What is half of 4 3/4?

Steps to Solve

1. Convert the mixed number to an improper fraction

To convert the mixed number ( 4 \frac{3}{4} ) to an improper fraction, we use the formula:

$$ \text{Improper Fraction} = \left(\text{whole number} \times \text{denominator} + \text{numerator}\right) / \text{denominator} $$

For ( 4 \frac{3}{4} ):

• Whole number = 4
• Numerator = 3
• Denominator = 4

Calculating this gives:

$$ \text{Improper Fraction} = \left(4 \times 4 + 3\right) / 4 = \left(16 + 3\right) / 4 = \frac{19}{4} $$

2. Divide the improper fraction by 2

Now, we need to divide the improper fraction ( \frac{19}{4} ) by 2. Dividing by a whole number is the same as multiplying by its reciprocal. The reciprocal of 2 is ( \frac{1}{2} ).

So we have:

$$ \frac{19}{4} \div 2 = \frac{19}{4} \times \frac{1}{2} $$

3. Simplify the multiplication

Now multiply the fractions:

$$ \frac{19 \times 1}{4 \times 2} = \frac{19}{8} $$

Thus, ( \frac{19}{8} ) is our answer in improper fraction form.

4. Convert back to a mixed number (optional)

If needed, we convert ( \frac{19}{8} ) back to a mixed number:

Divide ( 19 ) by ( 8 ):

The quotient is ( 2 ) and the remainder is ( 3 ).

Thus, we can write:

$$ \frac{19}{8} = 2 \frac{3}{8} $$