Tape diagrams are useful for representing how quantities are related and can help us answer questions about a situation. 

Example: A school receives 46 copies of a popular book. The library takes 26 copies and the remainder are split evenly among 4 teachers. How many books does each teacher receive?

This situation involves a total formed by 4 equal parts and one other part. We can represent the situation with a diagram labeled 46 for the total number of books. That total length is divided into parts—one long part labeled 26 for the books given to the library and 4 equal-sized parts for the books split among 4 teachers. We label each of those parts with a variable, , because we don’t know how many books each teacher got. Using the same variable, , in each part means that the same number is represented four times.

Some situations have parts that are all equal, but each part has been increased from an original amount:

Example: A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams. How much did each sensor weigh originally?

We can represent this situation with a rectangle representing a total of 76 split into 4 equal parts. Each part shows that the new weight, , is 9 more than the original weight, .