Solve (12+2)×(3+5): Order of Operations Practice Problem

Order of Operations with Nested Parentheses

(12+2)×(3+5)= (12+2)\times(3+5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem together!
00:10 First, open the parentheses carefully.
00:14 Each term inside the first parentheses multiplies every term in the second set. Let's do this step by step.
00:30 Next, solve each multiplication. Then, add them all up together.
00:52 Now, tackle one addition at a time. You're almost there!
00:59 Great job! This is the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(12+2)×(3+5)= (12+2)\times(3+5)=

2

Step-by-step solution

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

Thus, let's begin by simplifying the expressions within the parentheses, and following this, the multiplication between them.

(12+2)(3+5)=148=112 (12+2)\cdot(3+5)= \\ 14\cdot8=\\ 112

Therefore, the correct answer is option C.

3

Final Answer

112

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve expressions inside parentheses first
  • Technique: Calculate (12+2)=14 and (3+5)=8, then multiply: 14×8=112
  • Check: Verify by working left to right: 14×8 equals 112 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying before solving parentheses
    Don't multiply 12×3 first = 36+2×5 = wrong setup! This ignores the parentheses which must be solved first according to PEMDAS. Always complete all parentheses calculations before any multiplication.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why can't I just multiply 12×3 and 2×5 first?

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Because parentheses come first in PEMDAS! The parentheses group 12+2 together and 3+5 together. You must solve these groups completely before multiplying.

What if I forget which operations to do first?

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Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Always work from left to right within each level!

Can I solve the parentheses in any order?

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Yes! You can solve (12+2) (12+2) first or (3+5) (3+5) first - both give the same final answer because multiplication is commutative.

How do I check if 112 is really correct?

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Work backwards: 112 ÷ 8 = 14 and 112 ÷ 14 = 8. Since we got 14 from (12+2) and 8 from (3+5), our answer checks out!

What happens if I make an arithmetic mistake in the parentheses?

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Even one small error will give you the wrong final answer. That's why it's important to double-check each step: 12+2=14 and 3+5=8.

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