Solve Mixed Operations: 9÷3-1.5×2 Using Order of Operations

Order of Operations with Mixed Decimal Operations

9:31.5×2= 9:3-1.5\times2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Multiplication and division come before addition and subtraction, so we'll start with them
00:12 Let's solve the exercises we marked
00:21 We're left with a simple subtraction exercise
00:23 That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

9:31.5×2= 9:3-1.5\times2=

2

Step-by-step solution

According to the order of operations, we place the multiplication and division exercise within parentheses:

(9:3)(1.5×2)= (9:3)-(1.5\times2)=

Now we solve the exercises within parentheses:

9:3=3 9:3=3

1.5×2=3 1.5\times2=3

And we obtain the exercise:

33=0 3-3=0

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Division and multiplication have equal priority, solve left to right
  • Technique: Calculate 9÷3=3 9÷3=3 and 1.5×2=3 1.5×2=3 first
  • Check: Final subtraction gives 33=0 3-3=0 , verify each step ✓

Common Mistakes

Avoid these frequent errors
  • Solving operations strictly left to right without grouping
    Don't calculate 9÷3-1.5×2 as ((9÷3)-1.5)×2 = 1×2 = 2! This ignores that multiplication and division have equal priority. Always group multiplication and division operations first: (9÷3)-(1.5×2).

Practice Quiz

Test your knowledge with interactive questions

\( 13+5+5= \) ?

FAQ

Everything you need to know about this question

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

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Mathematics has a specific order that's different from reading! Division and multiplication must be done before addition and subtraction, even if they appear later in the expression.

How do I remember which operations to do first?

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Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). The key is that M and D have equal priority!

What if I get confused about which operations to group together?

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When you see mixed operations, mentally add parentheses around each multiplication/division pair first: (9÷3)(1.5×2) (9÷3)-(1.5×2) . This helps you visualize the correct order!

Can decimals make order of operations harder?

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No! Decimals follow the same rules as whole numbers. Just be careful with your decimal multiplication: 1.5×2=3.0=3 1.5×2=3.0=3 .

How do I check if my final answer is correct?

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Work backwards! Start with your answer and verify each step: 33=0 3-3=0 ✓, where 9÷3=3 9÷3=3 ✓ and 1.5×2=3 1.5×2=3 ✓.

What's the difference between ÷ and / symbols?

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They mean exactly the same thing! 9÷3 9÷3 and 9/3 9/3 both equal 3. The ÷ symbol is just another way to write division.

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