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## 5th grade (Eureka Math/EngageNY)

### Course: 5th grade (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Fraction expressions and word problems# Evaluating expressions with & without parentheses

CCSS.Math:

Sal evaluates an expression with and without parentheses. Created by Sal Khan.

## Want to join the conversation?

- why does the math seem easier in the videos than in reality(48 votes)
- Because the people who makes the videos know how to do math really good.(17 votes)

- can you please show more examples because those two were helpful and i did understand it but it is still pretty confusing(11 votes)
- like confused wondering why your ugly or what(2 votes)

- Oui ( ͡° ͜ʖ ͡°)(10 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.(14 votes)

- why is math so easy in videos(6 votes)
- Isn't this basically Bidmas??(5 votes)
- Yes, that's exactly what it is. You follow order of operations rules.(1 vote)

- what is { } im still trying to know?(5 votes)
- For parentheses, we use regular parentheses ( ); curly brackets { }, and also square brackets [ ].

Hope this helps.(0 votes)

- What's the difference between parentheses(), curly brackets{}, and brackets[]?(2 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.(5 votes)

- Can you please give more examples it would really help me thank you(4 votes)
- Example: (10 x 6) - 5

1.) Solve what is in parentheses first: 60 - 5

2.) Then, subtract: 55(1 vote)

- so in this,you basically solve the problem in the paretheses and then solve the problem outside the paretntheses with the answers of both.Am i correct?(2 votes)
- yes correct. you do the parentheses first then you go from left to right and solve the problem.(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.