Join Karin Hutchinson for an in-depth discussion in this video Introduction to integers, part of Foundations of Algebra: Pre-Algebra.
- As you leave the world of basic math and enter the world of algebra, you'll be introduced to a whole new set of numbers. This set of numbers is called integers. So what is an integer? Well, we're gonna take a look at a number line. You're very familiar with the numbers that are to the right of zero, these are the positive numbers. All positive whole numbers are integers. To the left of zero we have negative numbers. The negative whole numbers are also integers.
And zero, zero is also considered an integer. So now that you know what an integer is we're going to categorize a few numbers and see if we can determine if they are integers or if they are not integers. Remember that an integer is a whole number that can be positive, negative, or zero. In order to help us to better understand integers we're going to categorize a few numbers together. Let's start with the number -2. - 2 is an integer because it's a whole number and it's negative.
Let's take a look at another example. - 1.25. This number is not an integer. Notice that it is a decimal. Decimals are not whole numbers and therefore they cannot be considered integers. So we're gonna write this on the not integer side. 12/4ths. Many students get very confused by this problem. They want to put it on the not integer side because they see that it's a fraction. And we've talked about fractions not being an integer.
But we need to see what happens when we simplify this number. 12 divided by 4 is equal to three. Three is a whole number. Since 12/4ths is equivalent to three it's actually an integer. So one thing that we need to remember when we are classifying numbers as integers, is we need to make sure that the number is in simplest form. Let's take a look at 0. We know that zero is also an integer, it's not negative or positive, but it is an integer.
What about 1/2? Hopefully you're remembering that we need to simplify this if possible before we determine whether or not it is an integer or not an integer. 1/2 actually cannot be simplified any further. So therefore it is not an integer. This is a different number, this is the square root of four. Again, with this type of number we need to make sure that it is in simplest form before we categorize it.
So the square root of four is actually equal to two. Because two squared, or two times two, is equal to four. Because the square root of four is equal to two and two is a whole number it is an integer. So I'm going to write the square root of four on the integer side. The square root of five is also a radical, however five is not a perfect square. So when we evaluate the square root of five we get about 2.24.
This number is a decimal and therefore it is not an integer. So the square root of five will go on the not integer side. Hopefully by categorizing these numbers together you have a better idea of what numbers are considered integers and what numbers are not considered integers. Let's just review a few of the important facts that we need to remember about integers. Remember that integers are negative or positive whole numbers. They are not fractions or decimals.
They must be whole numbers. Zero is also an integer. But it is not considered negative or positive. And lastly, remember to evaluate or simplify a number before determining whether or not it is or is not an integer.
This course includes practice challenges and worksheets, as well as tips for educators who are helping students master pre-algebra for Common Core. Karin Hutchinson also helps you evaluate, write, and simplify expressions, and solve word problems and complex algebraic expressions.
- Adding integers
- Multiplying and dividing
- Understanding the order of operations
- Evaluating expressions
- Breaking down word problems and algebraic expressions
- Distributing positive and negative numbers
- Simplifying expressions