It works better if you know how the scales are constructed and get familiar with properties of logarithms (mainly variations on log ab = log a + log b)
C and D are plain log scales, where one decade is the length of the rule. They're sort of the default scales to use.
Multiplication is commutative, so you put either number on either scale. The important thing is that the distance from the left index of the scale is proportional to the log of the number (reading the scale as 1 to 10), so you want to arrange the scales to add the lengths corresponding to your numbers such that the lengths add up. (Or so that you subtract the length of the divisor from the dividend, if you're dividing).
You can get by without the approximation if you're willing to set up the multiplication, see that the product is out there in thin air, then move the slide to put the right index where you originally put the left index. (3 times 5: on the d scale find 3 and put the left index of the C scale there; opposite 5 on the C scale read nothing because there's no D scale there; try again using the right index of the C scale, which is the same thing as having another copy of the D scale out there to the right where the air was).
A and B are each 2 copies of a log scale. You can absolutely use the left side of A and B for your numbers to multiply, and the product will always be on the scale.
People normally use(d?) C and D because the precision is better and because the rest of the scales (like the trig and log-log) are constructed to work with them.
Nit: while multiplication is commutative, the property you meant to use was symmetry. I'm sure it was a mistake and you know this, I'm just pointing it out to prevent confusion for others.
Huh. I heard (US high school algebra in a recent unspecified century) the fact that ab=ba called "the commutative property of multiplication", and the "symmetric property of equality" meant a=b <=> b=a, and didn't run across anything later on (comp sci from a department of the engineering college rather than the math department) inconsistent with that. Symmetry sounds like a reasonable term for both, but it sounds like there's a distinction I don't get?
C and D are plain log scales, where one decade is the length of the rule. They're sort of the default scales to use.
Multiplication is commutative, so you put either number on either scale. The important thing is that the distance from the left index of the scale is proportional to the log of the number (reading the scale as 1 to 10), so you want to arrange the scales to add the lengths corresponding to your numbers such that the lengths add up. (Or so that you subtract the length of the divisor from the dividend, if you're dividing).
You can get by without the approximation if you're willing to set up the multiplication, see that the product is out there in thin air, then move the slide to put the right index where you originally put the left index. (3 times 5: on the d scale find 3 and put the left index of the C scale there; opposite 5 on the C scale read nothing because there's no D scale there; try again using the right index of the C scale, which is the same thing as having another copy of the D scale out there to the right where the air was).
A and B are each 2 copies of a log scale. You can absolutely use the left side of A and B for your numbers to multiply, and the product will always be on the scale.
People normally use(d?) C and D because the precision is better and because the rest of the scales (like the trig and log-log) are constructed to work with them.