He has the same as well 6.5
We can bring the ratios to a similar form, because 2:5 is the same as 4:10 (we can mupltiply rations by the same number)
so one ratio is 4:10 and the other is 4:15 and the difference is is 75 beads
in this ratio, we can see each number corresponding to a "unit" of beads: that means that what changed is that Patricia now has 5 more such groups (15-10=5), and since she has 75 beads more each unit must be 75/5=15.
so afterwards (and before) Karen had 4 such units, that is 60, and Patricia before had 10 such units, that is 150.
He needed to divide instead of subtracting it on the last step.
The decimal form for 5.63 x 10^-6 is 0.00000563