Solve the Expression: (3×5+5)÷(4+3×2) Using Order of Operations

Q: Why do I solve what's in parentheses first?

Parentheses have the highest priority in PEMDAS! They tell you exactly which operations to group together. Without solving $ (3\times5+5) $ first, you'll get the wrong answer.

Q: Inside parentheses, do I still follow PEMDAS?

Yes! Even inside parentheses, multiplication comes before addition. So calculate $ 3\times5=15 $ first, then add 5 to get 20.

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

The colon means division - it's the same as ÷. So $ 20:10 $ equals $ 20÷10=2 $.

Q: How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Order of Operations with Nested Parentheses

Solve the following expression:

$(3\times5+5):(4+3\times2)=$

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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

00:08 Multiplication and division precede addition and subtraction

00:35 Continue calculating all the parentheses and only then divide

00:43 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$(3\times5+5):(4+3\times2)=$

Step-by-step solution

Use the order of operations to simplify the given operation. The order of operations states that exponents precede multiplication and division, which precede addition and subtraction, and that parentheses precede all of the above:

In the given expression, there is a division operation between two expressions inside of parentheses. Therefore we will first simplify these expressions (due to the fact that they are inside of parentheses)

We will simplify the expressions simultaneously, whilst following the aforementioned order of operations. Given that multiplication precedes addition, we will begin by calculating the results of the multiplications operations and then proceed to perform the addition:

$(3\cdot5+5):(4+3\cdot2)= \\ (15+5):(4+6)=\\ 20:10=\\ 2$

In the final step, we perform the remaining division operation (located between the parentheses in the original expression).

Therefore, the correct answer is answer C.

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication, then division left to right
Technique: Calculate $3\times5=15$ and $3\times2=6$ before adding
Check: Final division $20÷10=2$ should give whole number ✓

Common Mistakes

Avoid these frequent errors

Solving left to right without following order of operations
Don't calculate $(3\times5+5)÷4+3\times2$ from left to right = wrong answer 11.5! This ignores multiplication priority inside parentheses. Always solve parentheses completely first, doing multiplication before addition inside each set.

Practice Quiz

Test your knowledge with interactive questions

Solve the following problem:

$187\times(8-5)=$

FAQ

Everything you need to know about this question

Why do I solve what's in parentheses first?

Parentheses have the highest priority in PEMDAS! They tell you exactly which operations to group together. Without solving $(3\times5+5)$ first, you'll get the wrong answer.

Inside parentheses, do I still follow PEMDAS?

Yes! Even inside parentheses, multiplication comes before addition. So calculate $3\times5=15$ first, then add 5 to get 20.

What does the colon (:) symbol mean?

The colon means division - it's the same as ÷. So $20:10$ equals $20÷10=2$ .

How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

What if I get a different answer?

Double-check each step! Most mistakes happen when students skip the multiplication inside parentheses. Make sure you get $(15+5)$ and $(4+6)$ before dividing.

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