Convert 20.5 to Simplified Fraction: Decimal to Reduced Form

Question

Write 20.5 as a fraction and reduce.

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

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 $20\frac{1}{2}$ .

$20\frac{1}{2}$