Write 2.25 as a mixed number and as an improper fraction. write your answers in simplest form.
The Correct Answer and Explanation is :
To convert the decimal 2.25 into a mixed number and an improper fraction, we can follow a systematic approach.
Step 1: Understanding Mixed Numbers and Improper Fractions
A mixed number consists of a whole number and a proper fraction. An improper fraction has a numerator that is greater than or equal to the denominator. Both forms represent the same value, but they express it differently.
Step 2: Converting 2.25 to a Mixed Number
- Identify the whole number part: The number 2.25 has a whole number part of 2.
- Identify the fractional part: The decimal .25 can be converted to a fraction. Since .25 means 25 hundredths, it can be written as:
[
\frac{25}{100}
] - Simplify the fraction: To simplify (\frac{25}{100}), we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 25:
[
\frac{25 \div 25}{100 \div 25} = \frac{1}{4}
] - Combine into a mixed number: Thus, 2.25 can be expressed as:
[
2 \frac{1}{4}
]
Step 3: Converting 2.25 to an Improper Fraction
- Convert the mixed number to an improper fraction: To convert (2 \frac{1}{4}) into an improper fraction, multiply the whole number (2) by the denominator (4) and add the numerator (1):
[
2 \times 4 + 1 = 8 + 1 = 9
]
So, we have:
[
\frac{9}{4}
]
Summary of Answers
- As a mixed number, 2.25 is (2 \frac{1}{4}).
- As an improper fraction, 2.25 is (\frac{9}{4}).
Both forms are in their simplest state. Understanding these conversions enhances mathematical fluency, allowing one to easily switch between different numerical representations based on the context or requirement.