find the next three numbers in the pattern
2/3, 1 5/12, 2 1/6, 2 11/12 _, _, _
8/12, 17/12, 26/12, 35/12 _, _, _
ah ha, each is 9/12 bigger than the one before it
To find the next three numbers in the given pattern, we need to look for a relationship or pattern between the consecutive terms.
Let's start by converting the mixed numbers into improper fractions:
2/3 = 2/3
1 5/12 = 12/12 + 5/12 = 17/12
2 1/6 = 12/6 + 1/6 = 13/6
2 11/12 = 12/12 + 11/12 = 23/12
Now, let's analyze the pattern:
From 2/3 to 17/12, the numerator increases by 1, and the denominator increases by 9.
From 17/12 to 13/6, the numerator decreases by 4, and the denominator remains the same.
From 13/6 to 23/12, the numerator increases by 10, and the denominator increases by 6.
Based on this pattern, we can derive the next three terms as follows:
Starting with 23/12:
23/12 - 4/12 = 19/12
From 19/12:
19/12 + 10/12 = 29/12
From 29/12:
29/12 + 6/12 = 35/12
Therefore, the next three numbers in the pattern are 19/12, 29/12, and 35/12.