Convert 7.5 to a fraction in simplest form.
Understand the Problem
The question is asking us to convert the decimal 7.5 into a fraction and simplify it to its simplest form.
Answer
The simplest form of the fraction for the decimal 7.5 is $\frac{15}{2}$.
Answer for screen readers
The simplest form of the fraction for the decimal 7.5 is $\frac{15}{2}$.
Steps to Solve
- Write the Decimal as a Fraction
To convert the decimal 7.5 to a fraction, we can express it as:
$$ 7.5 = \frac{75}{10} $$
This is because 7.5 is the same as 75 tenths.
- Simplify the Fraction
Now we need to simplify the fraction $\frac{75}{10}$. We do this by finding the greatest common divisor (GCD) of the numerator (75) and the denominator (10).
The GCD of 75 and 10 is 5. Therefore, we divide both the numerator and the denominator by 5:
$$ \frac{75 \div 5}{10 \div 5} = \frac{15}{2} $$
- Final Fraction Form
Now we have simplified the fraction to its simplest form, which is:
$$ \frac{15}{2} $$
The simplest form of the fraction for the decimal 7.5 is $\frac{15}{2}$.
More Information
Converting decimals to fractions can help in various mathematical calculations, especially when working with rational numbers. Additionally, the ability to simplify fractions is crucial for further operations like addition and subtraction.
Tips
- Failing to identify the GCD correctly and thus not simplifying the fraction properly.
- Forgetting to write the fraction in its proper format when converting.