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### Course: 6th grade > Unit 4

Lesson 5: More on order of operations- Order of operations examples: exponents
- Comparing exponent expressions
- Order of operations
- Order of operations example: fractions and exponents
- Order of operations with fractions and exponents
- Order of operations review
- Exponents and order of operations FAQ

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# Order of operations example: fractions and exponents

The order of operations is essential for accurately evaluating complex math expressions. By following the steps of parentheses, exponents, multiplication and division, and finally addition and subtraction, you can simplify expressions and find the correct answer. Mastering these steps ensures a strong foundation in mathematics. Created by Sal Khan.

## Want to join the conversation?

- can you use fractions with a exponent?!(10 votes)
- Yes you totally could.(14 votes)

- Why do we divide numbers with fractions when there is no division sign anywhere?(11 votes)
- there is one 1/2 is the same thing as 1 /2 "/" also means to divide(13 votes)

- why do we square everything(at 2.08 minutes in the video) please?(3 votes)
- is BODMAS the same as PEMDAS in this example? and if so what would parenthasis and exponents mean in bodmas(4 votes)
- Well, ya, all the different acronyms communicate the same order.

In BODMAS, B means brackets and O means other (includes exponents).

The first step in the Order of Operations is operations within**groupings**, which can be in the form of: parentheses (), brackets {}, square brackets [], absolute value signs ||, and the numerator/denominator in fractions separated by the vinculum.

The second step is then exponents/roots.

Happy learning!(1 vote)

- If there are parenthesis, do i still follow the order of operation within the parenthesis? If this is the case, why does sal at2:15add 1 + 12 and 7 + 6 BEFORE the division? Order of operations states addition comes after the division.

Here's my work,

1/14 ( 1+ 2²×3 ÷ 7 + 2×3 + 1)²

Parenthesis: Order of operations, Exponents

1/14 ( 1+ 4x3 ÷ 7 + 2x3 + 1)²

Parenthesis: Order of operations, Multiplication/division

1/14 ( 1+ 12 ÷ 7 + 6 + 1)²

And now, I stopped because 12 ÷ 7 with long division is EXTREMELY long, and I knew something was wrong -- that's when I saw Khan do addition before division.

Hopefully someone can help out! Thanks.(1 vote)- What you need to do is solve the first half, solve the second half, and then divide them. Even if the top half or bottom half have addition or subtraction, you still need to solve both halves before dividing.

Hope this makes sense! :))(5 votes)

- why do we square everything(at 2.08 minutes in the video) please?(2 votes)
- If you look in the
**top right corner of the parentheses**, you can see a 2**which shows that everything in the parentheses is squared**, or rather, to the power of 2.(4 votes)

- what happens if you do PEMDAS backward?(3 votes)
- you would get the wrong answer(1 vote)

- i knew all the parts except the last part where i didn't know if i should add, subtract, divide or multiply the 1/14 and 4(3 votes)
- can we use fractions on exponent(2 votes)
- How did Sal get to 4 over 14 if he said we should times 1 over 14 by 4?(3 votes)
- because 1/14 times 4 would be 1/14 times 4/1 so 4x1 is 4 and 14x1 is 14 so you would get 4/14(0 votes)

## Video transcript

- [Instructor] Pause this video and see if you can
evaluate this expression before we do it together. All right, now let's
work on this together. And we see that we have a lot
of different operations here. We have exponents. We have multiplication. We have addition. We have division. We have parentheses. And so to interpret this properly, we just have to remind ourselves
of the order of operations. So you start with parentheses,
then go to exponents, then multiplication and division, then addition and subtraction. So we see that we're going
to, whatever is over here, we're eventually going to square it. That's the only place that
we have the parentheses. But how are we going to evaluate what's inside of these parentheses? So let's, then, think about, all right, we have an exponent here
that we can evaluate. We know that 2 squared is
the same thing as 2 times 2, which is the same thing as 4. No more exponents to evaluate. So then we go to
multiplication and division. So we know by how this
fraction sign is written that we need to evaluate the numerator and then divide it by
the entire denominator right over here. Now in this numerator, we
have to remind ourselves that we do this multiplication
before we do this addition. We don't just go left to right. So we know that it's 1 plus, and I could put parentheses
here to really emphasize that we do the multiplication first. So before this gets too messy, let me just rewrite everything. I'm going to do this
multiplication up here first, and actually in the denominator I'm going to do this
multiplication first as well. So this is all going to
simplify to 1 over 14 or 1/14 times, Now this numerator here is going to be 1 plus 4 times 3. 4 times 3 is 12. All of that is going to be over 7 plus 2 times 3, which is of course equal to 6. And then I am going to
have our plus 1 here, and then I square everything. Well now we can evaluate this numerator and this denominator. Find another color to do it in. This numerator, 1 plus 12, is going to be equal to 13. And 7 plus 6, interestingly,
is also equal to 13. So we 1/14 or 1 divided by 14 times this whole thing squared, and inside you have 13
divided by 13 plus 1. Well, we know we need to do
division before we do addition. So we will want to evaluate this part before we do the addition. What is 13 divided by 13? Well that's just going to be equal to 1. So I can rewrite this as 1 over 14 times 1 plus 1, all of that squared. And now we'll want to do this
parentheses. So let's do that. 1 plus 1 is going to be
equal, of course, to 2. And then we're going to do the exponents. 2 squared is, of course, equal to 4. And then we're going to
multiply 1 over 14 times 4. Now you could interpret
this, and they're equivalent. You could say, hey, this is the same thing as multiplying 1/14 times 4. Or you could say this is the same thing as multiplying 1 times 4 divided by 14. 1 times 4 divided by 14. Either way you look at it, you're going to get 4
over 14, and we're done. If you want, you could rewrite this by dividing both the numerator
and the denominator by 2, and you could get 2 over 7. But that's how we can evaluate this pretty complex expression just step-by-step looking at
what we can simplify first.