how do I solve (step by step)

Hi Lydia;

[z] /[3/4] = 4 1/4

We must isolate z.

We therefore must multiply by sides by 3/4...

([z]/[3/4])(3/4)=4 1/4(3/4)

z=4 1/4(3/4)

We have to solve.

We can begin by converting 4 1/4 into something easily multiplied by 3/4...

4 1/4=16/4 + 1/4=17/4

Plug-in 17/4....

z=17/4(3/4)

z=(17x3)/(4x4)=51/16

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There is another approach...

[z] /[3/4] = 4 1/4

Let's work with [z] /[3/4] only.

[z] /[3/4] = [z][4/3]

Do you understand? Because it is a double-division, it becomes a multiplier.

4/3 z = 4 1/4

Let's multiply both sides by 3/4

(3/4)(4/3)z=4 1/4 (3/4)

z=4 1/4 (3/4)

z=17/4 (3/4)=51/16