Fractions / Dividing a Fraction by a Whole Number

Understanding

To divide (a/b) by a whole number c, students can consider dividing the unit fraction (1/b) into c parts, then multiplying that number by a.

What to look for

Asking students how the representation of the unit square is connected to the process of dividing by a whole number can lead to a productive discussion about their interpretation both of the unit square and of the mathematical question.

Sample Assessment

(3/4) of a package of pens is to be shared among six people.

a. How much of the whole package does each person get?
Answer: Each person will get (3/24) or (1/8) of the package.

b. If each package has 16 pens, how many pens will each person get?
Answer: 2 pens

The Big Idea

Students can use the relationship between division and multiplication to solve problems involving dividing fractions by whole numbers.

What are the students doing?

Students will use unit squares to investigate dividing a fraction by a whole number.

What is the teacher doing?

Have students begin with a unit fraction and observe the result of dividing by whole numbers beginning with 1. The mathematical relationship should become clear and they can generalize what they observe.