Convert Decimal Number: Express 15.2 in Different Forms

Q: How do I know when a fraction is fully simplified?

A fraction is simplified when the numerator and denominator share no common factors except 1. For $ \frac{2}{10} $, both numbers are divisible by 2, so divide: $ \frac{2÷2}{10÷2} = \frac{1}{5} $.

Q: Why can't I just write 15.2 as 152/10?

You could, but the question asks for a mixed number, not an improper fraction. Mixed numbers separate the whole part (15) from the fractional part ($ \frac{1}{5} $).

Q: What if the decimal has more places, like 15.25?

Same process! Write 0.25 as $ \frac{25}{100} $, then simplify by dividing by the GCD (25): $ \frac{25÷25}{100÷25} = \frac{1}{4} $. Answer: $ 15\frac{1}{4} $.

Q: Can I check my answer by converting back to decimal?

Absolutely! Convert $ 15\frac{1}{5} $ back: $ \frac{1}{5} = 0.2 $, so $ 15\frac{1}{5} = 15 + 0.2 = 15.2 $ ✓

Decimal to Mixed Number with Simplification

$15.2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed fraction

00:03 Break down the number into whole number and remainder

00:08 Convert the remainder to fraction

00:21 Reduce the fraction by dividing both numerator and denominator

00:27 Add to mixed fraction

00:32 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

$15.2=$

Step-by-step solution

To solve this problem, we'll convert the decimal number 15.2 into a mixed number:

Step 1: Identify the whole number: The number 15.2 has a whole part of 15.
Step 2: Convert the decimal part to a fraction:
The decimal 0.2 can be expressed as $\frac{2}{10}$ .
Step 3: Simplify the fraction:
The fraction $\frac{2}{10}$ simplifies to $\frac{1}{5}$ (dividing both numerator and denominator by 2).
Step 4: Form the mixed number:
Combine the whole number 15 with the simplified fraction $\frac{1}{5}$ to obtain the mixed number $15\frac{1}{5}$ .

Based on the provided choices, the correct answer is choice 2: $15\frac{1}{5}$ .

Final Answer

$15\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Separate whole number from decimal part (15 and 0.2)
Technique: Write decimal as fraction: 0.2 = $\frac{2}{10}$ then simplify
Check: Convert back to decimal: $15\frac{1}{5} = 15 + 0.2 = 15.2$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction part
Don't leave $15\frac{2}{10}$ as your final answer! This is not simplified and won't match answer choices. The fraction 2/10 reduces to 1/5 by dividing both numerator and denominator by their GCD of 2. Always simplify fractions to lowest terms.

Practice Quiz

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FAQ

Everything you need to know about this question

How do I know when a fraction is fully simplified?

A fraction is simplified when the numerator and denominator share no common factors except 1. For $\frac{2}{10}$ , both numbers are divisible by 2, so divide: $\frac{2÷2}{10÷2} = \frac{1}{5}$ .

Why can't I just write 15.2 as 152/10?

You could, but the question asks for a mixed number, not an improper fraction. Mixed numbers separate the whole part (15) from the fractional part ( $\frac{1}{5}$ ).

What if the decimal has more places, like 15.25?

Same process! Write 0.25 as $\frac{25}{100}$ , then simplify by dividing by the GCD (25): $\frac{25÷25}{100÷25} = \frac{1}{4}$ . Answer: $15\frac{1}{4}$ .

How do I find the GCD to simplify fractions?

List factors of both numbers and find the largest common one. For 2 and 10: factors of 2 are 1, 2 and factors of 10 are 1, 2, 5, 10. The greatest common factor is 2.

Can I check my answer by converting back to decimal?

Absolutely! Convert $15\frac{1}{5}$ back: $\frac{1}{5} = 0.2$ , so $15\frac{1}{5} = 15 + 0.2 = 15.2$ ✓

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