What's the Order of Operations?

Summary

Grouping symbols are symbols like parentheses, brackets, and fraction bars
Powers are those numbers that show up in the top right. Like in the expression a^b, b is the power
Remember to start on the left and work your way right as you multiply and divide
Remember to start on the left and work your way right as you add and subtract
Make sure you follow order of operations so that you don't get wrong answers!

Notes

1. You can try, but you'll need some pretty stretchy socks!
1. If you have lots of grouping symbols, then start evaluating the math in the innermost symbols and work your way out to the outermost grouping symbols
1. Powers are those numbers that show up in the top right. Like in the expression a^b, b is the power
1. It doesn't matter if you multiply first or divide. You really can do that in any order you like!
1. Remember that subtraction is just like addition of a negative number, and that's why you can do addition and subtraction in any order once you get to this step!
1. Our example has grouping symbols, a power of 2, multiplication and addition!
1. The parentheses in (2+3) are the grouping symbols that we need to deal with first
1. We start with the 2+3 inside the parentheses
2. Once we find that 2+3 is 5, we can rewrite our expression without the 2+3!
1. Remember, powers are those numbers on top and to the right of a number. Like if you have 3², 2 is the power that 3 is raised to
1. 2 is the power that 3 is raised to, and we move on to working on powers because we've dealt with grouping symbols already
2. 3² is just 3•3, which is 9
3. Once we know what 3² equals, we can rewrite our expression so that there are no powers left!
1. Remember to start on the left and work your way right as you multiply and divide
1. There is only one multiplication symbol and no division symbols, so we only need to multiply once
2. Know your times tables! 9•5 is 45 and we use that to rewrite our expression that that there are no multiplication symbols left!
1. Save the best for last: With all of our other steps done, we just need to add and subtract, and then we'll have our answer
1. Adding 45 and 5 gives us 50, which is the correct value for the expression!
1. Applying the wrong order will always give you the wrong answer, unless you happen to be very lucky :)
1. Parentheses come first and adding comes last, so doing this is a big mistake!
1. Once you get good at order of operations, seeing mistakes like this will make your eyes bleed :)
2. The 3 was supposed to be multiplied by 3², and by taking it out of the parentheses and adding it to 5, we're not letting that multiplication happen :(
3. Notice we use a not equal sign (≠) because the two expressions are definitely not equal! If you breaks rules like order of operations, you lose the right to claim that things are equal!
1. Remember that multiplication happens after we take care of powers! Doing it in reverse will mess everything up!
1. The power of 2 is connected to the 3, so multiplying 3 by 2 before squaring it is bound to get us into trouble!
2. Again we use the not equal to sign (≠), because we failed to follow the rules, and so we can't get equality!
1. Now we have an expression with a power and an addition, so simplifying the power is the correct thing to do. But we've already gone down the wrong path, and following the rules now won't bring us back!
1. 6² is definitely 36, but we made a mistake early on by not following the order of operations. So even if we follow the rules now, we are going to get the wrong answer!
1. We use the not equal sign (≠) because we broke the order of operations rules at the start, and that make us lose the right to use the equal sign!
1. The right answer was 50, and when we broke the order of operations rules, we got 44.
2. Make sure you follow order of operations so that you don't get wrong answers!

Definition: Order of Operations

Summary

Notes