4.25 as a fraction in simplest form
Understand the Problem
The question is asking to convert the decimal number 4.25 into a fraction and simplify it to its simplest form. To solve this, we will convert the decimal to a fraction by recognizing that 4.25 is equal to 4 + 0.25, which can be expressed as 4 + 25/100. Then we will simplify the resulting fraction.
Answer
The decimal 4.25 as a simplified fraction is $\frac{17}{4}$.
Answer for screen readers
The final answer for the decimal 4.25 expressed as a simplified fraction is $\frac{17}{4}$.
Steps to Solve
- Convert the Decimal to a Fraction
The decimal 4.25 can be split as follows:
$$ 4.25 = 4 + 0.25 $$
We can express 0.25 as a fraction:
$$ 0.25 = \frac{25}{100} $$
So we can rewrite the whole number as:
$$ 4.25 = 4 + \frac{25}{100} $$
- Express as a Fraction
Now we need to convert the whole number 4 into a fraction. We can express 4 as:
$$ 4 = \frac{4 \times 100}{100} = \frac{400}{100} $$
So now we have two fractions:
$$ 4.25 = \frac{400}{100} + \frac{25}{100} $$
Combining the two fractions:
$$ 4.25 = \frac{400 + 25}{100} = \frac{425}{100} $$
- Simplify the Fraction
Next, we simplify the fraction $\frac{425}{100}$. To do this, we find the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 425 and 100 is 25.
Now, we divide both the numerator and denominator by 25:
$$ \frac{425 \div 25}{100 \div 25} = \frac{17}{4} $$
The final answer for the decimal 4.25 expressed as a simplified fraction is $\frac{17}{4}$.
More Information
The fraction $\frac{17}{4}$ is an improper fraction. This means that the numerator is larger than the denominator. If needed, it can also be converted back to a mixed number as $4 \frac{1}{4}$.
Tips
- Failing to find the GCD correctly may lead to incorrect simplification.
- Forgetting to convert whole numbers properly into fractions can cause confusion.