Main content

### Course: 5th grade > Unit 13

Lesson 1: Writing expressions# Evaluating expressions with & without parentheses

Explore the concept of order of operations, emphasizing the importance of parentheses in mathematical expressions.Learn how the placement of parentheses can drastically change the outcome of an expression, highlighting the need to follow the correct sequence: parentheses, multiplication and division, then addition and subtraction. Created by Sal Khan.

## Want to join the conversation?

- why does the math seem easier in the videos than in reality(71 votes)
- Because the people who makes the videos know how to do math really good.(30 votes)

- plz give me a vote so i can get a badge(46 votes)
- can you please show more examples because those two were helpful and i did understand it but it is still pretty confusing(19 votes)
- Doesn't a negative plus a negative equal a positive number.(7 votes)
- A negative plus a negative will always equal a negative because you are taking a value less than zero and "applying more negativity to it" For example, you are already underground, and adding a negative distance means you will be digging even deeper underground.

However, a negative times a negative will become positive.(14 votes)

- what if there is two perethisis and that's what I don't get and what I mean is witch one should I do first if you know lease explain it to me thanks so much!(1 vote)
- In the example equation:

(10 × 4) + (4 ÷ 2)

You must solve the parenthesis first (Moving left to right)

(10 × 4 = 40) + (4 ÷ 2)

40 + (4 ÷ 2 = 2)

40 + 2 = 42

In this other example parentheses inside of parentheses:

((10 × (4 ÷ 2)) × 2) + 2

You solve the most nested parentheses first.

((10 × (4 ÷ 2 = 2)) × 2) + 2

((10 × 2 = 20) × 2) + 2

(20 × 2 = 40) + 2

40 + 2 = 42

Did this help? If so, great! If not, explain to me what you still don't understand.(19 votes)

- What's the difference between parentheses(), curly brackets{}, and brackets[]?(3 votes)
- Parentheses () are used to group numbers or expressions that you want to calculate first. For example, in 2 + (3 × 4), you do 3 × 4 first because it is inside the parentheses.

Curly brackets {} are used to show sets of numbers or objects. A set is a collection of things that have something in common. For example, {1, 2, 3} is a set of three numbers.

Brackets [] are basically only used when you have more than one pair of parentheses in an expression. You use them outside the parentheses to show what to do next. For example, in [2 + (3 × 4)] ÷ 5 , you do 2 + (3 × 4) first because it is inside the brackets.

In a complicated expression, all three can be used, in this order: parentheses first, then brackets, then curly brackets. For example:

4 - 3 [4 - 2 {6 - (5 + 1)}] ÷ 3

First: 4 -3 [4 -2 {6 - 6}] ÷ 3

Then: 4 -3 [4 -2 × 0] ÷ 3

Then: 4 - 3 × 4 ÷ 3

Then: -8 ÷ 3

So the answer is -8 divided by 3.(7 votes)

- I have a Quick Questions how bo you do that(6 votes)
- 1-(4-2x12)+7 in that problem,inside the parentheses, do i do the multiplication first, or the subtraction?(5 votes)
- you do the multiplication, because you have to do PEMDAS(2 votes)

- Isn't this basically Bidmas??(5 votes)
- Yes, that's exactly what it is. You follow order of operations rules.(2 votes)

- Math is good for you(3 votes)

## Video transcript

What I want to do is think about
whether this expression right over here would evaluate
the same way whether or not we had parentheses. So to think about
that, let's first think about how
it would evaluate if we add the parentheses. So if we add the
parentheses, we want to do what's ever in
the parentheses first. And so here we have 8 minus
3, which is equal to 5. So this simplifies to 5
times 5 times 8 minus 3. And now we want to
do the multiplication before we do subtraction. This goes back to
order of operations. You do your multiplication
and division first. Well, you do your
parentheses first. Then if you have multiplication,
division, addition, and subtraction
all in a row, you want to do your multiplication
and your division first. So here we're going to
multiply 5 times 8 to get 40, and then we're going to
subtract 3 to get 37. Now, let's think about
what this would evaluate to if we did not
have the parentheses. So it would be 8 minus
3 times 8 minus 3. So we just have to
remind ourselves about the order of operations. The convention is to do
your multiplication first. So you're actually going to
multiply the 3 times the 8 before you subtract
it from this 8 and then before you
subtract this 3. So we took away the parentheses,
but the order of operations say, hey, do this
multiplication first. We could even put a parentheses
here to emphasize that. So this will become
8 minus 8 minus 24. Let me write it this way. 8 minus 24 minus 3. 8 minus 24 minus 3. Now, 8 minus 24 is negative 16. You subtract another 3, you're
going to get to negative 19. So clearly, you get very,
very different values depending on whether or
not you have parentheses.