Evaluate the Expression: (7+2)×(3+8) Using Order of Operations

Order of Operations with Nested Parentheses

(7+2)×(3+8)= (7+2)\times(3+8)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this exercise together. Are you ready?
00:09 First, we always start by solving what's inside the parentheses.
00:14 Great! Now we can move on to multiplying the numbers.
00:19 And there you have it! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(7+2)×(3+8)= (7+2)\times(3+8)=

2

Step-by-step solution

Simplify this expression paying attention to the order of operations. Whereby exponentiation precedes multiplication, division precedes addition and subtraction and that parentheses precede all of the above.

Therefore, let's first start by simplifying the expressions within the parentheses. After which we perform the multiplication between them:

(7+2)(3+8)=911=99 (7+2)\cdot(3+8)= \\ 9\cdot11=\\ 99 Therefore, the correct answer is option B.

3

Final Answer

99

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always solve expressions inside parentheses first before multiplying
  • Technique: Calculate (7+2)=9 (7+2) = 9 and (3+8)=11 (3+8) = 11 , then multiply
  • Check: Verify final answer: 9×11=99 9 \times 11 = 99 matches our result ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying before solving parentheses
    Don't multiply 7 × 3 = 21 first and then add = 79! This ignores the parentheses and breaks PEMDAS order. Always solve what's inside parentheses completely before doing any other operations.

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 multiply the first numbers in each parentheses?

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Because parentheses come first in the order of operations! You must complete the addition inside each set of parentheses before moving to multiplication between them.

What if I forget to do the parentheses first?

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You'll get the wrong answer! For example, if you multiply 7×3=21 7 \times 3 = 21 first, then add, you'd get 79 instead of the correct answer 99.

Is PEMDAS the only way to remember order of operations?

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No! You can also use BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or GEMDAS (Grouping symbols first). They all mean the same thing!

Do I always work from left to right?

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Not exactly! You follow the order of operations first, then work left to right within operations of the same priority. Parentheses always come first, regardless of position.

What if there were no parentheses in this problem?

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Without parentheses, it would be 7+2×3+8 7 + 2 \times 3 + 8 . Then you'd multiply first: 7+6+8=21 7 + 6 + 8 = 21 , which is completely different!

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