For example : -4(2) x 1 = -4( 2 x 1)

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Integer word problems:


Problem 1:

A team won 4 times as many matches as it lost. If it won 16 matches, how many games did it lose?

Solution:

Step 1: First we assign variable, A team won 4 time s as many matches as it lost.

            Let P be number of matches lost and

            4P is number of matches won.

            It won 16 matches

            So 4P = 16

Step 2: Solve the equation,

            Divide by 4 on both sides.

            We get `(4P)/4` = `16/4`

                              P = `16/4`

                              P = 4.

Answer: The team lost 4 games.

Problem 2:

          John and his friends were selling cookies. They sold 5 more boxes the third week than they did the second. On the fourth week, they doubled the sale of their third week.Altogether, they sold a total of 459 boxes. How many boxes did they sell in the fourth week?

Solution:

Step 1:

        They sold 5 more boxes the third week than they did the second. On the fourth week, they doubled the sale of their third week.

       Assign variables Let,   P be boxes sold in the second week 

                                       P + 5 boxes were sold in the third week 

                                       2(P + 5)  =   boxes sold in the third week

       John sold a total of 444 boxes.

       So, P + P + 5 + 2(P + 5) = 459

       Then remove brackets and combine like terms,

                   P + P + 5 + 2P + 10 = 459

                  4P + 15 = 459

       Subtract -15 on both sides

                4P + 15 – 15 = 459 -15

                    4P = 444

       Divide by 4 on both sides

                     `(4P) / 4` = `444 / 4`

                        P = 111

Step 2:  Plug P = 111 into 2(P+4)

             We get, 2(111 + 4)

                         = 222 + 8

                         = 230

Answer: In the fourth week, they sold 230 boxes.