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

how do I solve (step by step)

### 2 Answers by Expert Tutors

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
1
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
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
Z / (3/4 ) = 4 1/4

Just multiply both sides by 3/4  ( cross multiplication).

z = 3/4 * 4 1/4

Z = 3/4 * 17/4 = 51/16 = 3 3/16 = 3. 1875