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german
3 years ago
12

Simplify the expression 3/2 (5/3) -1 1/4 + 1/2 Given the answer as a simplified fraction. The simplified expression is a/b.

Mathematics
2 answers:
ella [17]3 years ago
8 0
<h2>Hello!</h2>

The answer is:

The simplified fraction is:

\frac{7}{4}

<h2>Why?</h2>

To solve this problem we must remember the following:

- Addition or subtraction of fractions, we add or subtract fractions by the following way:

\frac{a}{b}(+-)\frac{c}{d}=\frac{ad(+-)bc}{bd}

- Product of fractions, the multiplication of fraction is linear, meaning that we should multiply the numerator by the numerator and denominator by denominator, so:

\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}

- Convert mixed number to fraction,

a\frac{b}{c}=a+\frac{b}{c}=\frac{ac+b}{c}

So, solving we have:

\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}

\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}

Hence, the simplified fraction is:

\frac{7}{4}

Have a nice day!

Natalka [10]3 years ago
6 0

Answer:

a=7

b=4

Step-by-step explanation:

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