Convert Mixed Number to Decimal: Solving 5⅕

Q: Why can't I just write 5.15 since it's 5 and 1/5?

That's a common mistake! 1/5 is not the same as 0.15. You must actually divide: $ \frac{1}{5} = 1 ÷ 5 = 0.2 $. So $ 5\frac{1}{5} = 5.2 $, not 5.15.

Q: How do I convert any fraction to a decimal?

Divide the top number by the bottom number. For example: $ \frac{3}{4} = 3 ÷ 4 = 0.75 $. Use long division or a calculator if needed!

Q: What if the division doesn't come out evenly?

Some fractions create repeating decimals like $ \frac{1}{3} = 0.333... $ But $ \frac{1}{5} = 0.2 $ divides evenly, giving us a terminating decimal.

Q: Can I check my answer by converting back?

Yes! Convert 5.2 back: 5.2 = 5 + 0.2, and 0.2 = $ \frac{2}{10} = \frac{1}{5} $. So 5.2 = $ 5\frac{1}{5} $ ✓

Q: Why is this skill important?

Converting between mixed numbers and decimals helps with measurements, money problems, and comparing values. You'll use this in cooking, construction, and many real-world situations!

Mixed Number Conversion with Simple Fractions

$5\frac{1}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Break down to whole number and fraction

00:06 We want to convert fraction to decimal fraction, so we'll change the denominator to 10

00:09 Make sure to multiply both numerator and denominator

00:17 Convert fraction to decimal fraction

00:24 Add

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5\frac{1}{5}=$

Step-by-step solution

To solve this problem, we need to convert the mixed number $5\frac{1}{5}$ into a decimal form.

Here are the steps we'll follow:

Step 1: Convert the fractional part $\frac{1}{5}$ to a decimal.
Step 2: Add the converted decimal to the whole number part.

Let's work through these steps:
Step 1: Convert $\frac{1}{5}$ into a decimal:
To do this, divide the numerator (1) by the denominator (5). So, $\frac{1}{5} = 0.2$ .

Step 2: Add the decimal result to the whole number:
Now that we have converted the fraction to 0.2, we can add this to the integer part:
$5 + 0.2 = 5.2$ .

Therefore, the decimal equivalent of the mixed number $5\frac{1}{5}$ is $5.2$ .

Final Answer

$5.2$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fraction part to decimal, then add to whole number
Technique: Divide numerator by denominator: $\frac{1}{5} = 1 ÷ 5 = 0.2$
Check: Verify $5.2 = 5 + 0.2 = 5\frac{1}{5}$ by converting back ✓

Common Mistakes

Avoid these frequent errors

Adding the fraction's numerator and denominator to the whole number
Don't add 5 + 1 + 5 = 11! This treats the fraction parts as separate whole numbers instead of a single fraction. Always convert the fraction to decimal first: $\frac{1}{5} = 0.2$ , then add to get 5.2.

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

Why can't I just write 5.15 since it's 5 and 1/5?

That's a common mistake! 1/5 is not the same as 0.15. You must actually divide: $\frac{1}{5} = 1 ÷ 5 = 0.2$ . So $5\frac{1}{5} = 5.2$ , not 5.15.

How do I convert any fraction to a decimal?

Divide the top number by the bottom number. For example: $\frac{3}{4} = 3 ÷ 4 = 0.75$ . Use long division or a calculator if needed!

What if the division doesn't come out evenly?

Some fractions create repeating decimals like $\frac{1}{3} = 0.333...$ But $\frac{1}{5} = 0.2$ divides evenly, giving us a terminating decimal.

Can I check my answer by converting back?

Yes! Convert 5.2 back: 5.2 = 5 + 0.2, and 0.2 = $\frac{2}{10} = \frac{1}{5}$ . So 5.2 = $5\frac{1}{5}$ ✓

Why is this skill important?

Converting between mixed numbers and decimals helps with measurements, money problems, and comparing values. You'll use this in cooking, construction, and many real-world situations!

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