Respuesta :
Answer:
Teagan is dividing 6 by 11. If she continues the process, what will keep repeating in the quotient?
The sequence 05
Only the digit 5
The sequence 54
Only the digit 4
The sequence 54 is the final answer.
Step-by-step explanation:
Given:
A a fraction 6/11 which Teagan is dividing we have to find the repeating quotient.
Here the divisor is 11 and the dividend is 6.
Lets say that the quotient is "q" .
And we know that:
⇒ Dividend / divisor = quotient
Or
In mixed fraction.
⇒ Dividend / divisor = quotient + (remainder/ divisor)
Finding the values of "q".
⇒ [tex]\frac{Dividend}{divisor} = quotient[/tex]
⇒ [tex]\frac{6}{11} = 0.5454....[/tex]
Explanation:
- To divide [tex]6[/tex] with [tex]11[/tex] we have to take a decimal in quotient which allows us to have a zero in each step in the quotient.
- After putting zero the dividend will become [tex]60[/tex] and then we can apply [tex]11\times 5 = 55[/tex] ...[tex]5[/tex] in the quotient and [tex]55[/tex] in the numerator.
- In third step we will subtract [tex]55[/tex] with [tex]60[/tex] that will give us [tex]5[/tex] putting a zero with it it will be now [tex]50[/tex] ,and the closet multiple of [tex]11[/tex] is [tex]11\times 4=44[/tex], [tex]4[/tex] with the quotient and and [tex]50-44=06[/tex] will continue to be divided.
- The fraction is a rational numbers as the decimals occurring are repeating decimals in the quotient.
Our final answer from the option is : C
The sequence 54 will be repeating.
