We learned to divide with whole numbers and unit fractions. First, we used diagrams to solve problems involving division of a unit fraction by whole numbers.

Example:

Diagram A shows equals . We find the size of one part if is split into 4 equal parts.

Next, we used diagrams to solve problems involving division of whole numbers by unit fractions. We also wrote equations to represent these problems.

Example:

Diagram B shows that if a strip of paper 2 feet long is cut into foot pieces, there will be 12 pieces. Therefore, because we are finding how many -size pieces are the same length as 2.

Finally, we noticed patterns when dividing whole numbers and unit fractions.

• We noticed whole numbers divided by unit fractions were greater than 1.

  Example:

  The value of is greater than 1. The number of -size pieces with length 12 (or any whole number) is greater than 1.

• We also noticed unit fractions divided by whole numbers were less than 1.

  Example:

  The value of is less than 1. When a whole number less than 1 is divided into many pieces, each piece is less than 1.