66/(-33)*|-9|

[sphilip]

66/(-33)*|-9| from the problem set in chapter 3 of the Number Properties book question# 2 The result is -18 according to the book. Now I understand how they got it, but doesnt that violate PEMDAS? Doesn't division come after multiplication? And that is how I came up with a totally different #.

[Guest]

How would use do this? It only makes sense the way it was done, IMO.

Even if you follow PEMDAS, you'd be multiply 9 x 66/(-33) which would still be -2

9 times 66 divided -33 is still -18

[sphilip730]

66/(-33)*|-9| No you wouldn't. it would be -33 x 9 first and that results in -297 so it would be

66/-297

[sphilip730]

66/(-33)*|-9| No you wouldn't. it would be -33 x 9 first and that results in -297 so it would be

66/-297

[rfernandez]

The PEMDAS acronym is a helpful mnemonic, but it does have a shortcoming because it appears to place multiplication before division and addition before subtraction. In fact, this is not how one should approach the order of operations. Instead of 6 steps as the PEMDAS acronym might suggest, there are in fact only 4. Here's the proper interpretation of PEMDAS:

1 - Evaluate all expressions within grouping symbols (parentheses, brackets, braces, absolute value bars, numerators, denominators, etc.)
2 - Evaluate all exponents
3 - Evaluate all multiplications and divisions (or divisions and multiplications) FROM LEFT TO RIGHT
4 - Evaluate all additions and subtractions (or subtractions and additions) FROM LEFT TO RIGHT

The reason we can lump M and D together is that these two operations are essentially identical. Dividing by 3 is the same as multiplying by 1/3, for example. Similarly, addition and subtraction are the same operation: subtracting 7 is identical to adding -7.

So, here's how the solution would go:

66/(-33)*|-9|
66/(-33)*9
-2*9
-18

[sphilip730]

thank you

[rfernandez]

You're welcome.