Solve Decimal Division: Calculate 0.5 ÷ 2 Step by Step

Decimal Division with Fraction Conversion

0.52= \frac{0.5}{2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this math problem together.
00:07 First, change the decimal into a fraction.
00:11 Next, switch division to multiplication by using the reciprocal.
00:15 Remember, multiply the numerators together, and then the denominators.
00:21 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

0.52= \frac{0.5}{2}=

2

Step-by-step solution

Let's convert the decimal fraction to a simple fraction:

0.5=510 0.5=\frac{5}{10}

We'll write the division problem as follows:

5102 \frac{\frac{5}{10}}{2}

Let's convert the division problem to a multiplication problem.

We'll multiply 510 \frac{5}{10} by the reciprocal of 2 2 as follows:

510×12 \frac{5}{10}\times\frac{1}{2}

We'll solve it this way:

5×110×2=520 \frac{5\times1}{10\times2}=\frac{5}{20}

We'll reduce both the numerator and denominator by 5 and get:

5:520:5=14 \frac{5:5}{20:5}=\frac{1}{4}

3

Final Answer

14 \frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert decimals to fractions before dividing by whole numbers
  • Technique: Change 0.5÷2 0.5 ÷ 2 to 510×12 \frac{5}{10} \times \frac{1}{2}
  • Check: Verify 14=0.25 \frac{1}{4} = 0.25 and 0.5÷2=0.25 0.5 ÷ 2 = 0.25

Common Mistakes

Avoid these frequent errors
  • Treating decimal division like whole number division
    Don't think 0.5 ÷ 2 = 4 because 5 ÷ 2 ≈ 2.5! This ignores the decimal point placement. When dividing a decimal by a whole number, the result must be smaller than the original decimal. Always convert to fractions or use proper decimal division rules.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

\( \frac{5}{100}= \)

FAQ

Everything you need to know about this question

Why do I need to convert 0.5 to a fraction first?

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Converting 0.5 to 510 \frac{5}{10} makes division easier to understand! It shows exactly what you're dividing and lets you use fraction multiplication rules instead of tricky decimal division.

Can I just do 0.5 ÷ 2 = 0.25 directly?

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Yes! But understanding the fraction method helps you see why the answer is correct. Both 14 \frac{1}{4} and 0.25 are the same number - just written differently.

What does 'multiply by the reciprocal' mean?

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Instead of dividing by 2, you multiply by 12 \frac{1}{2} (the reciprocal of 2). Division and multiplication by reciprocals give the same answer: 510÷2=510×12 \frac{5}{10} ÷ 2 = \frac{5}{10} \times \frac{1}{2}

How do I reduce fractions like 5/20?

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Find the greatest common factor of both numbers. Since both 5 and 20 can be divided by 5: 5÷520÷5=14 \frac{5÷5}{20÷5} = \frac{1}{4}

Why is my answer smaller than what I started with?

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When you divide by a number greater than 1, the result is always smaller! Think of it as sharing: 0.5 0.5 shared between 2 people gives each person 0.25 0.25 .

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