Convert Mixed Number 3½ to Decimal: Step-by-Step Solution

Q: Why can't I just add the numerator to the whole number?

Because that's not how mixed numbers work! The fraction $ \frac{1}{2} $ represents half of one whole unit, not just the number 1. You must convert it to its decimal value first.

Q: How do I convert fractions with other denominators?

Divide the numerator by the denominator! For example: $ \frac{3}{4} = 3 ÷ 4 = 0.75 $. Some fractions create repeating decimals, which is normal.

Q: What if I get a long decimal when dividing?

That's okay! Some fractions like $ \frac{1}{3} = 0.333... $ create repeating patterns. You can round to a reasonable number of decimal places if needed.

Q: Can I convert the whole thing to an improper fraction instead?

Yes! $ 3\frac{1}{2} = \frac{7}{2} = 3.5 $. Multiply whole number by denominator, add numerator: $ \frac{(3×2)+1}{2} = \frac{7}{2} $.

Q: How do I check if my decimal answer is correct?

Convert your decimal back to a mixed number! 3.5 = 3 + 0.5 = 3 + ½. If you get the original mixed number, you're right!

Mixed Number Conversions with Common Fractions

$3\frac{1}{2}=$

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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 into whole number and fraction

00:08 Convert from whole number to proper fraction

00:20 Add with common denominator

00:27 Change the fraction so denominator is 10

00:30 Make sure to multiply both numerator and denominator

00:34 Convert from fraction to decimal fraction

00:42 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

$3\frac{1}{2}=$

Step-by-step solution

To solve this problem, we’ll convert the mixed number $3 \frac{1}{2}$ to a decimal:

Step 1: Convert the fraction $\frac{1}{2}$ into a decimal.

A fraction with a denominator of 2 can be converted to a decimal by finding an equivalent value. $\frac{1}{2}$ is equivalent to 0.5, as 1 divided by 2 is 0.5.

Step 2: Add the decimal equivalent of the fraction part to the whole number.

This means adding 0.5 to the whole number 3, resulting in $3 + 0.5 = 3.5$ .

Therefore, the solution to the problem is $3.5$ .

Final Answer

$3.5$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fraction part to decimal first, then add to whole
Technique: $\frac{1}{2} = 1 ÷ 2 = 0.5$ , then 3 + 0.5
Check: Verify $3.5 = 3\frac{1}{2}$ by converting back: 0.5 = ½ ✓

Common Mistakes

Avoid these frequent errors

Adding the numerator directly to the whole number
Don't add 3 + 1 = 4 and ignore the denominator! This gives you a completely wrong answer because you're not actually converting the fraction. Always convert the fraction part (1/2) to a decimal (0.5) first, then add to the whole number.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why can't I just add the numerator to the whole number?

Because that's not how mixed numbers work! The fraction $\frac{1}{2}$ represents half of one whole unit, not just the number 1. You must convert it to its decimal value first.

How do I convert fractions with other denominators?

Divide the numerator by the denominator! For example: $\frac{3}{4} = 3 ÷ 4 = 0.75$ . Some fractions create repeating decimals, which is normal.

What if I get a long decimal when dividing?

That's okay! Some fractions like $\frac{1}{3} = 0.333...$ create repeating patterns. You can round to a reasonable number of decimal places if needed.

Can I convert the whole thing to an improper fraction instead?

Yes! $3\frac{1}{2} = \frac{7}{2} = 3.5$ . Multiply whole number by denominator, add numerator: $\frac{(3×2)+1}{2} = \frac{7}{2}$ .

How do I check if my decimal answer is correct?

Convert your decimal back to a mixed number! 3.5 = 3 + 0.5 = 3 + ½. If you get the original mixed number, you're right!

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