Write 4.25 as a mixed number and as an improper fraction. Write your answers in simplest form.
The Correct Answer and Explanation is:
Correct Answer:
- Mixed number: 4 ¼
- Improper fraction: 17/4
Explanation (300 words):
To convert 4.25 to both a mixed number and an improper fraction, we need to understand the place value of the decimal and how to represent it as a fraction.
Step 1: Understand the Decimal
The decimal 4.25 means 4 whole units and 25 hundredths. In other words: 4.25=4+0.254.25 = 4 + 0.25
Now we focus on converting the 0.25 portion to a fraction.
Step 2: Convert 0.25 to a Fraction
0.25=251000.25 = \frac{25}{100}
To simplify this fraction, divide both the numerator and denominator by their greatest common factor (GCF), which is 25: 25÷25100÷25=14\frac{25 \div 25}{100 \div 25} = \frac{1}{4}
So, 4.25=4+14=4144.25 = 4 + \frac{1}{4} = 4\frac{1}{4}
This is the mixed number form.
Step 3: Convert Mixed Number to Improper Fraction
A mixed number like 4144\frac{1}{4} has a whole number and a fraction. To convert it to an improper fraction, follow these steps:
- Multiply the whole number by the denominator:
4×4=164 \times 4 = 16 - Add the numerator:
16+1=1716 + 1 = 17 - Keep the same denominator: 174\frac{17}{4}
So, 414=1744\frac{1}{4} = \frac{17}{4}
Final Answers:
- Mixed number: 414\boxed{4\frac{1}{4}}
- Improper fraction: 174\boxed{\frac{17}{4}}
These are in simplest form, as the fraction 14\frac{1}{4} cannot be simplified further and 174\frac{17}{4} is already reduced