What is half of 4 and 3/4?
Understand the Problem
The question is asking to find half of the number 4 and 3/4. To solve it, we will first convert 4 and 3/4 into an improper fraction and then divide by 2.
Answer
The answer is $\frac{19}{8}$ or $2 \frac{3}{8}$.
Answer for screen readers
The final answer is $\frac{19}{8}$ or $2 \frac{3}{8}$.
Steps to Solve
- Convert the mixed number to an improper fraction
To convert the mixed number $4 \frac{3}{4}$ into an improper fraction, we multiply the whole number by the denominator and add the numerator.
$$ 4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} $$
- Divide the improper fraction by 2
Next, we need to divide the improper fraction $\frac{19}{4}$ by 2. Dividing by a number is the same as multiplying by its reciprocal. Therefore, we multiply by $\frac{1}{2}$.
$$ \frac{19}{4} \div 2 = \frac{19}{4} \times \frac{1}{2} = \frac{19 \times 1}{4 \times 2} = \frac{19}{8} $$
- Convert the improper fraction back to a mixed number (if needed)
If necessary, we can convert $\frac{19}{8}$ back to a mixed number. To do this, we divide 19 by 8.
$$ 19 \div 8 = 2 \quad \text{(remainder 3)} $$
Thus, we can write:
$$ \frac{19}{8} = 2 \frac{3}{8} $$
The final answer is $\frac{19}{8}$ or $2 \frac{3}{8}$.
More Information
Finding half of a mixed number often involves converting it into an improper fraction. Once it's in that form, dividing by 2 is straightforward and helps in understanding the relationship between mixed numbers and improper fractions.
Tips
- Forgetting to convert the mixed number into an improper fraction can lead to incorrect answers.
- Confusing the order of operations, especially when dealing with fractions and whole numbers.
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