Order of Operations and Properties of Whole Numbers

Is 2 + 3 x 4 equal to 20 or is it equal to 14? Why are there different answers? To prevent different answers to a calculation, we need to follow a specific order. Thus, we need to apply the order of operations.

If you watch this lesson, you will learn what should be done first. In short, we can follow BODMAS. First, we need to do brackets – thus, calculating the value inside of the brackets. Then we should do orders (and “of”). Orders refer to exponents and roots, while the word “of” means multiplication. Division and multiplication should be done next. As the D is before the M in BODMAS, does this mean that division is more important than multiplication? No! Division and multiplication are equally important and should be done from left to right in the calculations.

The same rule applies for addition (the A in BODMAS) and subtraction (the S in BODMAS). Addition and subtraction are equally important and should be done from left to right. When doing calculations you can also make use of the properties of whole numbers. The associative property for addition also holds for integers as in the following example: 15 + 24 – 4 = 15 + 24 + (-4) = 35.

The commutative property for multiplication and addition holds for integers as well, implying that 3 x (-2) = (-2) x 3 = -6 and 3 + (-2) = (-2) + 3 = 1. The third property is the distributive property. Examples of the distributive property of multiplication over addition and subtraction are: 2(3 + 4) = (2 x 3) + (2 x 4) and 5(8 – 3) = (5 x 8) – (5 x 3).

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