PEDMAS Operation Order and Grouping

Boxes of Oranges 2×3+2

What’s the Point?

In the real world, all problems start out as word problems that have to be translated in algebra to solve them using math. To get the correct answer if you have an expression with several operations, you have to do them in the standard order.

This is it: the order to do the operations in.
P – Parenthesized blocks first – Evaluate stuff inside parenthesis
E – Exponents next
MD – Multiplication and Division next. Do these in left to right order.
AD – Addition Subtraction last. Do these in left to right order.


First Problem

A) Read the word problem to see what’s being asked.

B) Translate into algebra. In this case, there are 2 boxes with 3 each, so that’s just 2 multiplied by 3. The extra 2 oranges are on their own, not multiplied by anything.


C) Now that it’s an algebraic expression, so just simplify it and you’re done. But, you have to do the operations in the correct order. First do the 2*3 multiplication because in PEDMAS, division/multiplication come before addition/subtraction.

2×3+2 = 6 + 2

Now just do the addition, there’s nothing else.

6+2 = 8

Second Problem with different parenthesis

This shows what grouping using parenthesis can do. It’s the same as the First Problem, but rather than doing the 2*3 first, this is set up to do the 3+2 first.

A) As always read the problem and create an algebraic expression. Note that this time, the expression has to express the idea that there are 2 boxes, and each with a set of 3 oranges and another of 2 oranges. This is it:


B) Now start simplifying. But, now we’ve got some parenthesis. The P in PEDMAS is parenthesis and because it’s first, that means we have to first to whatever is inside them. In this case it’s addition, so we do that first and get rid of the parenthesis.

2(3+2) = 2*5

C) Note that we’re now multiplying 2 times the 5 that we got from adding 3+2. It’s a multiply because that’s what is implied by the 2 followed by the parenthesis without any other operation. So that gives us:

2×5 = 10

Just by regrouping the expression by using parenthesis, the results of these two expressions are different.

2*3+2 = 8
2(3+2) = 10

Negatives More Complex

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