Adding and Subtracting Mixed Numbers

In my opinion the easiest way to add and subtract mixed numbers is to change them into improper fractions. This will put an end to having to regroup (or borrow from the whole number). Here are the steps laid out in an easy to understand way:

Step 1: Change both Mixed Numbers into Improper Fractions

            How?: Multiply the Whole number by the Denominator (the bottom number of the fraction) and
                       add the fraction's numerator (the top number in the fraction).

Step 2: Find the Least Common Denominator

           How?: Find the Lowest Common Multiple between the denominators. The Lowest Common
                      Multiple can be found several ways: List all of the multiples until you get to the first number
                      that they both go into; Use Prime Factorization; etc.

Step 3: Solve by Adding or Subtracting the Numerators
            (Write your answer over the Least Common Denominator)

Step 4: Change your Improper Fraction back into a Mixed Number

           How?: Divide the Numerator by the Denominator. The quotient (the answer) will be the new whole
                      number. The remainder (what's left over) will be the new numerator (the top number). Write
                      the remainder over the denominator.

Adding and Subtracting Fractions with Unlike Denominators

Unlike fractions have different denominators. To add or subtract
unlike fractions, first rewrite them as equivalent fractions with a
common denominator. You can use any common denominator or
the least common denominator to add and subtract unlike
fractions. The least common denominator (LCD) is the least
common multiple of the denominators.

Here is an example:

To get more practice with Adding and Subtracting Fractions with Unlike Denominators Click the Links Below:

Page 1: Word Problems
Page 2: Practice Page 1
Page 3: Practice Page 2

A Little Simi-Rap about Fractions

This is a song about fractions that I found at http://www.educationalrap.com

Chorus
How do I work with fractions?
Oh, multiply and divide, you know?
Add, subtract can seem so hard at first
But on this track you’ll learn by the third verse

Verse I
Somebody told me that they was having a problem with
Fractions and how to solve them in math style equations
Like how to add them, subtract them, and multiply them
And then divide them and have the right answer before the day’s end
Though complicated it seems, it’s not as hard if you know
The formulaic approach to find the answer
So if we start at the top and make our way to the bottom
We’ll understand through our mathematical banter

Let’s first examine a fraction, exactly what it’s
Composed of and get a little bit closer to understanding
You’ve got a number on top that’s followed next by a line
Balanced on top of a number on which it’s standing
The number on top is known as the numerator
Denominator’s the number that’s chilling down at the bottom
And all we do is just use this very knowledge as tools
To figure out computations and then we’ve got ‘em

Chorus

Verse II
So let’s say that we take 1∕5 + 1∕5
How do we go about coming up with an answer?
Whether addition with fractions or you’re using subtraction
There are a couple of steps you must adhere to
Since there’s a common denominator we take the 5
And drag it over and add the top numbers
1 and 1 is just 2; 2 over the 5
Makes 2∕5 the solution with no blunders.

Subtraction is just the same except you go in reverse
So 2 minus the 1 would give you 1∕5
And 1∕5 plus 1∕2 requires a li’l different math
We need the bottom numbers the same to start with
To get the lowest common denominator
Which is the smallest number that 5 and 2 go in
Divide the product of 5 and 2 by their greatest common factor (which is 1!)
And you get 10


Chorus

Verse III
Now, in 1∕5 you times the 5 by the 2
And then the 1 by the 2
And wind up with 2∕10
And in 1∕2, you times the 5 in the math
And wind up with 5∕10 + 2∕10 and solve that
And it’s the same if you want to subtract
So we’ll move on to multiplication and figure out that
And these ones have the easiest steps
You just times the tops by the tops
And then the bottom by the lower deck, and simplify

So now we move onward to divide
‘Cause we have cruised smoothly through this ride
So when dividing fractions, you just flip the last one
And after that, then you multiply
Example! 2∕3 ÷ 3∕4 = 2∕3 × 4∕3 = 8∕9
And that’s how you divide
It’s a fraction computation party!

Adding and Subtracting Fractions with Unlike Denominators

This week we will be discussing how to add and subtract fractions with different denominators (bottom numbers).

Let's start with adding fractions with unlike denominators.

In order to solve this type of problem, we need to find the least common multiple of the denominators. Once we figured out the least common multiple, we need to multiply the denominator (the bottom number) and numerator (the top number) by the same value that was used to get the least common multiple.

Example:

The least common multiple between my denominators 6 and 4 is 24.

I can find that by making a list of each numbers multiples or by finding the prime factors of 6 and 4.

Now I ask myself, "Self, what is the number that I multiplied 6 by in order to get 24?" Yep! "I multiplied 4 times 6 to get 24." So that means I must also multiply 4 by 5, my numerator (my top number) in order to get an equal fraction. So 4 times 5 is 20, and 4 times 6 is 24. My new fraction is 20/24.

Now I follow the same steps with the other fraction.

4 times 6 is 24. So 3 times 6 is 18. My new fraction is 18/24

Now I just add the numerators and put my answer over my denominator 24.

20 + 18= 38

Now, I place 38 over my denominator 24. 

My answer is   38  .

                        24

I can simplify 38 twenty-fourths, by dividing 38 by 24 to get a mixed number. 24 goes into 38 one time, so 1 is my whole number in front of my new fraction. I take the remainder 14 and place it over the denominator 24.

My simplified answer looks like this.

If you are a visual learner, and you need to see how the fractions are equal with a common denominator, then you can use the fraction strip picture below. Feel free to print and cut the picture below. You may need to print a few copies to get to the right numerator.

Fraction Strips

Least Common Multiple

There are three different methods that we can use to find the Least Common Multiple of a set of numbers.

Method 1: Use a Number Line

Method 2: Use a List of Multiples

Method 3: Use Prime Factorization

Here are some examples of how each method can be used to find the Least Common Multiple of a set of numbers.

Method 1: The Number Line Method

To use a number line in finding the least common multiple of a group of numbers, you must basically count by that number as you make your way down the number line. This method may be helpful for those students who have trouble with their multiplication facts.

The downside to this method is that it can take a long time to draw the number line and find the least common multiple. It also takes up a great deal of space in your notebook. If you are trying to find the LCM of more than two numbers or if the set of numbers that you are given contains numbers larger than ten, then I would recommend a different method to find the LCM.

As you can see from the sample above, the student still had to find the multiples of each number using the list method. This also gives you an idea of how much space this method could really take.

images from the Oakland Terrace Elementary School website

Method 2: Listing Multiples

To find the LCM of  2, 3, and 6

Create a list of multiples for each number in the group by multiplying by whole numbers greater than zero.

2: 2, 4, 6
3: 3, 6
6: 6,

LCM of 2, 3, and 6 = 6

Method 3: Prime Factorization

Here are some links that will give you more examples of finding the Least Common Multiple
Least Common Multiple Power Point: Click Here to View
More Examples from Mc Graw Hill: Click Here to View