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Lesson 5: More on order of operations

# 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?!
• Yes you totally could.
• Why do we divide numbers with fractions when there is no division sign anywhere?
• there is one 1/2 is the same thing as 1 /2 "/" also means to divide
• why do we square everything(at 2.08 minutes in the video) please?
• is BODMAS the same as PEMDAS in this example? and if so what would parenthasis and exponents mean in bodmas
• 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 at add 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! :))
• why do we square everything(at 2.08 minutes in the video) please?
• 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.
• what happens if you do PEMDAS backward?
• 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