What are fair shares?

Remember that a fraction is the relationship between a part and whole Remember that a fraction is the relationship between a part and whole. Let's look at the fraction four sixths.

In a fraction, the part is called the numerator…

…and the whole is called the denominator …and the whole is called the denominator. In the fraction four sixths, there are four parts out of the whole of six total parts.

Each of these shapes… 5

…represents four sixths. 6

Let’s see how this works using this shape. 7

We see that there are six equal parts, or fair shares… 8

…and there are four parts shaded …and there are four parts shaded. This shape represents a part-to-whole relationship. 9

Let's look at examples of shapes that have been divided into fair shares. Notice how each shape has been divided into equal parts.

These shapes are not divided into fair shares These shapes are not divided into fair shares. Some of the parts are bigger than others. This is how we know that they are not divided into fair shares.

How do we add and subtract fractions with the same denominators?

When fractions have the same fair shares, we can add them easily When fractions have the same fair shares, we can add them easily. Let’s add two fourths…

…and one fourth. Can you find the answer?

The sum is three fourths The sum is three fourths. There are four total parts, and three are shaded.

We can also subtract fractions that have the same fair shares We can also subtract fractions that have the same fair shares. Let’s look at the problem three fourths…

…minus one fourth. Notice that we take away one part, or one fourth …minus one fourth. Notice that we take away one part, or one fourth. What is the answer to this problem?

The difference is two fourths.

Sometimes when we add fractions, the sum is greater than one Sometimes when we add fractions, the sum is greater than one. For example, five sixths…

…plus two sixths…

…equals seven sixths There is one array that is completely shaded, and a second array with one part shaded.

We can also subtract from a fraction greater than one We can also subtract from a fraction greater than one. The model shows seven fourths…

…minus two fourths…

…equals five fourths.