Convert 18.25 to a Simplified Fraction: Decimal to Fraction Exercise

Q: How do I know what denominator to use for the decimal part?

Count the decimal places! For 0.25, there are 2 decimal places, so use $ \frac{25}{100} $. For 3 decimal places, you'd use 1000 as the denominator.

Q: What if I can't find the GCD easily?

Start by dividing both numbers by obvious factors like 2, 5, or 10. For 25/100, both divide by 5 to get 5/20, then by 5 again to get $ \frac{1}{4} $!

Q: Why can't I just write 18.25 as 1825/100?

That would be an improper fraction, not a mixed number! The question asks for a mixed number, which separates the whole number (18) from the proper fraction ($ \frac{1}{4} $).

Q: How do I check if my mixed number is correct?

Convert back to decimal: $ 18\frac{1}{4} = 18 + \frac{1}{4} = 18 + 0.25 = 18.25 $. If it matches the original decimal, you're right!

Q: What does 'simplified' or 'lowest terms' mean?

Simplified means the numerator and denominator have no common factors except 1. So $ \frac{25}{100} $ simplifies to $ \frac{1}{4} $ because 25 and 100 both divide by 25.

Decimal to Mixed Number with Simplification

Convert into a mixed fraction:

$18.25$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's write this as a simple fraction.

00:08 Divide each number after the decimal by its place value.

00:13 Add the correct denominator.

00:16 Don't forget to add 18 to your total.

00:28 Reduce the fraction. Divide both the top and bottom as much as you can.

00:43 And there you have it! That's the answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into a mixed fraction:

$18.25$

Step-by-step solution

Let's write the decimal fraction as a mixed fraction.

Since there are 2 digits after the decimal point, we'll divide 25 by 100 and add 18, as follows:

$18+\frac{25}{100}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 25:

$18+\frac{25:25}{100:25}=18+\frac{1}{4}=18\frac{1}{4}$

Final Answer

$18\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Use place value to create fraction then simplify completely
Technique: Convert 0.25 to 25/100, then divide by GCD of 25
Check: Convert back: 18¼ = 18 + 0.25 = 18.25 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fractional part
Don't leave 25/100 unsimplified = wrong final answer like 18 25/100! This fraction isn't in lowest terms and looks messy. Always find the GCD and divide both numerator and denominator to get the simplest form like 1/4.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

How do I know what denominator to use for the decimal part?

Count the decimal places! For 0.25, there are 2 decimal places, so use $\frac{25}{100}$ . For 3 decimal places, you'd use 1000 as the denominator.

What if I can't find the GCD easily?

Start by dividing both numbers by obvious factors like 2, 5, or 10. For 25/100, both divide by 5 to get 5/20, then by 5 again to get $\frac{1}{4}$ !

Why can't I just write 18.25 as 1825/100?

That would be an improper fraction, not a mixed number! The question asks for a mixed number, which separates the whole number (18) from the proper fraction ( $\frac{1}{4}$ ).

How do I check if my mixed number is correct?

Convert back to decimal: $18\frac{1}{4} = 18 + \frac{1}{4} = 18 + 0.25 = 18.25$ . If it matches the original decimal, you're right!

What does 'simplified' or 'lowest terms' mean?

Simplified means the numerator and denominator have no common factors except 1. So $\frac{25}{100}$ simplifies to $\frac{1}{4}$ because 25 and 100 both divide by 25.

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