Word problems for the division problem, A ÷ B, can either use the “how-many-groups” interpretation of division or the “how-many-units-in-one-group” interpretation.

How many groups?

A ÷ B represents, “How many groups are there if A units are divided into groups of B units?” For example,

• Arithmetic problem: Solve 12 ÷ 4.
• Word problem: A pizza cut into 12 slices is to be divided among friends such that each friend gets 4 slices. How many friends can share the pizza?
• 12 ÷ 4 = 3, so 3 friends can share the pizza.
• Here, each friend is a “group,” the pizza slices are the units, and we’re finding the number of friends: 12 slices ÷ 4 slices per fried = 3 friends.
• Equivalently, 3 friends times 4 slices per friend equals 12 slices in total.

How many units in one group?

A ÷ B represents, “How many units are in one group if A units are divided into B groups?” For example,

• Arithmetic problem: Solve 12 ÷ 4.
• Word problem: A pizza cut into 12 slices is to be divided among 4 friends. How many slices do they each get?
• 12 ÷ 4 = 3, so each friend gets 3 slices.
• Again, each friend is a “group” and the pizza slices are the units, but now we’re finding the number of slices per friend: 12 slices ÷ 4 friends = 3 slices per friend.
• Equivalently, 3 slices per friend times 4 friends equals 12 slices in total.

The video below works through some examples of word problems for dividing integers.