Question

Solve each proportion and give the answer in simplest form 1. 6:8= n: 12 2. 2/7 = 8/n 3. n/6= 11/3 4. 4:n = 6:9

Answer 1

The first proportion:

`6\colon8=n\colon12`

can be written like this:

`(6)/(8)=(n)/(12)`

then, we have the following:

`\begin{gathered} (6)/(8)=(n)/(12) \\ \Rightarrow n=((6)/(8))\cdot12=(72)/(8)=9 \\ n=9 \end{gathered}`

For the next proportions, we have the following:

`\begin{gathered} (2)/(7)=(8)/(n) \\ \Rightarrow n=(8)/((2)/(7))=(8\cdot7)/(2)=(56)/(2)=23 \end{gathered}`
`\begin{gathered} (n)/(6)=(11)/(3) \\ \Rightarrow n=(11)/(3)\cdot6=(66)/(3)=22 \end{gathered}`

and finally:

`\begin{gathered} (4)/(n)=(6)/(9) \\ \Rightarrow n=(4)/((6)/(9))=(4\cdot9)/(6)=(36)/(6)=6 \end{gathered}`