Reason for Order of Operations – Part 2

Elementary Math (K-6th) Tutorial

Reason for Order of Operations - Part 2


In this tutorial, we will look at a simple mixed addition and multiplication to illustrate the reason for order of operations from unit perspective.

Sample Problem

On Sat morning, I jogged from my home to the field. After I got to the field, I jogged along the field 2 times and then jogged back to my home. If the field is 600 m from my home and the perimeter of the field is 1 km, find the total distance I jogged on Sat morning?


First, consider this problem as a multi-steps word problem. We can solve this problem step-by-step.

Jogging from home to the field = 600 m
Jogging along the field = 2 x 1 km = 2 km = 2 x 1000 m = 2000 m
Jogging from the field back to home = 600 m

Total distance = 600 m + 2000 m + 600 m = 3200 m

As we can see, a lot of word problems are naturally solved by following the order of operations. Even if we do not know the rule, we can still solve this problem by analyzing it step-by-step.

If we want to write the calculation in ONE mathematical sentence, we will need to follow the order of operations. The mathematical sentence is

600 + 2 x 1 x 1000 + 600

We need to perform the calculation 2 x 1 x 1000 first before addition. If we take a closer look of the unit, the perimeter of the field is in km but the distance between the home and the field is in m. In order to perform addition (and subtraction), we need to make sure that the units for different numbers are the same. In this example, performing multiplication first is to convert the total distance that I jogged along the field from km to m. Therefore, we have

600 m + 2000 m + 600 m

Now, all numbers are in the same unit. We can perform addition to get the final answer of 3200 m.

In real-life word problems, multiplication and division can change the unit of a number. Performing multiplication and division first ensures that units for different numbers are the same before we can add (or subtract) these numbers.

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