Solve (8:4:2)-3-1: Order of Operations with Sequential Division

Sequential Division with Negative Results

(8:4:2)31= (8:4:2)-3-1=

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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
00:07 Solve the expression according to the order of operations, solve from left to right
00:17 Use the commutative law and arrange in a way that's convenient to solve
00:21 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(8:4:2)31= (8:4:2)-3-1=

2

Step-by-step solution

According to the rules of the order of operations, we first solve the exercise within parentheses from left to right:

8:4=2 8:4=2

2:2=1 2:2=1

Now we get the exercise:

131= 1-3-1=

We solve the exercise from left to right:

13=2 1-3=-2

21=3 -2-1=-3

3

Final Answer

3-

Key Points to Remember

Essential concepts to master this topic
  • Parentheses First: Solve operations inside parentheses completely before moving outside
  • Left-to-Right: Sequential division 8:4:2 8:4:2 means (8:4):2=2:2=1 (8:4):2 = 2:2 = 1
  • Check Final Answer: Verify 131=21=3 1-3-1 = -2-1 = -3

Common Mistakes

Avoid these frequent errors
  • Solving division operations out of order
    Don't solve 8:4:2 8:4:2 as 8:(4:2)=8:2=4 8:(4:2) = 8:2 = 4 = wrong result of 1! This violates left-to-right order and changes the mathematical meaning. Always solve sequential operations from left to right within parentheses.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

\( 36-4\div2 \)

FAQ

Everything you need to know about this question

Why do we solve from left to right in the parentheses?

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Division and multiplication have the same priority level, so when they appear together, we solve from left to right. Think of 8:4:2 8:4:2 as two separate steps: first 8:4=2 8:4 = 2 , then 2:2=1 2:2 = 1 .

What if I solved the subtraction from right to left?

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Subtraction must also go left to right! If you do 1(31)=12=1 1-(3-1) = 1-2 = -1 instead of (13)1=21=3 (1-3)-1 = -2-1 = -3 , you'll get the wrong answer because subtraction isn't associative.

How do I remember PEMDAS with negative numbers?

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Use PEMDAS normally, but be extra careful with negative signs. When you get 13=2 1-3 = -2 , that negative stays with the 2 in the next step: 21=3 -2-1 = -3 .

Is there a difference between : and ÷ symbols?

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No difference at all! Both : and ÷ mean division. Some countries prefer one symbol over the other, but they work exactly the same way in calculations.

Can I check my work a different way?

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Yes! You can substitute back: if the answer is 3 -3 , then (8:4:2)31 (8:4:2)-3-1 should equal 131=3 1-3-1 = -3 ✓. You can also use a calculator to verify each step.

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