- a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Now that we know how how to compare fractions, we can work on adding fractions. For the purpose of this post, I will assume that the students I am working with with understand the concept of adding and subtracting whole numbers, equivalent fractions, and how to find the least common multiple of two numbers.
For a practical example of how adding fractions may play a part in your life, let's work with pizza. Let's say that as a class, we decide to have a pizza party. After the party, there are partial boxes of pizza left. I say that Ralph can take the left overs home as long as the remaining pizza is less that one whole pizza. Since there are multiple boxes filled with different number of slices of pizza, we must add fractions in order to determine whether the remaining pieces are less than one whole pizza.
Example 1: Adding fractions with the same denominator
We'll say that there are two pizza boxes remaining after the class party. It is important to note that each pizza was cut into 8 equal slices originally. One box of pizza has 3 pieces left in the box. The other pizza box has 1 piece left in it. The first pizza box can be described to have 3 of the 8 pieces left, or 3/8 of the whole pizza. The second pizza box can be described to have 1 of the 8 pieces left, or 1/8 of the whole pizza. In order to find out if the remaining pieces make up less than one whole pizza, we add our two fractions. Since our denominators are the same in this case, we can add our numerators and put the sum over our denominator of 8.
So:
As you can see, 3/8 + 1/8 = 4/8 or 1/2 of a pizza. Since 1/2 of a pizza is less than 1 whole pizza, Ralph will be able to take the leftover pizza home in this situation.
Using our example as a reference, do the following problems and record your work in your math journals:
Example 2: Adding Fractions with unlike denominators
For this example, we'll say that there are two pizza boxes containing a portion of a whole pizza in each box. However, this time, one pizza was cut into 8 slices and the other was cut into 6 slices. Out of the pizza cut into 8 slices, 3 slices are left. Since 3 slices, of 8 slices remain, we can determine that 3/8 of the pizza is left. Of the pizza cut into 6 slices, 4 slices are left. Therefore, we can determine that 4/6 of the second pizza is left. In order to determine if the two fractions is less than 1, we must find the sum of the fractions.
Unlike the first example, these fractions do NOT share a common denominator. Before we add the two fraction, we need to find the least common multiple of our denominators (8 and 6). Using our previous knowledge of least common multiples, we already know that the LCM of 8 and 6 is 24. This means that our two fractions need to be translated as units composed of 1/24 parts.
In the case of our fraction 3/8, in order to get an equivalent fraction consisting of 1/24 parts, we must multiply the numerator and denominator by 3.
As you can see, our 3/8 fraction can now be represented as 9/24.
In the case of our 4/6 fraction, in order to get an equivalent fraction consisting of 1/24 parts, we must multiply the numerator and denominator by 4.
As you can see, our 4/6 fraction can now be represented as 16/24.
Now that our two fractions have a common denominator, we can add the numerators and put the sum over our denominator of 24.
So:
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As you can see, 9/24 + 16/24 is equivalent to 25/24. Since 25/24 is greater than 1, Ralph would not be able to take home the leftover pizza in this situation.
Do the following problems and record your work in your math journals:
After you've read the blog, watched the videos, and worked the practice problems, feel free to play FRUIT SHOOT FRACTION ADDITION for extra practice.
