Solve 8+5-6×(2+1)+7: Order of Operations Practice

Order of Operations with Grouped Expressions

8+5−6×(2+1)+7= 8+5-6\times(2+1)+7=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

8+5−6×(2+1)+7= 8+5-6\times(2+1)+7=

2

Step-by-step solution

To solve this expression, we need to follow the order of operations: Parentheses, Exponents (not in this problem), Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Start with the parentheses: (2+1)=3(2+1) = 3

Substitute back into the expression: 8+5−6×3+78+5-6\times3+7

Then, perform the multiplication: 6×3=186\times3 = 18

Substitute back into the expression: 8+5−18+78+5-18+7

Next, perform the addition and subtraction from left to right:

8+5=138+5 = 13

Then: 13−18=−513-18 = -5

Finally: −5+7=2-5+7 = 2

So, the final answer is 2 2 .

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication, finally addition and subtraction left to right
  • Technique: Calculate (2+1)=3(2+1) = 3, then 6×3=186 \times 3 = 18 before other operations
  • Check: Work left to right: 8+5−18+7=13−18+7=−5+7=28+5-18+7 = 13-18+7 = -5+7 = 2 ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following PEMDAS
    Don't calculate 8+5−6=78+5-6 = 7 first = wrong answer of 28! This ignores parentheses and multiplication priority, completely changing the result. Always handle parentheses and multiplication before any addition or subtraction.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

\( 25 - (8 + 5) = \)

FAQ

Everything you need to know about this question

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

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Mathematics has a special order called PEMDAS that ensures everyone gets the same answer! Without this order, 2+3×42+3 \times 4 could equal 20 or 14 - very confusing!

What if there are no parentheses in the problem?

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You still follow PEMDAS! Skip the parentheses step and go straight to multiplication and division, then addition and subtraction from left to right.

Do I multiply 6×(2+1) or 6×2+1?

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Always solve what's inside parentheses first! So 6×(2+1)=6×3=186 \times (2+1) = 6 \times 3 = 18, not 6×2+1=136 \times 2 + 1 = 13.

How do I remember the order of operations?

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Use the memory trick "Please Excuse My Dear Aunt Sally" for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction!

What if I get a negative number during the calculation?

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That's completely normal! In this problem, 13−18=−513-18 = -5, then −5+7=2-5+7 = 2. Just keep following the order carefully.

Can I use a calculator for these problems?

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Yes, but make sure your calculator follows PEMDAS! Some basic calculators work left to right only. Scientific calculators automatically follow the correct order of operations.

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