5.25 as a fraction in simplest form

Steps to Solve

1. Convert the Decimal to a Fraction

To convert the decimal number $5.25$ into a fraction, we recognize it as $5.25 = 5 + 0.25$.

We can convert $0.25$ into a fraction:

$$ 0.25 = \frac{25}{100} $$

So the entire number becomes:

$$ 5.25 = 5 + \frac{25}{100} $$

2. Express the Whole Number as a Fraction

Next, we can express the whole number $5$ as a fraction with a denominator of $1$:

$$ 5 = \frac{5}{1} $$

Now, we can add the two fractions:

$$ 5.25 = \frac{5}{1} + \frac{25}{100} $$

3. Finding a Common Denominator

To add these fractions, we need a common denominator. The common denominator between $1$ and $100$ is $100$. So, we convert $\frac{5}{1}$:

$$ \frac{5}{1} = \frac{5 \times 100}{1 \times 100} = \frac{500}{100} $$

Now we can add the fractions:

$$ 5.25 = \frac{500}{100} + \frac{25}{100} = \frac{500 + 25}{100} = \frac{525}{100} $$

4. Simplify the Fraction

Finally, we simplify the fraction $\frac{525}{100}$.

To simplify, we need to find the greatest common divisor (GCD) of $525$ and $100$. The GCD is $25$:

$$ \frac{525 \div 25}{100 \div 25} = \frac{21}{4} $$

So, the simplest form of the fraction is $\frac{21}{4}$.