Separate the whole numbers from the fractions: 10+11 + 13/15+17/20.
We can easily add the whole numbers: 10+11=21.
To add the fractions we need to find the LCD.
15=3*5 and 20=4*5, so 15 and 20 must divide into 3*4*5=60.
We can see that 3*5 must go into 60 4 times and 4*5 must go into 60 3 times. We see this because, if we cover up the 3 and 5 in 3*4*5, we're left with 4; and if we cover up the 4 and 5, we're left with 3. We use these numbers as multipliers for the numerator of each fraction: 4*13/60=52/60 and 3*17/60=51/60.
So we have 52 sixtieths plus 51 sixtieths. 52+51 of any object is 103 of that object, whether it's apples, pencils or sixtieths. So we have 103 sixtieths, written 103/60. This is an improper fraction so we want a mixed number: a whole number plus a fraction. We can write 103 as 60+43, so 103/60=60/60+43/60. 60/60=1, a whole number which can be added to the sum of the other whole numbers we found earlier: 21+1=22 and we place the remaining fraction 43/60 next to this to give us 22 43/60.