problem solving in integers

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Education and Communications
Mathematics

How to Solve Integers and Their Properties

Last Updated: June 30, 2018

This article was reviewed by Joseph Meyer . Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. This article has been viewed 29,506 times.

An integer is a set of natural numbers, their negatives, and zero. However, some integers are natural numbers, including 1, 2, 3, and so on. Their negative values are, -1, -2, -3, and so on. So integers are the set of numbers including (…-3, -2, -1, 0, 1, 2, 3,…). An integer is never a fraction, decimal, or percentage, it can only be a whole number. To solve integers and use their properties, learn to use addition and subtraction properties and use multiplication properties.

Using Addition and Subtraction Properties

Step 1 Use the commutative property when both numbers are positive.

a + b = c (where both a and b are positive numbers the sum c is also positive)
For example: 2 + 2 = 4

Step 2 Use the commutative property if a and b are both negative.

-a + -b = -c (where both a and b are negative, you get the absolute value of the numbers then you proceed to add, and use the negative sign for the sum)
For example: -2+ (-2)=-4

Step 3 Use the commutative property when one number is positive and the other is negative.

a + (-b) = c (when your terms are of different signs, determine the larger number's value, then get the absolute value of both terms and subtract the lesser value from the larger value. Use the sign of the larger number for the answer.)
For example: 5 + (-1) = 4

Step 4 Use the commutative property when a is negative and b is positive.

-a +b = c (get the absolute value of the numbers and again, proceed to subtract the lesser value from the larger value and assume the sign of the larger value)
For example: -5 + 2 = -3

Step 5 Understand the additive identity when adding a number to zero.

An example of the additive identity is: a + 0 = a
Mathematically, the additive identity looks like: 2 + 0 = 2 or 6 + 0 = 6

Step 6 Know that adding the additive inverse is equal to zero.

The additive inverse is when a number is added to the negative equivalent of itself.
For example: a + (-b) = 0, where b is equal to a
Mathematically, the additive inverse looks like: 5 + -5 = 0

For example: (5+3) +1 = 9 has the same sum as 5+ (3+1) = 9

Using Multiplication Properties

When a and b are positive numbers and not equal to zero: +a * + b = +c
When a and b are both negative numbers and not equal to zero: -a*-b = +c

However, understand that any number multiplied by zero, equals zero.

Step 2 Understand that the multiplicative identity of an integer states that any integer multiplied by 1 is itself.

For example: a(b+c) = ab + ac
Mathematically, this looks like: 5(2+3) = 5(2) + 5(3)
Note that there is no inverse property for multiplication because the inverse of a whole number is a fraction, and fractions are not an element of integer.

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COMMENTS

3.E: Integers (Exercises)
This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers. If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand.