Convert 20.5 to Simplified Fraction: Decimal to Reduced Form

Q: Why do I separate the whole number from the decimal?

Mixed numbers show whole parts separately from fractional parts. This makes it easier to see that 20.5 means 20 complete units plus half of another unit.

Q: How do I know if my fraction is fully simplified?

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

Q: Can I write this as an improper fraction instead?

Yes! $ 20\frac{1}{2} $ equals $ \frac{41}{2} $ (multiply: 20 × 2 + 1 = 41). Both forms are correct, but mixed numbers are often preferred for this type of problem.

Q: What if the decimal has more than one digit?

Use the same process! For example, 0.75 = $ \frac{75}{100} $. Then find the GCD of 75 and 100 (which is 25) and divide: $ \frac{75÷25}{100÷25} = \frac{3}{4} $

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

Convert it back to decimal: $ 20\frac{1}{2} $ means 20 + $ \frac{1}{2} $ = 20 + 0.5 = 20.5 ✓. If it matches your original decimal, you're right!

Mixed Numbers with Decimal Conversion

Write 20.5 as a fraction and reduce.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple and reduced fraction

00:04 Break down the number into whole number and remainder

00:12 Convert the remainder to a fraction

00:15 Place the digits in the numerator

00:18 Move the decimal point right until the number becomes whole and not decimal

00:22 We moved once, therefore the denominator will be equal to 10

00:33 Now let's reduce as much as possible

00:36 Factor 10 into factors of 5 and 2

00:40 Reduce what is possible

00:48 Combine into a complex fraction

00:51 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

Write 20.5 as a fraction and reduce.

Step-by-step solution

To solve the problem of expressing $20.5$ as a fraction and simplifying, we will follow these steps:

Step 1: Recognize the whole number part: $20$ .
Step 2: Convert the decimal $0.5$ to a fraction. Since $0.5 = \frac{5}{10}$ , and dividing the numerator and denominator by their GCD, 5, gives $\frac{1}{2}$ .
Step 3: Combine the whole number and the fraction: $20 \frac{1}{2}$ , which is read as $20$ and $\frac{1}{2}$ .

Hence, the number $20.5$ as a fraction is $20\frac{1}{2}$ .

Therefore, the solution to the problem is $20\frac{1}{2}$ .

Final Answer

$20\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Whole and Decimal Parts: Separate 20.5 into whole number 20 and decimal 0.5
Fraction Conversion: Convert 0.5 to $\frac{5}{10}$ , then simplify to $\frac{1}{2}$
Check Simplification: Verify $20\frac{1}{2} = 20.5$ by converting back ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the decimal fraction to lowest terms
Don't write $20\frac{5}{10}$ as your final answer = not fully reduced! This leaves common factors in numerator and denominator. Always divide both by their GCD (5) to get $20\frac{1}{2}$ .

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I separate the whole number from the decimal?

Mixed numbers show whole parts separately from fractional parts. This makes it easier to see that 20.5 means 20 complete units plus half of another unit.

How do I know if my fraction is fully simplified?

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

Can I write this as an improper fraction instead?

Yes! $20\frac{1}{2}$ equals $\frac{41}{2}$ (multiply: 20 × 2 + 1 = 41). Both forms are correct, but mixed numbers are often preferred for this type of problem.

What if the decimal has more than one digit?

Use the same process! For example, 0.75 = $\frac{75}{100}$ . Then find the GCD of 75 and 100 (which is 25) and divide: $\frac{75÷25}{100÷25} = \frac{3}{4}$

How can I check if my mixed number is correct?

Convert it back to decimal: $20\frac{1}{2}$ means 20 + $\frac{1}{2}$ = 20 + 0.5 = 20.5 ✓. If it matches your original decimal, you're right!

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