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

Answer:

$\frac{1}{6},\frac{1}{2},\frac{5}{6},1\frac{1}{6},1\frac{1}{2}$

Step-by-step 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:

$\frac{1}{2}-\frac{1}{6} =\frac{1}{3}$

$\frac{1}{6}+\frac{1}{3}=\frac{1}{2}\\\\\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\\\\\frac{5}{6}+\frac{1}{3}=\frac{7}{6}=1\frac{1}{6}\\\\\frac{7}{6}+\frac{3}{2}=\frac{3}{2} =1\frac{1}{2}$

we found that the rule is adding up $\frac{1}{3}$ 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.