Solve Decimal Division: 0.4 ÷ 3 with Positive Numbers

Q: Why do I need to convert 0.4 to a fraction first?

Converting 0.4 to 4/10 makes the division much clearer! Working with fractions lets you use the flip-and-multiply rule easily, while dividing decimals by whole numbers can be confusing.

Q: How do I know when to flip the second fraction?

You flip the second fraction (the divisor) every time you convert division to multiplication. So $ 3 = \frac{3}{1} $ becomes $ \frac{1}{3} $ when you flip it!

Q: Why is my answer a fraction instead of a decimal?

Both forms are correct! $ \frac{2}{15} $ equals approximately 0.133... The fraction form is often more precise than the rounded decimal.

Q: How do I simplify the final fraction?

Look for common factors in the numerator and denominator. Here, $ \frac{4}{30} = \frac{2 \times 2}{15 \times 2} = \frac{2}{15} $ after canceling the common factor of 2.

Fraction Division with Decimal Conversion

$+\text{0}.4:+3=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together.

00:11 First, change the decimal to a fraction.

00:19 Now, substitute this fraction into our exercise.

00:30 Remember, division means multiplying by the reciprocal.

00:36 So, switch the numerator and denominator.

00:43 Multiply the numerators together and the denominators to gether.

00:59 Factor four as two times two.

01:03 Factor thirty as two times fifteen.

01:07 Now reduce any common factors.

01:12 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$+\text{0}.4:+3=\text{ ?}$

Step-by-step solution

First, let's convert 0.4 to a simple fraction:

$0.4=\frac{4}{10}$

Let's now convert 3 into a simple fraction:

$3=\frac{3}{1}$

Now the exercise we have is:

$\frac{4}{10}:\frac{3}{1}=$

Next, let's convert the division exercise into a multiplication exercise, remembering to switch the numerator and denominator in the second fraction:

$\frac{4}{10}\times\frac{1}{3}=$

Let's now combine everything into one multiplication exercise:

$\frac{4\times1}{10\times3}=\frac{4}{30}$

We can now break down the numerator and denominator into multiplication exercises:

$\frac{2\times2}{15\times2}=$

Finally, we reduce the 2 in the numerator and denominator to get:

$\frac{2}{15}$

Final Answer

$\frac{2}{15}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert decimals to fractions before dividing
Technique: Flip divisor and multiply: $\frac{4}{10} \div 3 = \frac{4}{10} \times \frac{1}{3}$
Check: Verify $\frac{2}{15} \times 3 = 0.4$ gives original dividend ✓

Common Mistakes

Avoid these frequent errors

Converting division to multiplication incorrectly
Don't multiply by the whole divisor instead of its reciprocal = wrong operation! Students often do 0.4 × 3 instead of 0.4 × 1/3, getting 1.2 instead of the correct answer. Always flip the divisor (make 3 into 1/3) when converting division to multiplication.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why do I need to convert 0.4 to a fraction first?

Converting 0.4 to 4/10 makes the division much clearer! Working with fractions lets you use the flip-and-multiply rule easily, while dividing decimals by whole numbers can be confusing.

How do I know when to flip the second fraction?

You flip the second fraction (the divisor) every time you convert division to multiplication. So $3 = \frac{3}{1}$ becomes $\frac{1}{3}$ when you flip it!

Can I just use long division instead?

You could, but it's much harder! Long division with 0.4 ÷ 3 involves decimals and can be tricky. The fraction method is cleaner and less error-prone.

Why is my answer a fraction instead of a decimal?

Both forms are correct! $\frac{2}{15}$ equals approximately 0.133... The fraction form is often more precise than the rounded decimal.

How do I simplify the final fraction?

Look for common factors in the numerator and denominator. Here, $\frac{4}{30} = \frac{2 \times 2}{15 \times 2} = \frac{2}{15}$ after canceling the common factor of 2.

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