Question

1. simplify if necessary.

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

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(2\frac{1}{2}\) can be converted to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{1}{2}\), we have \(a = 2\), \(b=1\), \(c = 2\). Then \(\frac{2\times2+ 1}{2}=\frac{4 + 1}{2}=\frac{5}{2}\).

Step2: Multiply the two fractions

Now we multiply \(\frac{5}{2}\) by \(\frac{3}{5}\). When multiplying fractions, we multiply the numerators together and the denominators together, i.e., \(\frac{5}{2}\times\frac{3}{5}=\frac{5\times3}{2\times5}\).

Step3: Simplify the fraction

We can cancel out the common factor of 5 in the numerator and the denominator. So \(\frac{5\times3}{2\times5}=\frac{3}{2}\) (the 5s cancel) and \(\frac{3}{2}=1\frac{1}{2}\) or as an improper fraction it can also be simplified to \(\frac{3}{2}\), but if we want a mixed number or a simplified fraction, \(\frac{3}{2}\) is equal to \(1\frac{1}{2}\), but let's check the multiplication again. Wait, \(\frac{5}{2}\times\frac{3}{5}=\frac{15}{10}=\frac{3}{2}=1.5\) or \(1\frac{1}{2}\). But also, we can see that 5 in the numerator of the first fraction and 5 in the denominator of the second fraction cancel, leaving \(\frac{3}{2}\) which is \(1\frac{1}{2}\), but actually, \(\frac{5}{2}\times\frac{3}{5}=\frac{3}{2}=1\frac{1}{2}\), but let's do it step by step. \(\frac{5\times3}{2\times5}=\frac{15}{10}\), then divide numerator and denominator by 5, we get \(\frac{3}{2}\), which is \(1\frac{1}{2}\), but also, \(\frac{3}{2}\) can be written as \(1.5\), but the simplest form is \(\frac{3}{2}\) or \(1\frac{1}{2}\). Wait, but actually, when we multiply \(\frac{5}{2}\times\frac{3}{5}\), the 5s cancel, so we have \(\frac{3}{2}\), which is \(1\frac{1}{2}\), but let's check the value. \(2\frac{1}{2}\) is 2.5, and \(\frac{3}{5}\) is 0.6, and \(2.5\times0.6 = 1.5\), which is \(\frac{3}{2}\) or \(1\frac{1}{2}\).

Answer:

\(\frac{3}{2}\) (or \(1\frac{1}{2}\))