Solve: 0.6 × (1+2) - Order of Operations with Decimals

Order of Operations with Decimal Multiplication

0.6×(1+2)= 0.6\times(1+2)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:03 Always solve the parentheses first
00:11 Continue to solve the remaining expression
00:14 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

0.6×(1+2)= 0.6\times(1+2)=

2

Step-by-step solution

The problem to be solved is 0.6×(1+2)= 0.6\times(1+2)= . Let's go through the solution step by step, following the order of operations.


Step 1: Evaluate the expression inside the parentheses.
Inside the parentheses, we have 1+21+2. According to the order of operations, we first solve expressions in parentheses. Thus, we have:

1+2=3 1 + 2 = 3

So, the expression simplifies to 0.6×3 0.6\times3 .


Step 2: Perform the multiplication.
With the parentheses removed, we now carry out the multiplication:

0.6×3=1.8 0.6 \times 3 = 1.8

Thus, the final answer is 1.8 1.8 .

3

Final Answer

1.8

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve parentheses first, then multiplication
  • Technique: Evaluate (1+2) = 3, then calculate 0.6 × 3
  • Check: Verify 0.6 × 3 = 1.8 by multiplying step by step ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying before solving parentheses
    Don't multiply 0.6 × 1 = 0.6 first, then add 2 = 2.6! This ignores order of operations and gives the wrong answer. Always solve expressions in parentheses first, then multiply the result.

Practice Quiz

Test your knowledge with interactive questions

\( 20\div(4+1)-3= \)

FAQ

Everything you need to know about this question

Why can't I just multiply 0.6 by each number inside the parentheses?

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You actually can use the distributive property: 0.6×(1+2)=0.6×1+0.6×2=0.6+1.2=1.8 0.6 \times (1+2) = 0.6 \times 1 + 0.6 \times 2 = 0.6 + 1.2 = 1.8 . Both methods give the same answer!

How do I multiply a decimal by a whole number?

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Multiply as if both were whole numbers, then count decimal places. For 0.6×3 0.6 \times 3 : multiply 6 × 3 = 18, then place the decimal one position from the right to get 1.8.

What if I forgot PEMDAS and got 2.6 as my answer?

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That's a common mistake! You likely multiplied 0.6×1=0.6 0.6 \times 1 = 0.6 first, then added 2. Remember: Parentheses always come first in the order of operations.

Is there an easy way to remember the order of operations?

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Yes! Use PEMDAS:

  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)

Can I check my answer by working backwards?

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Absolutely! If your answer is 1.8, divide by 0.6: 1.8÷0.6=3 1.8 ÷ 0.6 = 3 . This should equal what's in parentheses: 1+2=3 1 + 2 = 3 . It matches, so you're correct!

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