Multiply.
$4 \frac{1}{2} \times \frac{3}{5}$
Write your answer as a mixed number in simplest form.
The problem requires computing the product of a mixed number and a fraction: \(4 \frac{1}{2} \times \frac{3}{5}\). To solve this, we first convert the mixed number to an improper fraction to simplify the multiplication process, then perform the multiplication of the numerators and denominators, and finally convert the resulting improper fraction back into a mixed number.
To convert \(4 \frac{1}{2}\) into an improper fraction, we multiply the whole number by the denominator and add the numerator:
\[4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}.\]
Now we multiply the two fractions:
\[\frac{9}{2} \times \frac{3}{5} = \frac{9 \times 3}{2 \times 5} = \frac{27}{10}.\]
To convert the improper fraction \(\frac{27}{10}\) back into a mixed number, we divide the numerator 27 by the denominator 10. Since \(27 = 2 \times 10 + 7\), the quotient is 2 and the remainder is 7. Thus, the mixed number is \(2 \frac{7}{10}\). Since the greatest common divisor of 7 and 10 is 1, the fraction is already in its simplest form. The final result is \(2 \frac{7}{10}\).
If you are baking and a recipe calls for \(4 \frac{1}{2}\) cups of flour, but you only want to make \(\frac{3}{5}\) of the recipe, you need to multiply the amount of flour by the factor \(\frac{3}{5}\). This calculation helps you determine the exact amount of flour to use, ensuring your baked goods come out perfect every time. Understanding how to handle mixed numbers and fractions is essential for scaling measurements in cooking, construction, and design.