I'm a type 1 diabetic for 18 years, so although I'm not an RN, I think I can help answer your question.
So ICR is the amount of carbohydrates that one 1 unit of insulin will cover. For instance, I'm 1:7 at breakfast. If I eat 50 grams of carbs at breakfast, I take approximately 7.14 units (on an insulin pump, if I'm on injections, 7 units).
My ISR is how many mg/dls my blood sugar will drop if I take 1 unit of insulin. My ratio is 1 unit for every 40 mg/dls and my target is 100 mg/dl. If I wake up at breakfast and my blood glucose reads at 215 mg/dl, then I want to drop 115 mg/dl, and I take 2.87 (on an insulin pump, 3 if I'm on injections).
So, if I woke up with a blood sugar of 215 mg/dl and I'm eating 50 carbs, then i would take a TOTAL of 10.01 units (or 10 on injections). Get it?
What you wrote doesn't really make sense. If someone is prescribed to take 10 units of Novolog at each meal, then they need to eat the corresponding amount in the equation: carbohydrates / insulin ratio = 10. What's their ratio? Do they take 1 unit for 7 carbs? Then they eat 70 carbohydrates. If their ratio is 1:9, then for 10 units they need to eat 90 carbs.
However, if what you meant to write was that their mealtime ratio is 1:10 (1 unit for every 10 carbs), then yes, if they ate 60 carbs, they'd take 6 units of insulin. Plus whatever they need for the correction.
There are specific baselines for starting on insulin that you can calculate based on weight. There's a general guideline for units of insulin per kilogram of body weight. You start out conservatively, test blood glucose regularly, and adjust dosing from there. Similar for figuring out bolus ratios.
If you give a patient 19 units with only 60 carbs when they have an insulin to carb ratio of 1:10, they are overdosing and risking a seizure.