Respuesta :
Hello!
The answer is:
The simplified fraction is:
[tex]\frac{7}{4}[/tex]
Why?
To solve this problem we must remember the following:
- Addition or subtraction of fractions, we add or subtract fractions by the following way:
[tex]\frac{a}{b}(+-)\frac{c}{d}=\frac{ad(+-)bc}{bd}[/tex]
- Product of fractions, the multiplication of fraction is linear, meaning that we should multiply the numerator by the numerator and denominator by denominator, so:
[tex]\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}[/tex]
- Convert mixed number to fraction,
[tex]a\frac{b}{c}=a+\frac{b}{c}=\frac{ac+b}{c}[/tex]
So, solving we have:
[tex]\frac{3}{2}*\frac{5}{3}-1\frac{1}{4}+\frac{1}{2}=\frac{3*5}{2*3} -1\frac{1}{4}+\frac{1}{2}\\\\\frac{3*5}{2*3} -1\frac{1}{4}+\frac{1}{2}=\frac{15}{6} -1\frac{1}{4}+\frac{1}{2}\\\\\frac{15}{6} -1\frac{1}{4}+\frac{1}{2}=\frac{15}{6} -(1+\frac{1}{4})+\frac{1}{2}\\\\\frac{15}{6} -(1+\frac{1}{4})+\frac{1}{2}=\frac{15}{6}-(\frac{4+1}{1*4})+\frac{1}{2}\\\\\frac{15}{6}-(\frac{4+1}{4})+\frac{1}{2}=\frac{15}{6}-\frac{5}{4}+\frac{1}{2}[/tex]
[tex]\frac{15}{6}-\frac{5}{4}+\frac{1}{2}=(\frac{5}{2}-\frac{5}{4})+\frac{1}{2}\\\\(\frac{5}{2}-\frac{5}{4})+\frac{1}{2}=(\frac{(4*5)-(2*5)}{8})+\frac{1}{2}\\\\(\frac{(4*5)-(2*5)}{8})+\frac{1}{2}=(\frac{20-10}{8})+\frac{1}{2}\\\\(\frac{20-10}{8})+\frac{1}{2}=(\frac{10}{8})+\frac{1}{2}\\\\(\frac{10}{8})+\frac{1}{2}=\frac{5}{4}+\frac{1}{2}\\\\\frac{5}{4}+\frac{1}{2}=\frac{(5*2)+(4*1)}{2*4}\\\\\frac{(5*2)+(4*1)}{2*4}=\frac{10+4}{8}=\frac{14}{8}\\\\\frac{14}{8}=\frac{7}{4}[/tex]
Hence, the simplified fraction is:
[tex]\frac{7}{4}[/tex]
Have a nice day!
