I wanted You to help work on 204 Base five divide by 14 Base five. Please, calculate as you explain in English Language

English

ScanSolve AI Answer

Answer

11five11_{\text{five}}

Step-by-step solution

4 steps

To solve this problem, we will convert both numbers to base ten, perform the division, and then convert the result back to base five.

  1. Convert 204five204_{\text{five}} to base ten.

    204five=(2×52)+(0×51)+(4×50)204_{\text{five}} = (2 \times 5^2) + (0 \times 5^1) + (4 \times 5^0) =(2×25)+(0×5)+(4×1)= (2 \times 25) + (0 \times 5) + (4 \times 1) =50+0+4= 50 + 0 + 4 =54ten= 54_{\text{ten}}
  2. Convert 14five14_{\text{five}} to base ten.

    14five=(1×51)+(4×50)14_{\text{five}} = (1 \times 5^1) + (4 \times 5^0) =(1×5)+(4×1)= (1 \times 5) + (4 \times 1) =5+4= 5 + 4 =9ten= 9_{\text{ten}}
  3. Perform the division in base ten.

    54ten÷9ten=6ten54_{\text{ten}} \div 9_{\text{ten}} = 6_{\text{ten}}
  4. Convert the result 6ten6_{\text{ten}} back to base five.

    We divide 6 by 5 and record the remainders:
    6÷5=16 \div 5 = 1 remainder 1
    1÷5=01 \div 5 = 0 remainder 1
    Reading the remainders from bottom to top, we get 11five11_{\text{five}}.

    Therefore,

    204five÷14five=11five204_{\text{five}} \div 14_{\text{five}} = \boxed{11_{\text{five}}}
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