Solve (3·5+5)÷(4+3·2): Order of Operations Practice

Q: Why can't I just work left to right?

Order of operations has specific rules that must be followed! Working left to right ignores these rules and gives wrong answers. Always use PEMDAS to get the correct result.

Q: What does the colon symbol (:) mean in math?

The colon (:) means division, just like ÷. So $ 20:10 $ is the same as $ 20 ÷ 10 = 2 $.

Q: Do I really need to show all these steps?

Yes! Showing each step helps you avoid mistakes and makes it easy to check your work. It also shows your teacher that you understand the process.

Q: What if I get confused about which operation to do first?

Remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). When in doubt, always start with parentheses!

Q: How do I know if 2 is really the right answer?

Work backwards! Calculate $ (3 \cdot 5 + 5) = 20 $ and $ (4 + 3 \cdot 2) = 10 $, then $ 20 ÷ 10 = 2 $. The math checks out perfectly!

Order of Operations with Parentheses First

$(3\cdot5+5):(4+3\cdot2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following expression

00:03 Always solve the parentheses first

00:07 Multiplication and division precede addition and subtraction

00:10 Calculate the parentheses and only then divide

00:19 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(3\cdot5+5):(4+3\cdot2)=$

Step-by-step solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

In the given expression, there is a division operation between two expressions in parentheses, so we'll start by simplifying each of the expressions in parentheses in parallel. Since multiplication comes before addition and subtraction, we'll first perform the multiplications in the expressions and then calculate the results of the addition and subtraction operations in the expressions:

$(3\cdot5+5):(4+3\cdot2)= \\ (15+5):(4+6)= \\ 20:10 \\$ Let's complete the simplification of the expression and perform the division operation:

$20:10= \\ 2$ Therefore, the correct answer is answer B.

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication/division, then addition/subtraction
Technique: Calculate $3 \cdot 5 = 15$ and $3 \cdot 2 = 6$ before adding
Check: Substitute back: $20 ÷ 10 = 2$ matches our answer ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying inside parentheses
Don't calculate (3+5+5) and (4+3+2) first = wrong values 13 and 9! This ignores multiplication priority and gives 13÷9 instead of 2. Always multiply first within parentheses: 3·5 and 3·2 before adding.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why can't I just work left to right?

Order of operations has specific rules that must be followed! Working left to right ignores these rules and gives wrong answers. Always use PEMDAS to get the correct result.

What does the colon symbol (:) mean in math?

The colon (:) means division, just like ÷. So $20:10$ is the same as $20 ÷ 10 = 2$ .

Do I really need to show all these steps?

Yes! Showing each step helps you avoid mistakes and makes it easy to check your work. It also shows your teacher that you understand the process.

What if I get confused about which operation to do first?

Remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). When in doubt, always start with parentheses!

How do I know if 2 is really the right answer?

Work backwards! Calculate $(3 \cdot 5 + 5) = 20$ and $(4 + 3 \cdot 2) = 10$ , then $20 ÷ 10 = 2$ . The math checks out perfectly!

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