Mixed Number Coefficients: Definition & Examples

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will discuss the basic definition of a coefficent and what a mixed number is. Then, we will discuss what it means to have a mixed number as a coefficent and see examples showing you how to work with them.


So you are trying to add up some different terms and things are going along nicely until that pesky coefficient comes along... 2x + 3x....What to do? Take a breath; coefficients aren't that scary! To add those terms together, simply add 2 and 3 to give an answer of 5x. It's like having two apples and adding three apples; you now have five apples.

Coefficients are the numbers that come before a variable like x or y. They are numbers being multiplied by some unknown value. In our example with 2x + 3x, 2 and 3 are both coefficients because they are being multiplied by x.

Like Terms

Let's talk about terms for a second because they are going to come up quite a bit! Terms are either numbers or numbers multiplied by variables that are separated in a mathematical expression or equation by a plus or minus sign. Let's go back to our example for a second, 2x + 3x. 2x would be one term and 3x would be another term.

Something to keep in mind with coefficients is an important concept called like terms. This refers to the fact that terms can only be combined (added or subtracted) when the variables match. This is why 2x + 3x can be combined to give 5x-- they both have x as the variable. We can add 2 apples and 3 apples to give five apples, but we cannot add 2 apples and 3 oranges to give 5 aplanges!

Looking at another example of 2x - 6y, these terms cannot be combined because the variables are not the same! It's like having 2 apples and trying to take away six oranges! It won't work!

Mixed Numbers

Now that we dealt with those pesky coefficients, what about mixed numbers?! I promise, these aren't so bad either! Mixed numbers are whole numbers and fractions put together. They are a way to represent improper fractions that are greater than one.

For example, 5/4 is an improper fraction because five divided by four equals 1.25, which is greater than one. We can represent 5/4 as a mixed number by pulling a whole number out of the fraction. Here, 4/4 is equal to 1, so we can use 1 as the whole number. Then, we have 1/4 left over, leaving us with a mixed number of 1 and 1/4.


Let's look at one more example. This time, we will start with the improper fraction of 29/13. To change it to the mixed number, let's think about how many times 13 goes into 29. Well, 13 multiplied by 2 equals 26. That means we can pull out 26/13 from our improper fraction as the whole number 2. When we do this, we are left with 3/13. Thus, our mixed number is 2 and 3/13.


Putting it all together

Now let's look at some cases where mixed numbers are coefficients! In the example in the image, you can see that the coefficient is not just a simple 2 like in the term 2x. In this term, the coefficient is the mixed number of 4 and 2/5. This would be 22/5 as an improper fraction. This may seem confusing at first, but nothing really changes when our coefficient becomes a mixed number. It is still just a number being multiplied by a variable.


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