Question

I need help the second problem I don’t get this concept?

Answer 1

In general,

`(a)/(b)+(c)/(d)=(ad+bc)/(bd)`

In our case,

`(3)/(4)+(1)/(8)=(3*8+1*4)/(4*8)=(24+4)/(32)=(28)/(32)`

Simplifying,

`\begin{gathered} (28)/(32)=(4*7)/(4*8)=(4)/(4)*(7)/(8)=1*(7)/(8)=(7)/(8) \\ \Rightarrow(3)/(4)+(1)/(8)=(7)/(8) \end{gathered}`

The simplified answer is 7/8.

a) Given

`(1)/(2)+(2)/(3)+(9)/(2)`

Notice that

`(1)/(2)+(2)/(3)+(2)/(9)=((1)/(2)+(2)/(3))+(2)/(9)`

First, calculate the term between parentheses

`(1)/(2)+(2)/(3)=(1*3+2*2)/(2*3)=(3+4)/(6)=(7)/(6)`

Then,

`\begin{gathered} \Rightarrow(1)/(2)+(2)/(3)+(2)/(9)=(7)/(6)+(2)/(9)=(7*9+2*6)/(6*9)=(63+12)/(54)=(75)/(54) \\ \Rightarrow(1)/(2)+(2)/(3)+(2)/(9)=(75)/(54) \end{gathered}`

Simplifying,

`\begin{gathered} (75)/(54)=(3*25)/(3*18)=(25)/(18) \\ \Rightarrow(1)/(2)+(2)/(3)+(2)/(9)=(25)/(18) \end{gathered}`

The answer to (a) is 25/18

(b)

`\begin{gathered} (2)/(3)*(42)/(5)*(10)/(7)=((2)/(3)*(42)/(5))*(10)/(7)=((2*42)/(3*5))*(10)/(7)=(84)/(15)*(10)/(7)=(840)/(105)=8 \\ \Rightarrow(2)/(3)*(42)/(5)*(10)/(7)=8 \end{gathered}`

The answer to part (b) is 8.