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