## Work With Fractions

**Comparing and Ordering Fractions**

At this grade level, comparing and ordering fractions is limited to unit fractions or to fractions with a common denominator. Many students may need to use pictures to compare and order fractions. For unit fractions, > if and only if a < b. For example, > because 3 < 4. To compare fractions with a common denominator, > if and only if a > b. For example, which is greater, or ? Since 4 unit fractions of are greater than 3 unit fractions of , is greater than .

**Equivalent Fractions**

Two fractions and **are equivalent** if there exists a number m such that [ m × × b ] = . For example, the fact that [2 × × 4] = implies that is equivalent to .

Equivalent fractions can be modeled by using a picture in which there are two ways of representing the same “part of the whole.” The fact that is equivalent to can be shown as follows.

The word **of** is often used to pose problems involving the multiplication of a whole number by a fraction. At this level, students have not yet learned to multiply fractions. However the phrase “ of 6” can be modeled in terms of a group of 6 objects that is separated into 3 smaller groups, each of which has 2 objects.

**Addition and Subtraction of Fractions**

To add or subtract fractions with like denominators, find the sum or difference of the numerators and keep the common denominator. Answers should be expressed in simplest form.

For example, in + three unit fractions of are added to two unit fractions of . The sum equals five unit fractions of . So the answer is , or 1. In − , one unit fraction of is subtracted from three unit fractions of . The result is two unit fractions of . So the answer is , or .

**Teaching Model 19.1:** Compare Fractions