HELP! Input:1 1/3 Output 7/12 Input 2 3/5 Output 1 17/20 Input 3 5/6 Output ? Input ? Output 3 5/8. What is the rule, and what are the question marks values?
consider it to be the ordered pairs
(4/3 , 7/12) and (13/5 , 37/20) and the relation is linear , since only 2 points were given
slope = (37/20 - 7/12) / (13/5 - 4/3) = 1
so y - 7/12 = x - 4/3
multiply be 12
12y - 7 = 12x - 16
12x - 12y = 9
or
4x - 4y = 3
so the input is your x , the output is your y
for input 3 5/6 or 23/6
4(23/6) + 4y = 3
4y = 3 - 46/3
y = - 37/12 ---> output
You try the other one
Based on the provided inputs and outputs, we need to determine the rule or pattern that relates the inputs to the outputs.
Let's analyze the given examples:
Input: 1 1/3 → Output: 7/12
Input: 2 3/5 → Output: 1 17/20
Input: 3 5/6 → Output: ?
To find the rule, let's convert the inputs and outputs to improper fractions for easier comparison:
Input: 1 1/3 → 4/3 → Output: 7/12
Input: 2 3/5 → 13/5 → Output: 1 17/20
Input: 3 5/6 → 23/6 → Output: ?
Notice that the output in each example is obtained by subtracting the input from 2. Let's verify this rule with the second example:
Output: 1 17/20
= 1 (2 - 2/5)
= 1 (10/5 - 2/5)
= 1 (8/5)
= 1 8/5
= 1 (2 + 3/5)
= 2 3/5
Based on this observation, we can deduce that the rule is to subtract the input fraction from 2, then express the result as a mixed number.
Now, to find the values represented by the question marks, let's apply the rule to the third example:
Input: 3 5/6 → 23/6
Output: ?
To find the output, we subtract the input fraction from 2:
2 - 23/6 = 12/6 - 23/6 = -11/6
Since we need to express the result as a mixed number, we can simplify -11/6:
-11/6 = -(1 5/6) = -1 5/6
Therefore, the value represented by the question mark in the third example is -1 5/6.
Now, for the last example:
Input: ? → Output: 3 5/8
We need to reverse the process and add 3 5/8 to 2 to find the input value:
2 + 3 5/8 = 16/8 + 29/8 = 45/8
Therefore, the value represented by the question mark in the last example is 45/8.
In summary:
The rule is to subtract the input fraction from 2 and express the result as a mixed number.
The value represented by the question mark in the third example is -1 5/6.
The value represented by the question mark in the last example is 45/8.