Question

1. simplify if necessary.

$4\frac{1}{2} \times 1\frac{3}{5}$
type a response

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(4\frac{1}{2}\) to an improper fraction, we multiply the whole number \(4\) by the denominator \(2\) and add the numerator \(1\). So, \(4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2}\).

To convert \(1\frac{3}{5}\) to an improper fraction, we multiply the whole number \(1\) by the denominator \(5\) and add the numerator \(3\). So, \(1\frac{3}{5}=\frac{1\times5+3}{5}=\frac{8}{5}\).

Step2: Multiply the improper fractions

Now we multiply \(\frac{9}{2}\) and \(\frac{8}{5}\). When multiplying fractions, we multiply the numerators together and the denominators together. So, \(\frac{9}{2}\times\frac{8}{5}=\frac{9\times8}{2\times5}=\frac{72}{10}\).

Step3: Simplify the fraction

We can simplify \(\frac{72}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\). So, \(\frac{72\div2}{10\div2}=\frac{36}{5}\). We can also convert this improper fraction to a mixed number, but \(\frac{36}{5}\) or \(7\frac{1}{5}\) (since \(36\div5 = 7\) with a remainder of \(1\)) are both simplified forms. However, \(\frac{36}{5}=7.2\) as a decimal, but the fraction form is more appropriate here. Wait, actually, let's check the multiplication again. Wait, \(9\times8 = 72\) and \(2\times5=10\), then \(\frac{72}{10}\) simplifies to \(\frac{36}{5}\) or \(7\frac{1}{5}\). Wait, but let's do the multiplication again. Wait, \(4\frac{1}{2}\) is \(\frac{9}{2}\) and \(1\frac{3}{5}\) is \(\frac{8}{5}\). Then \(\frac{9}{2}\times\frac{8}{5}=\frac{9\times8}{2\times5}=\frac{72}{10}\). Now, \(\frac{72}{10}\) can be simplified by dividing numerator and denominator by \(2\) to get \(\frac{36}{5}\), which is equal to \(7\frac{1}{5}\) (because \(5\times7 = 35\), and \(36-35 = 1\)).

Answer:

\(7\frac{1}{5}\) (or \(\frac{36}{5}\) or \(7.2\))