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
300-Word Explanation:
To convert 4.25 into a mixed number and an improper fraction, we first need to understand what the decimal 4.25 represents.
Step 1: Convert Decimal to Fraction
The decimal 4.25 means 4 wholes and 0.25 (which is one-quarter of a whole). So first, isolate the decimal part:
- 0.25 = 25/100
Next, simplify 25/100:
- Divide both numerator and denominator by 25: 25100=25÷25100÷25=14\frac{25}{100} = \frac{25 \div 25}{100 \div 25} = \frac{1}{4}
So, 4.25 = 4 + ¼ = 4 ¼ (this is the mixed number).
Step 2: Convert Mixed Number to Improper Fraction
Now convert 4 ¼ into an improper fraction.
A mixed number consists of a whole number and a fraction. To convert it:
- Multiply the whole number by the denominator of the fraction: 4×4=164 \times 4 = 16
- Add the numerator: 16+1=1716 + 1 = 17
- Keep the same denominator: 174\frac{17}{4}
So, 4 ¼ = 17/4 as an improper fraction.
Why Simplest Form Matters
Both 4 ¼ and 17/4 are already in their simplest form because:
- The fraction ¼ cannot be simplified further.
- The improper fraction 17/4 has no common factors between 17 and 4 other than 1.
Summary:
- Mixed Number: 4 ¼
- Improper Fraction: 17/4
These forms are helpful in different contexts: mixed numbers are easier to visualize quantities, while improper fractions are often used in math operations like multiplication or division.