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### Course: Operations and Algebraic Thinking 189-200 > Unit 5

Lesson 1: 2-step expressions# Order of operations (2-step expressions)

Sal evaluates 2-step whole number expressions with different operations.

## Want to join the conversation?

- there are questions that i get wrong because i choose to do multiplication before division why is that?

shouldn't i be following PEMDAS?(31 votes)- PEMDAS does not mean multiplication before division, even though it might appear that way. These two operations have equal priority and so should be done left to right. PEMDAS should really be presented as P E MD AS.(53 votes)

- One of the questions was 9-1+9+3 to the 4th power.

According to PEMDAS, I did:

9-1+9+81 (exponents first)

1+9=10 and 10+81=91 (addition next since no mult. or div.)

9-91=-82 (subtraction after addition)

but it was supposed to be 98.

How do we decide when we're supposed to do A & D from left to right and when we're supposed to follow PEMDAS?!(10 votes)- It is really PE (MD) (AS) because multiplication and division are on same level and addition and subtraction is on the same level, so these go from left to right(5 votes)

- How about someone says, "What is 2 divided 6 times 7". What do you do first?(10 votes)
- Multiplication and Division are equal operators and should be performed left to right.

So, you would perform 2/6 first, then multiply that result by 7.(7 votes)

- how is a square a rectangle(3 votes)
- A
**rectangle**is a shape made of four sides with 90° angles at each corner. A**square**is a special kind of triangle where all the sides are equal. All squares are triangles, but not all rectangles are squares. Hope this helps!(3 votes)

- I watched it twice but I still don't understand why

5-3+2 is doing the - first, then the +, but doing the + first gives a different result. Did I miss an explanation? I only caught that multiplication or division is done before addition or subtraction, but not which of each is done first?(5 votes)- it is because 5-3=2 +2=4 and 3+2=5 -5=0! multiplication is first as well as addition

whenever you're stuck, just remember PEMDAS parentheses, exponents, multiplication, division, addition, subtraction

hope this is helpful!(1 vote)

- can you learn math in any age(3 votes)
- yes I guess(3 votes)

- Why do we not use the PEMDAS order of operations?(2 votes)
- All the examples in this video
**do**use PEMDAS. I'm going to assume that the probelm you find confusing is the: 5-3+2 where Sal subtracts as the first step. You may not realize the "AS" are one group. You should work them left to right. This is why Sal does the subtraction then the addition.

Note: "MD" is also one group and should be done from left to right.

Hope this helps.(5 votes)

- like just put them into each other(3 votes)
- why is this so complicating.(4 votes)
- how do you vote(1 vote)
- Press the triangles next to a post.(4 votes)

## Video transcript

- [Instructor] If I were to ask you, what is five minus three plus two? What would you say that is? Pause this video and
try to figure that out. All right, well if you
wanted to tackle this, you would really just read
it from left to right, or you would compute
it from left to right. You'd first figure out
what five minus three is, and five minus three is equal to two. And so you'd say, okay,
that's going to be two plus two, which of course
we know is equal to four. Now, what if I were to
involve a little bit of multiplication or division? If I were to go up to
you and I were to say, what is five plus three times two? Pause this video and
try to figure that out. Well, you might be tempted
to do it in a similar way. You might be tempted to say, okay, I'll just go from left to right. I'll first compute what five plus three is and that of course,
would be equal to eight, and then I would multiply eight times two to get 16. But it turns out that this would not be the right
way to approach this, because for very good reasons that we'll study in perhaps future videos, we don't always go left to right, especially when we're dealing with different types of operations. And the standard way
that this is approached is that multiplication
and division will be done before addition and subtraction. So the way that you would
actually compute this is that you would compute
the three times two first. So you would say that
this is the same thing as five plus six, five plus six, which is going
to be equal to 11, not 16. So this is going to be equal to 11. So with that out of the way, let's do a few more examples. Let's say someone were
to approach you and say, what is nine minus six divided by three? Pause this video and see
if you can figure that out. Well, as I just said, we would
do multiplication or division before we do subtraction. So we'll actually do the
six divided by three first, and six divided by three is two. So this simplifies to nine minus two, which is equal to seven, and I really wanna emphasize, it's important that you get this idea that multiplication and
division should be done before the addition or subtraction, unless you're given some
other types of directions. Because if you just
went left to right here, you would have said
nine minus six is three, and then you would've
divided that by three, which would have given you one, which is clearly a
different number than seven. Let's do one more example, just for kicks. Let's say that someone were to ask you, what is two times three minus one? Pause the video and try
to figure that one out. Well, in this one, doing
our multiplication first is also the same as going
left to right first. So if we do two times three first, two times three is six, so that's six, and then we would wanna
calculate six minus one, which is of course equal to five. So big picture, if you
just have a bunch of things that are being added, subtracted,
multiply, and divided, and there is no parenthesis in it, you would always prioritize
the multiplication or the division over the
addition or the subtraction.