Solve Decimal Division: 0.3 ÷ 0.5 Step by Step

Decimal Division with Fraction Conversion

0.30.5= \frac{0.3}{0.5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem together.
00:07 First, change the decimal numbers into fractions.
00:11 Next, switch division to multiplication by using the reciprocal.
00:15 Now, simplify wherever possible.
00:19 And that gives us our final solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

0.30.5= \frac{0.3}{0.5}=

2

Step-by-step solution

Let's convert the decimal fractions to simple fractions:

0.3=310 0.3=\frac{3}{10}

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

We'll write the division problem as follows:

310510 \frac{\frac{3}{10}}{\frac{5}{10}}

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

We'll multiply 310 \frac{3}{10} by the reciprocal of 510 \frac{5}{10} as follows:

310×105 \frac{3}{10}\times\frac{10}{5}

We'll solve it this way:

3×1010×5 \frac{3\times10}{10\times5}

We'll cancel out the 10 in the numerator with the 10 in the denominator and get:

35 \frac{3}{5}

3

Final Answer

35 \frac{3}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert decimals to fractions then divide using reciprocal multiplication
  • Technique: 0.3÷0.5=310×105=35 0.3 \div 0.5 = \frac{3}{10} \times \frac{10}{5} = \frac{3}{5}
  • Check: Verify by converting back: 35=0.6 \frac{3}{5} = 0.6 and 0.3÷0.5=0.6 0.3 \div 0.5 = 0.6

Common Mistakes

Avoid these frequent errors
  • Dividing decimal digits directly without place value consideration
    Don't just divide 3 ÷ 5 = 0.6 thinking it's correct by accident! This ignores place values and only works coincidentally here. Always convert decimals to proper fractions first, then use the reciprocal method to ensure accurate division.

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 can't I just divide 0.3 by 0.5 using a calculator?

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You absolutely can! But learning the fraction method helps you understand why division works and builds skills for more complex problems where calculators might not be allowed.

How do I convert 0.3 and 0.5 to fractions?

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Look at the decimal places: 0.3=310 0.3 = \frac{3}{10} (3 tenths) and 0.5=510 0.5 = \frac{5}{10} (5 tenths). The denominator matches the place value!

What does 'multiply by the reciprocal' mean?

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Instead of dividing by 510 \frac{5}{10} , you multiply by its reciprocal 105 \frac{10}{5} . Just flip the fraction upside down and change ÷ to ×!

Why does the 10 cancel out in the solution?

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When you multiply 310×105 \frac{3}{10} \times \frac{10}{5} , you get 3×1010×5 \frac{3 \times 10}{10 \times 5} . The 10 appears in both numerator and denominator, so they cancel out, leaving 35 \frac{3}{5} .

Can I simplify the fraction answer further?

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Check if 35 \frac{3}{5} can be reduced by finding common factors. Since 3 and 5 share no common factors other than 1, it's already in simplest form!

What if I want the answer as a decimal?

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Just divide: 35=3÷5=0.6 \frac{3}{5} = 3 ÷ 5 = 0.6 . Both 35 \frac{3}{5} and 0.6 are correct - choose the format your teacher requests!

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