Question

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.

Answer 1

a=7

b=4

Explanation:

Answer 2

Hello!

The answer is:

The simplified fraction is:

`(7)/(4)`

Why?

To solve this problem we must remember the following:

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

`(a)/(b)(+-)(c)/(d)=(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:

`(a)/(b)*(c)/(d)=(ac)/(bd)`

- Convert mixed number to fraction,

`a(b)/(c)=a+(b)/(c)=(ac+b)/(c)`

So, solving we have:

`(3)/(2)*(5)/(3)-1(1)/(4)+(1)/(2)=(3*5)/(2*3) -1(1)/(4)+(1)/(2)\\\\(3*5)/(2*3) -1(1)/(4)+(1)/(2)=(15)/(6) -1(1)/(4)+(1)/(2)\\\\(15)/(6) -1(1)/(4)+(1)/(2)=(15)/(6) -(1+(1)/(4))+(1)/(2)\\\\(15)/(6) -(1+(1)/(4))+(1)/(2)=(15)/(6)-((4+1)/(1*4))+(1)/(2)\\\\(15)/(6)-((4+1)/(4))+(1)/(2)=(15)/(6)-(5)/(4)+(1)/(2)`

`(15)/(6)-(5)/(4)+(1)/(2)=((5)/(2)-(5)/(4))+(1)/(2)\\\\((5)/(2)-(5)/(4))+(1)/(2)=(((4*5)-(2*5))/(8))+(1)/(2)\\\\(((4*5)-(2*5))/(8))+(1)/(2)=((20-10)/(8))+(1)/(2)\\\\((20-10)/(8))+(1)/(2)=((10)/(8))+(1)/(2)\\\\((10)/(8))+(1)/(2)=(5)/(4)+(1)/(2)\\\\(5)/(4)+(1)/(2)=((5*2)+(4*1))/(2*4)\\\\((5*2)+(4*1))/(2*4)=(10+4)/(8)=(14)/(8)\\\\(14)/(8)=(7)/(4)`

Hence, the simplified fraction is:

`(7)/(4)`

Have a nice day!