Solve: 6×(3+5×2-13) Using Order of Operations

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

Parentheses are the highest priority in PEMDAS! They tell you exactly which operations to group together. Think of them as a 'do this first' instruction.

Q: Inside the parentheses, which operation do I do first?

Follow PEMDAS inside parentheses too! Since $ 5 \times 2 $ is multiplication and the rest are addition/subtraction, do the multiplication first.

Q: What if I get a different answer than 0?

Double-check your work inside the parentheses: $ 3 + 5 \times 2 - 13 = 3 + 10 - 13 = 0 $. Remember that any number times 0 equals 0!

Q: Can I skip steps when I see multiplication by zero?

It's tempting, but always show your work! You need to prove that what's in parentheses actually equals zero by following the order of operations step by step.

Order of Operations with Nested Parentheses

$6\times(3+5\times2-13)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Always solve the parentheses first

00:08 Multiplication and division precede addition and subtraction

00:11 Continue to solve the expression according to the proper order of operations

00:15 Calculate the parentheses

00:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$6\times(3+5\times2-13)=$

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 these,

We will start by simplifying the expression in parentheses, since multiplication comes before addition and subtraction, we will first perform the multiplication in this expression and then the addition and subtraction operations in the expression, in the final stage we will perform the multiplication outside the parentheses:

$6\cdot(3+5\cdot2-13)= \\ 6\cdot(3+10-13)= \\ 6\cdot0= \\ 0$ In the final stage we remembered that multiplying any number by 0 gives the result 0,

Therefore the correct answer is answer D.

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication and division left to right
Inside Parentheses: Calculate 5×2=10 first, then 3+10-13=0
Check: Verify 6×0=0 by confirming any number times zero equals zero ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following PEMDAS
Don't calculate 6×3=18 first and ignore parentheses = wrong answer of 33! This skips the most important rule. Always solve everything inside parentheses completely before multiplying by the number outside.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I solve what's in parentheses first?

Parentheses are the highest priority in PEMDAS! They tell you exactly which operations to group together. Think of them as a 'do this first' instruction.

Inside the parentheses, which operation do I do first?

Follow PEMDAS inside parentheses too! Since $5 \times 2$ is multiplication and the rest are addition/subtraction, do the multiplication first.

What if I get a different answer than 0?

Double-check your work inside the parentheses: $3 + 5 \times 2 - 13 = 3 + 10 - 13 = 0$ . Remember that any number times 0 equals 0!

Can I skip steps when I see multiplication by zero?

It's tempting, but always show your work! You need to prove that what's in parentheses actually equals zero by following the order of operations step by step.

What's the most common mistake students make here?

Working left to right like reading! Students often calculate $6 \times 3 = 18$ first, ignoring the parentheses completely. Always handle parentheses before anything else.

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