Question

Match each of the following expressions to an equivalent expression shown in the bins below.Consider each of the expressions in blue to be as you would type them into a typical calculator.

Answer 1

Given:

`xy\/z,(x\/y)z,xy\/z,x\/(yz),x\/y\/z.`

Required:

We need to find

`(xy)/(z),(x)/(yz),(xz)/(y)`

Step-by-step explanation:

We know that

`(xy)/(z)=xy\/z`
`(x)/(yz)=x\/(yz)`
`(xz)/(y)=xz\/y`
`We\text{ know that \lparen x/y\rparen z=xz/y}`
`(xz)/(y)\(=(x/y)\)z`
`We\text{ know that x/y/z=}(x)/((y)/(z))=((x)/(y))\/z=(x\/y)/(z)=(x)/(y)*(1)/(z)=(x)/(yz)`
`(x)/(yz)\(=x/y\/\)z`

By the typical calculator rule, first, we need to do division before multiplication.

`x\/yz=(x)/(y)z=(xz)/(y)`

Final answer:

`(xy)/(z)=xy\/z`

`(x)/(yz)=x\/(yz)\text{and }x\/y\/z\text{ }`

`(xz)/(y)\(=(x/y)\)z\text{ and }x\/yz`