Order of Operations: Multiplying and Dividing

You should already have studied the page on the order of operations when just adding or subtracting is involved. When multiplication or division are present as operations in your expression or equation, they are done first! Only when all the multiplication and division operations are carried out may you continue with the addition and subtraction.

What do you do if there is more than one operation involving multiplying or dividing? Again, many people think you do all the multiplication first. This is wrong! The multiplying and dividing must be done in order from left to right! Just like you read a book....

Let's look at this example: 10 x 3 - 16 / 4 + 6

No wrong answers this time. What I usually do is isolate all the multiplies and divides. In this example, we have two: 10 x 3 and 16 / 4 .
Here's the original equation after I highlight what I'm going to do first: 10 x 3 - 16 / 4 + 6

We do these from left to right ... 10 x 3 is 30 , and 16 / 4 is 4 .
We substitute these back in the original expression to get: 30 - 4 + 6 . Now we only have adding and subtracting left, and we know what to do (left to right, remember?). 30 - 4 is 26 and 26 + 6 is 32 . And remember - this is something you just have to remember.

Like with addition and subtraction, the only time this matters is when a division operation is present (or the multiplies are separated by addition and subtraction). If all the operations are multiplication, you can do them in any order (there is also a commutative property for multiplying!)

Til next time ....