Writing a Numerical Expression That Corresponds to a Sequence of Operations

At the market, you buy three cans of beans for $0.85 each and two bags of apples for $1.95 each.
If you pay with a $10 bill, how much change will you get?

Here is a detailed solution given by a student:

Is it possible to write a numerical expression that summarizes all the calculations carried out above? In other words, is it possible to write a numerical expression that contains all the data from the statement and that gives the result 3.55?

I. First example: total to pay and change

Use the example above. The total to pay is calculated by working out 2.55 + 3.9 or 0.85 × 3 + 1.95 × 2 (respecting the rules of the order of operations).

The change is the difference between 10 dollars and the total price to pay; this corresponds to the expression:
10 – (0.85 × 3 + 1.95 × 2). This expression summarizes the calculations carried out step by step in the introduction.

II. Second example: calculating an area

Figure 1 shows the plan of a house. We want to write an expression that will allow us to calculate the area of the backyard.

The backyard is rectangular. Its dimensions (in meters) are:
— length: 14 m – 5 m;
— width: 10 m – 6 m.

The area of the backyard (in square meters) is therefore equal to: (14 m – 5 m) × (10 m – 6 m).
This expression summarizes the stages of the calculation and allows us to calculate the area of the backyard (equal to 36 m²).


Read more:

Applying the Distributive Law
Calculating a Numerical Expression (1)
Calculating a Numerical Expression (2)
Determining the Common Factors of Two Integers
Recognizing a Proportional Relationship
Rounding to the Nearest Unit