Question

Joshua uses a rule to write the following sequence of numbers 1/6,1/2,5/6,_,1 1/2. What number is missing? What rule was used?

Answer 1

the number he is missing is 1 1/6. He was adding 2/6 or 1/3 every time.

Answer 2

`(1)/(6),(1)/(2),(5)/(6),1(1)/(6),1(1)/(2)`

Explanation:

we will check if he is adding up a number in each step by substracting the first number to the second number and then test it with the sequence by adding from the first number:

`(1)/(2)-(1)/(6) =(1)/(3)`

`(1)/(6)+(1)/(3)=(1)/(2)\\\\(1)/(2)+(1)/(3)=(5)/(6)\\\\(5)/(6)+(1)/(3)=(7)/(6)=1(1)/(6)\\\\(7)/(6)+(3)/(2)=(3)/(2) =1(1)/(2)`

we found that the rule is adding up
`(1)/(3)` each step

Note: To converte the improper fraction to mixed fraction we divide the numerator by the denominator, write down the whole number answer then write down any remainder above the denominator.