Solve the Expression: 6·(3+5·2-13) Using Order of Operations

Order of Operations with Parentheses

6(3+5213)= 6\cdot(3+5\cdot2-13)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem together.
00:12 First, tackle what's inside the parentheses.
00:16 Next, remember that multiplication and division come before addition and subtraction.
00:24 Now, follow the order of operations to solve the rest of the expression.
00:37 Remember, any number times zero is always zero.
00:42 And there we have our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

6(3+5213)= 6\cdot(3+5\cdot2-13)=

2

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,

Therefore, we'll start by simplifying the expression in parentheses, since multiplication comes before addition and subtraction we'll first perform the multiplication in the expression and then calculate the result of the addition and subtraction operations in the expression:

6(3+5213)=6(3+1013)=60=0 6\cdot(3+5\cdot2-13)= \\ 6\cdot(3+10-13)= \\ 6\cdot0= \\ 0 We completed the calculation above by performing the remaining multiplication, and we also remembered that multiplying any number by 0 will always result in 0.

Therefore, the correct answer is answer B.

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication and division from left to right
  • Inside Parentheses: Do multiplication before addition/subtraction: 5·2 = 10 first
  • Final Check: Verify 6·(3+10-13) = 6·0 = 0 by substitution ✓

Common Mistakes

Avoid these frequent errors
  • Solving left to right without following order of operations
    Don't calculate 6·3 = 18 first just because it appears first = wrong answer of 42! This ignores parentheses and creates calculation errors. Always solve parentheses completely first, then multiply the result.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

\( 30 - (10 + 7) = \)

FAQ

Everything you need to know about this question

Why can't I just solve from left to right?

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Mathematical expressions have a specific order that must be followed! Just like reading instructions for a recipe, doing steps out of order gives you the wrong result. Always use PEMDAS order.

What do I do first inside the parentheses?

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Inside parentheses, you still follow order of operations! So in 3+52133+5\cdot2-13, do the multiplication first: 52=105\cdot2 = 10, then work left to right with addition and subtraction.

How do I remember the order of operations?

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Use the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Some people remember it as "Please Excuse My Dear Aunt Sally."

What happens when I multiply by zero?

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Any number multiplied by zero always equals zero! This is a fundamental math rule. So 60=06 \cdot 0 = 0, 10000=01000 \cdot 0 = 0, even 250=0-25 \cdot 0 = 0.

How can I check if my answer is correct?

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Work through the problem step-by-step again, or use a calculator to verify each step. For this problem: 3+1013=03 + 10 - 13 = 0, then 60=06 \cdot 0 = 0

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