Solve Decimal Expression: 0.5 - 0.1 ÷ 0.2 Using Order of Operations

Order of Operations with Decimal Division

Solve the following problem using the order of operations:

0.5−0.1:0.2= 0.5-0.1:0.2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this expression together.
00:12 First, convert the division operation into a fraction.
00:17 Remember! We solve multiplication and division before moving on to addition and subtraction.
00:26 Break down zero point two into a decimal fraction.
00:30 Now, simplify the remaining parts of the expression.
00:37 Convert any decimals into fractions, and solve it step-by-step.
00:42 And here is the solution! Great job, everyone!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem using the order of operations:

0.5−0.1:0.2= 0.5-0.1:0.2=

2

Step-by-step solution

According to the order of operations in arithmetic, multiplication and division take precedence over addition and subtraction.

We'll start with the division operation and write the fractions as decimal fractions, then as simple fractions:

0.1:0.2=0.10.2=12 0.1:0.2=\frac{0.1}{0.2}=\frac{1}{2}

In the next step, we'll write the decimal fraction 0.5 as a simple fraction:

0.5=12 0.5=\frac{1}{2}

Lastly we will solve the problem:

12−12=0 \frac{1}{2}-\frac{1}{2}=0

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division comes before subtraction in order of operations
  • Technique: Calculate 0.1 ÷ 0.2 = 0.5 first, then subtract
  • Check: Work left to right: 0.5 - 0.5 = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without considering operation priority
    Don't solve 0.5 - 0.1 = 0.4 first, then divide by 0.2 = 2! This ignores PEMDAS and gives the wrong answer. Always do division before subtraction, regardless of position.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

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

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Mathematics has a special order called PEMDAS (or BODMAS). Division must be done before subtraction, even if subtraction comes first when reading left to right.

How do I divide 0.1 by 0.2?

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Think of it as 0.10.2=12=0.5 \frac{0.1}{0.2} = \frac{1}{2} = 0.5 . You can also multiply both numbers by 10: 12=0.5 \frac{1}{2} = 0.5 .

What if I get confused about which operation to do first?

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Remember PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Division comes before subtraction!

Can I convert decimals to fractions to make it easier?

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Absolutely! Converting 0.5=12 0.5 = \frac{1}{2} and 0.1=110 0.1 = \frac{1}{10} , 0.2=15 0.2 = \frac{1}{5} can make the problem clearer: 12−110÷15 \frac{1}{2} - \frac{1}{10} ÷ \frac{1}{5}

How can I check my answer is 0?

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Substitute back: Does 0.5−0.1÷0.2=0 0.5 - 0.1 ÷ 0.2 = 0 ? Following PEMDAS: 0.5−0.5=0 0.5 - 0.5 = 0 ✓ Yes!

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