Answer: 34/105
Step-by-step explanation: The idea here is that the fractional parts of the circle graph will all add up to 1 exactly, but the blue segment represents an unknown fraction.
So, this is an exercise in adding fractions with different denominators to get the total known area and then finding the difference between 1 and that known area.
We cannot directly add fractions with different denominators.
To add 1/7 and 1/5 and 1/3, we need to find the least common denominator (LCD) and then express all three numbers in terms of that denominator. In other words, we want a whole number that is evenly divisible by 7, by 3, and by 5 and we want the smallest number for which that is true.
If we multiply all three numbers together, we get 7*5*3 = 105.
That is the LCD. It divides by all 3 numbers (7, 5, 3) and no smaller number will do.
Tan Segment - To take the denominator of 7 and get 105, we multiply by 5*3 = 15, so we do that to both the numerator and denominator of the fraction. We have 1 * 5*3 = 15 on top and 7 * 5*3 = 105 on the bottom, to get the fraction ---> 15/105
Orange Segment - To take the denominator of 5 and get 105, we multiply by 7*3 = 21, so we do that to both the numerator and denominator of the fraction. We have 1 * 7*3 = 21 on top and 5 * 7*3 = 105 on the bottom, to get the fraction ---> 21/105
Purple Segment - To take the denominator of 3 and get 105, we multiply by 7*5 = 35, so we do that to both the numerator and denominator of the fraction. We have 1 * 7*5 = 35 on top and 3 * 7*5* = 105 on the bottom, to get the fraction ---> 35/105
We add the known areas: 15/105 + 21/105 + 35/105 = 71/105
Now we need the Blue Segment:
1 - 71/105 = 105/105 - 71/105 = (105- 71)/105 = 34/105
Since 34 does not divide by any of the three factors of the denominator (3, 5, and 7) the answer cannot be reduced further.
The blue segment area is 34/105
I hope this helps.