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The question states that z divided by 8, or z/8 has a remainder of 5. That means that 8 goes into z 5 times, but has a remainder of 5, meaning that 8*5+5=z=45. To find 4z, we multiply 45 by 4 to get 180. Next, we use long division to divide that by 8.

     22
   ______
8 | 180
     -160
     ____
       20
       -16
       ___
          4. This can be done due to that 8 does not go into 1, but 8*2=16, and 8*3=24. Keep in mind that since 8 doesn't go into 1, the 1 moves over with the 8 to form 18. Next, we have 18-16=2, and we add a 0 at the end because 180 has 3 digits. We repeat the process for 20, and at the end, since 8 does not go into 4, we have a remainder of 4     

The remainder when 4z is divided by 8 is 4

From the question, when z is divide by 8, the remainder is 5. But we do not know the quotient.

From the formula

[tex]\frac{Dividend}{Divisor}= Quotient + \frac{Remainder}{Divisor}[/tex]

Here, the dividend is z, divisor is 8, and the remainder is 5.

Let the quotient be x, then we can write that

[tex]\frac{z}{8} = x + \frac{5}{8}[/tex]

Now, to determine the remainder when 4z is divided by 8,

Multiply both sides of the equation by 4

[tex]4 \times\frac{z}{8} =4\times( x + \frac{5}{8})[/tex]

[tex]\frac{4z}{8} = 4x + \frac{20}{8}[/tex]

Then,

[tex]\frac{4z}{8} = 4x +2+ \frac{4}{8}[/tex] (NOTE: [tex]\frac{Remainder}{Divisor}[/tex]must be a proper fraction)

[tex]\frac{4z}{8} = (4x +2)+ \frac{4}{8}[/tex]

Compare this to the formula [tex]\frac{Dividend}{Divisor}= Quotient + \frac{Remainder}{Divisor}[/tex]

The remainder is 4

Hence, the remainder when 4z is divided by 8 is 4.

Learn more here: https://brainly.com/question/17449230

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