Convert Fraction to Decimal: Solving 6/15 Step-by-Step

Q: Why do I need to simplify the fraction first?

Simplifying makes the conversion much easier! Working with $ \frac{2}{5} $ instead of $ \frac{6}{15} $ gives you smaller, cleaner numbers to work with.

Q: How do I know what to divide by to simplify?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For 6 and 15, the GCD is 3, so divide both by 3: $ \frac{6÷3}{15÷3} = \frac{2}{5} $

Q: Why multiply by 2 to get a denominator of 10?

We want a power of 10 in the denominator (10, 100, 1000...) to easily convert to decimal. Since 5 × 2 = 10, we multiply both parts: $ \frac{2×2}{5×2} = \frac{4}{10} $

Q: How does the decimal point move?

When dividing by 10, move the decimal point one place left. So 4.0 ÷ 10 = 0.40 = 0.4. Each zero in the denominator moves the point one more place left.

Q: Can I use long division instead?

Absolutely! You can divide 6 ÷ 15 directly using long division. Both methods work, but the simplification method often gives cleaner calculations.

Q: Why does 0.40 equal 0.4?

Trailing zeros after the decimal don't change the value! $ 0.40 = 0.4 = 0.400 $ - they're all the same number. We usually drop trailing zeros for the simplest form.

Fraction Conversion with Simplification Steps

Convert into decimal form:

$\frac{6}{15}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's convert a fraction into a decimal.

00:09 First, simplify the fraction as much as you can.

00:13 Make sure you divide both the top and bottom numbers evenly.

00:17 Next, change the fraction to have 10 as the bottom number.

00:21 Multiply both top and bottom numbers to do this.

00:27 When the bottom number is 10, your top number is the decimal.

00:33 Remember, dividing by 10 moves the decimal point one spot to the left.

00:38 And that's how you find the decimal number!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into decimal form:

$\frac{6}{15}$

Step-by-step solution

Let's divide both the numerator and denominator by a number that will help us get a denominator of 5:

$\frac{6:3}{15:3}=\frac{2}{5}$

Now let's multiply both the numerator and denominator by a number that will help us get a denominator of 10:

$\frac{2\times2}{5\times2}=\frac{4}{10}$

Let's write the simple fraction as a decimal fraction:

$4.0$

Since we are dividing by 10, the decimal point will move one place to the left, so we get:

$.40$

Let's add the 0 before the decimal point as follows:

$0.40=0.4$

Final Answer

0.4

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify fractions first by dividing by GCD
Technique: Convert $\frac{6}{15}$ to $\frac{2}{5}$ then multiply by 2 for decimal
Check: Verify $\frac{4}{10} = 0.4$ by counting decimal places ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't convert $\frac{6}{15}$ directly to decimal = messy calculation! This makes the process harder and increases error chances. Always simplify to lowest terms like $\frac{2}{5}$ first, then convert.

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 simplify the fraction first?

Simplifying makes the conversion much easier! Working with $\frac{2}{5}$ instead of $\frac{6}{15}$ gives you smaller, cleaner numbers to work with.

How do I know what to divide by to simplify?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For 6 and 15, the GCD is 3, so divide both by 3: $\frac{6÷3}{15÷3} = \frac{2}{5}$

Why multiply by 2 to get a denominator of 10?

We want a power of 10 in the denominator (10, 100, 1000...) to easily convert to decimal. Since 5 × 2 = 10, we multiply both parts: $\frac{2×2}{5×2} = \frac{4}{10}$

How does the decimal point move?

When dividing by 10, move the decimal point one place left. So 4.0 ÷ 10 = 0.40 = 0.4. Each zero in the denominator moves the point one more place left.

Can I use long division instead?

Absolutely! You can divide 6 ÷ 15 directly using long division. Both methods work, but the simplification method often gives cleaner calculations.

Why does 0.40 equal 0.4?

Trailing zeros after the decimal don't change the value! $0.40 = 0.4 = 0.400$ - they're all the same number. We usually drop trailing zeros for the simplest form.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime